Gesture, Form, Procedure: Toward a Deep Musical Grammar

Gesture, form and procedure are the three lenses I propose for understanding how music is born and how it is transformed. The proposal gathers archetypes, operations and practices of listening into a deep grammar meant for creation, performance, teaching and shared rehearsal.

Spanish version. Gesto, forma, procedimiento: hacia una gramática musical profunda. Translation by the author.

Toward a deep musical grammar

Toward a new instrumental class and a new way of rehearsing music

I. The three lenses

Gesture (hormé (ὁρμή))

The First Motion · The Ancestral Impulse · The Breath Before Musical Sound · The Primordial Sway · The Body’s Question · The Opening Trace · The Spark in the Air · The Unbidden Movement.

Form, táxis (τάξις)

Morphology as Ordering · The Shape That Endures · The Silent Architecture · The Inner Figure · The Dwelling of Musical Sound · The Contour of Becoming · The Room the Music Builds · The Pattern That Remembers Us · The Harbor of Motion.

Procedure, melopoiía (μελοποιία)

The Way the Motive, or Melodic Contour, Thinks · The Ancient Logic of Change · The Path of Transformation · The Craft Beneath the Surface · The Lineage of Operations · The Steps Musical Sound Takes to Become Itself · The Hidden Work of the Motive, or Melodic Contour · The Subterranean Grammar.

These three constellations, gesture, form, procedure, or hormé, táxis, melopoiía, work less as categories than as lenses, ways of loosening the grip that “classical music” keeps on its two foundational spaces, the instrumental lesson and the instrumental rehearsal. Both spaces, as we have inherited them, tend to reduce music to correction, coordination and conservation. The lesson today, in 2026, orbits around the score taken as a script to be decoded, and it does so with such naturalness that research on classical higher music education now describes it as the norm, and studies the attempts to move that centre as the exception, as the initiatives of individual teachers in the United Kingdom and on the Continent. The rehearsal orbits around the flawless execution of what was decided beforehand.

What I am attempting here is a nudge, a reorientation, a shift in the gravitational field of these practices. Gesture (hormé) reminds us of the body’s first motion, before language. Form (táxis) brings back the shapes that hold musical sound without fixing it. Procedure (melopoiía) reveals the invisible intelligence that carries a melodic contour from one state to another. The three lenses have little of the decorative metaphor about them and much of the working tool, embryonic and generative principles that can remake how we teach, how we practice and how we rehearse.

The three words are not mine, and it must be said where they come from. Rhetoric had the triad first, as actio, dispositio, inventio, the delivery of a discourse by voice and body, the ordering of its parts, the finding of what to say. Humboldt had it as enérgeia, érgon, téchne, activity, work, craft. Greek gives one word to each lens, a motto if one wants it, hormé, the Stoics’ word for the impulse that launches us into action, táxis, order and arrangement, the rhetorician’s word for dispositio and the general’s for battle order, melopoiía, “melody-making,” which was simply the Greek for composing. And music named three genres after the three lenses without noticing, the toccata, from toccare, to touch, which is gesture, the ricercar, the invention and the study, from seeking, finding and exercising, which are procedure, and the sonata, “the sounded thing,” the work as érgon, which is form. Spanish has a word better than all of them, the tiento, from tentar, to touch, to try, to feel one’s way, which fuses the first and the third in a single act.

They thus begin to return music to its condition as a living, generative process, where today it works as a system of maintenance. The logic of preservation has its last station in the concert and the recital, those public rituals we believe eternal and which are in fact recent. Kenneth Hamilton has shown that the recital as we know it, the silent hall, the printed programme carried out to the letter, the pianist who says only the notes he has brought written down, became fixed between the last third of the nineteenth century and the first decades of the twentieth, and that before then pianists preluded between pieces, linked works with improvised modulations, and reordered and glossed in public what they played. What the concert hall now displays as fidelity is a habit of little more than a century, and the lesson has inherited it without asking. That is why the work begins where music is actually made, in the lesson and in the rehearsal, those quiet workshops of becoming where a different musical world can still be born, or, more truly, remembered.

One possible lesson begins like this. A fifteen-year-old student brings Bach’s Invention in F major, the eighth, and brings it well read, clean, with her fingers where they ought to be and the face of someone who has carried out an errand. Before she plays, the teacher closes the score and asks her to sing the subject on any syllable at all, “pa,” “ta,” whatever comes. She laughs, her voice cracks at the top, where the arpeggio reaches its highest note, and in that crack she has already learned something the keyboard was hiding from her, that the subject climbs with effort and comes down with relief, that the run of semiquavers is a fall after a leap. The teacher then asks her to sing it walking around the room, one step to each quaver, and to stop where the body wants to stop. She stops at the summit. Then comes the question that truly matters, what would happen if the subject came down the way it goes up. She tries, gets it wrong, tries again, and at the third attempt she sings a clumsy, recognizable inversion. She plays it with the left hand while the right plays the subject as Bach wrote it, and it sounds wrong, and at last it sounds almost right. When she opens the score again and finds Bach doing with his own subject things she has just attempted with her hands, she recognises a colleague where she expected an example of counterpoint. That day the invention stops being an exercise in finger independence and becomes what its title page promised, a foretaste of composition, and the motive, for the first time for her, begins to think for itself.

Another possible scene, shorter and harder. A man in his sixties has come back to the piano after retiring and plays Schubert’s Impromptu in G flat major counting under his breath, like someone walking along a ledge. Every time the teacher speaks to him about the melody, he tightens his fingers further. So the teacher stops speaking about the melody. He asks him to stand up, to rock the triplets with his body the way one rocks a grandchild, from one foot to the other, without playing anything, and to hum over them whatever he remembers of the line. At first he is embarrassed. Within two minutes the swaying has found its width and the humming its breath, and the man discovers, without anyone telling him, that the triplets were a floor and that the melody floated above it. He sits down, plays, and for the first time does not count. Neither of these scenes needs a method. Each needs a teacher willing to close the score for ten minutes and a student willing to look ridiculous, and both are rarer in a conservatory than a good piano.

This framework also seeks to escape, quietly but decisively, the two prisons that dominate the classical instrumental lesson, style and technique. Style, with its endless taxonomy of historical periods, philological minutiae and inherited hierarchies of taste, tends to fossilise the student’s ear and imagination before they have even begun to inhabit musical sound. Technique, even when approached as somatic education or biomechanical refinement, too easily becomes an end in itself, a treadmill toward so-called “mastery,” divorced from all musical intention.

Gesture, form and procedure invite a departure from both. They place the student far from the museum of styles and the gymnasium of muscles, at the threshold of the process itself, where musical sound is made, shaped and sent forth before anyone can reproduce it. Here technical fluency and stylistic awareness remain in the room. They are reintegrated as servants of creation, after having been tyrants over it.

Prisons, I said. That is the polemic’s word. What actually happens is that each of the three is rehoused, and it matters to say where.

Technique goes into gesture. The hand learns the motion of the sung phrase before the motion of the exercise. What we call technique is sedimented gesture, the residue of a thousand breaths that found their shape. A student who has conducted, walked and sung a phrase arrives at the instrument with almost all of the technical problem already solved in the arm. The pages on gesture are, among other things, the place where technique is taught in this approach.

Style goes into form. The archetypes are the language. Styles are its dialects. A dialect is real, learnable and worth loving, yet no one learns a language by memorising the history of its periods. When I say that the classical conception of style collapses, I mean that it collapses as a first principle and remains standing as a fact. Baroque diminution and the approach tones of bebop are two dialects of one procedure, and whoever knows the procedure learns either of them in an afternoon.

Analysis goes into generative procedure. The laboratory I reject is analysis from the listener’s side, the neutral dissection of a finished object. What is practiced here is analysis from the maker’s side, transcription as reverse engineering, the recomposition of a passage to discover which operations produced it. Nattiez called this the poietic level. It is the only analysis that improves the hands.

The work begins in awakening. First one learns to move, breathe and think within music. The name, the period and the label come afterwards, and so do imitation and correction. The old word for this is maieutiké (μαϊευτική), maieutics, midwifery. The teacher delivers what others would merely deposit. And there is an older description still of what such a lesson hopes for. Plato, in the Seventh Letter, says of what cannot be put into words that it comes only after long synousía (συνουσία), a being-together of teacher and student, and that then it “is kindled suddenly, like light from a leaping fire, and thereafter feeds itself.” Synousía is a better word than “lesson,” and that sentence is the epistemology of everything that follows, the spark in the air included.

That spark resists being passed from hand to hand. What can be handed on is the ground where it catches, and the pages that follow give the concrete shape in which, over years of teaching, I have felt my way toward making room for it.

II. Introduction

After years of circling the question of how to teach without imprisoning music in mere technique, in histories or in categories, I have slowly given shape to a way of working that set in my lessons before it had a name. Its name is grammar, and the word is chosen with care. A method prescribes a sequence and promises a result to whoever obeys it. A grammar supplies elements and rules of combination and lets each speaker say what no one has yet said. What follows has the second shape. It is the record of a search that refuses to end because its object does not end either, the question of what a music lesson would be like if we stopped treating music as something inherited in boxes and let it arise from the generative procedures that reappear whenever a human being shapes sound in time. These are working notes, field observations, fragments of a grammar discovered by using it, as every living grammar is discovered, by speaking.

This approach begins with the voice, because the voice refuses to lie about presence, and with improvisation, because improvisation refuses to lie about time. (Bergson’s distinction is exactly this one. The score is time made spatial, laid out and surveyable at a glance. Improvisation is durée, duration lived forward, with no possibility of review.) Voice and song are weighty words in these pages, and further on I ground them with the rigour they demand, because today they sound like amateur sentimentality and here they carry the weight of the whole building. From the voice the approach passes to those generative procedures that appear, in different guises, across a great many musical cultures. They work less as rules than as kindlings, points of ignition, small mechanisms that help sound think itself forward. Heraclitus said the world was an ever-living fire “kindling in measures and going out in measures,” and that is as good a definition of a procedure as any. Counterpoint and the old formulaic engines of creation (poíesis (ποίησις)) enter here as tools, far from the monument, still warm from use, still capable of being transformed in the hands that touch them.

One phrase in my title needs a caution before it does any damage. Some will read “deep grammar” through Chomsky, and through Lerdahl and Jackendoff’s Generative Theory of Tonal Music, which is cognitivist and describes the listener’s competence. My sense is another, Humboldt’s, and it is poietic. Language, he says, is activity (enérgeia) before it is work (érgon), and it makes “infinite use of finite means.” That single sentence contains the entire essay. Music as something that happens before it is something that is, enérgeia against érgon. Few forms and few procedures whose combinations stretch outward without end, infinite use of finite means. Chomsky borrowed the formula for his “generative grammar” and installed it on the side of the one who understands. I borrow it back and return it to the side of the one who makes.

The grammar of a saying

It remains to say what kind of grammar this is, and everything else depends on the answer. A grammar can draw up the inventory of the structures left on the table once speech is over and dissect them cold, and then it describes a said object. It can also accompany the speakers while they speak and ask toward whom they turn, with what breath, from what body, and then it describes a saying. The deep grammar of these pages belongs to this second lineage, and Greek has the exact word for its object, léxis (λέξις). The word comes from légein (λέγειν), whose first sense, older than “to speak,” is to gather, to collect, to bring together what is scattered, as one gathers firewood or counts the head of a flock. Before the rhetoricians narrowed it to diction and style, before Aristotle placed it in the third book of the Rhetoric and Latin translated it as elocutio, léxis named the very act of saying, the voice that gathers and addresses. I call it, with a formula I shall try to live up to, the saying before the said. It is prior to articulate language, and prior in the same way that a newborn’s cry is prior to the first word while still being addressed to someone.

That address has a grammatical case of its own. The Greek grammarians called the vocative klētikḗ ptôsis (κλητικὴ πτῶσις), the case of calling, from kaleîn (καλεῖν), to call, the same root that gave ekklēsía, the assembly of those summoned. The vocative is a strange case. It stands outside the sentence, with no function as subject or object, and it predicates nothing of what it names. Whoever cries “Mother!” in the middle of the night says nothing about his mother, and yet everything that will follow begins there. My thesis is that music is vocative before it is representational. It calls before it says anything. Before expressing an affect, describing a landscape or unfolding a structure, a musical phrase turns toward someone, summons them and sets them before itself. The deep grammar I am seeking is the grammar of that turning, and its operations, all those in the catalogue of procedures, are ways of keeping a call alive in time, of repeating it without wearing it out, of varying it without losing the one who listens, of delaying its answer until the answer has weight. Humboldt and I meet here. The enérgeia of language is the saying, and a grammar of enérgeia is a grammar of léxis.

From this follows a reordering of the catalogues themselves. Among the gestures of song, the call appears in second place, as gesture G2, an upward leap, almost always of a fourth or a fifth, to a held high note, projected so as to be heard at a distance. The order of the catalogue is the order of the body, which draws breath before it calls. The order of meaning is the reverse, because one draws breath in order to call, and the call is in truth the founding gesture from which all the others derive. Its held note is already the birth of song, which is the call that stays, the voice that refuses to let go of the height it has reached. Song, entering a body that walks, rocks and breathes, becomes gesture. And gesture, touching a string, a drumhead or a key, becomes sound. Call, Song, Gesture, Sound. That ontological order grounds the pedagogical order this text repeats like a refrain, sing first, keyboard second, paper last. The inherited conservatory travels it backwards. It starts with paper, passes to the sound of the instrument, calls gesture technique and reaches song late or never, and the call, which should have founded everything, does not even have a place in its syllabus.

And warm the tools are. The generative lesson is the norm from which we departed, and not so long ago, and there is nothing utopian about it. The Neapolitan conservatories taught partimento to children who could compose a fugue before they could afford shoes, and the irony is worth holding on to, because a conservatory was the place where children were conserved, and the repertoire came much later. Gjerdingen has corrected the legend of the orphans. Alongside the foundlings and the poor whom the charitable foundation took in there lived students whose families paid for their keep, so that those houses were mixed institutions, half asylum and half trade school. The nuance enlarges the thesis instead of diminishing it. Those who paid were paying precisely for that training, in which a child learned to realise basses, to sing solfeggi and to unfold a whole piece over formulas learned by heart, until composition came from his hands the way speech comes from anyone’s mouth. The partimento, that bass sometimes figured and sometimes bare which the student had to turn into music, was the centre of the training and its test, and it was so as keyboard practice before it was ever written theory. The institution that now curates the museum was invented to teach the generative craft this essay wants to revive. The French tradition of écriture kept the basse donnée and the chant donné alive well into the twentieth century. The title page of Bach’s Inventions, of 1723, promises the student that he will learn “to proceed correctly and well” (wohl zu verfahren) in three obbligato parts, “not only to obtain good inventiones but to develop them well,” “above all to achieve a cantabile manner of playing,” and to receive “a strong foretaste of composition.” Invention, procedure, song, poíesis. The three lenses and their purpose, in a single sentence, from the most canonical pedagogue there is. Czerny published in 1829 a Systematic Introduction to Improvisation on the Pianoforte, op. 200. C. P. E. Bach closed his Versuch with a chapter on the free fantasia. Riepel taught a student the Monte, the Fonte and the Ponte in the form of a dialogue, and Koch catalogued the expansion and compression of phrases for the use of beginners. Outside Europe the lesson never left that condition, the Ottoman meşk, in which the student learns by repeating after the master and notation is secondary, the Hindustani talim and the daily riyaz, the gharana, the jam session, which is lesson and rehearsal at once.

Tinctoris, in 1477, already had the words for what I have been calling the opus and its alternative. Written counterpoint, he says, is commonly called res facta, “the made thing,” and the counterpoint we make in the mind over the book is called cantare super librum, “to sing upon the book.” The museum, then, is modern. Lydia Goehr dated its construction to around 1800, when the work-concept hardened and the imaginary museum opened its doors. Christopher Small gave its opposite a verb, musicking, and Valéry, defining poetics, said it was the study of le faire, of making, before it was the study of things made. What I propose is older than what it opposes. That changes the tone of the proposal, which asks to be recognised and is content with that.

It also changes the direction of the looking. Kierkegaard’s distinction is exact here. Repetition and recollection are the same movement in opposite directions. The museum recollects backwards, toward an origin it can only preserve. What I want is the other direction, the anamnesis that repeats forwards, and that is why the last sentence of these pages says that the lineage is waiting to be said once more.

Patterns begin to emerge when one listens long enough. Certain operations belong to human musicality itself, wherever one looks. A line stretches, or shrinks, or twists back on itself. A motive returns altered. A gesture calls forth another gesture. A drone anchors the world while something agile dances above it. Repetition becomes transformation. Tension seeks resolution and delays it. These movements resemble instincts more than techniques, and each culture refines them in its own way without ever exhausting them.

The small procedures that musicians everywhere use, lengthening, compressing, turning a line upside down, breaking it into pieces, sliding it into a new modal space, laying an ostinato beneath it, spinning sequences until they generate their own gravity, belong to no era and to no style. They behave like the basic verbs of musical thought, always there, waiting to be activated. Once a student internalises them, even imperfectly, something unexpected happens. The instrument begins to respond. The voice finds new pathways. The ear stops being a collector of impressions and becomes an engine of prediction. Creation (poíesis) returns to the centre of the lesson almost by accident.

I work with the voice because it makes every abstraction concrete. I work with improvisation because it reveals what the hands and ears truly know. I work with these generative, recurrent patterns because they give the student freedom to move among idioms without being trapped in any of them. Every lesson is an act of play, a stranger to the review of precedents, play in Gadamer’s sense, Spiel, where the work’s mode of being is its enactment, its Vollzug, so that a piece exists only while it is being played and never while it is being possessed. Every exercise is a small act of composition, never the imitation of something already perfected.

Before naming any structure, I name the impulse. I am looking for a vocabulary for the deep, recurrent patterns of musical thought, patterns that stubbornly re-emerge across disparate practices wherever human beings organise sound with intention, without anyone having imposed them from above as universals.

Song

For me, the ontological nucleus of music is song as such, and the word asks to be taken in a sense prior to any professional, technical or cultivated sense of “the voice.” Song here is the ancestral coupling of vocal utterance, bodily rhythm and verbal and poetic shaping. That triad, song, dance, poetry, keeps little of a superseded historical origin and much of a set of ontological categories that still underlie the way musical meaning is generated today, in any room, at any instrument. And since the word song, said like that, bare, sounds like schoolroom romanticism, it has to be defended from its root before the weight of the essay goes on resting on it.

I begin with Latin, which knew more than we usually grant it. Canere is to sing, and it is also what the cock does at dawn, what the trumpet does when it gives the signal and what the seer does when he announces what is to come. The poet who sings is a vates, the one who sees, and the verb shared by the bird, the bugle and the prophet shows that for a Roman to sing was to send forth a voice that does something, that wakes, summons or announces. From canere comes carmen, which means at once song, poem, ritual formula and spell. The law of the Twelve Tables punished whoever sang a malign carmen against another, and from there comes our enchant, incantare, to sing over something in order to bind it. Before it was a beautiful word, song was an efficacious word, a word that acts upon what it addresses. Cantus, finally, is what is sung, song already become a body of sound, and Western music kept it with all its weight in the cantus firmus, the firm song that sustains from below all the voices added to it. The three Latin words already give the three notes of the concept, the voice that acts, the formula that binds and the song that sustains.

Greek adds the decisive note. Mélos (μέλος) first meant a limb of the body. In Homer mélea are the limbs, almost always in the plural, the arms and legs that sleep loosens and death unties, and the phrase katà mélos meant limb by limb, part by part. Only later did the word come to name the limb of a song, the phrase, and at last the whole song and the melody. Melody is thus, in its very name, an articulated body, and Latin keeps the same intuition in another root, because articulus, from which our musical articulation comes, is the diminutive of artus, the joint of the bones. To articulate a phrase is to give it joints as an arm has them, and a badly articulated phrase limps in the most literal sense of the word.

The Greek genealogy of the concept confirms what the etymology suggests. Aristoxenus distinguished, in the first book of his Elementa harmonica, two movements of the voice, the continuous movement of speech, which glides without stopping at any pitch, and the intervallic movement of song, which settles on a pitch, holds it and leaps to another. For the first serious theorist of Greek music, the frontier between speaking and singing runs through the capacity of the voice to stay, and that staying is what I shall later call the art of sustaining. Centuries later, Aristides Quintilianus defined in his treatise the perfect melos as composed of melody, rhythm and léxis, and the word he chose for the third element, where Plato had written lógos, is exactly the one I defended a few lines above. And in the twentieth century Thrasybulos Georgiades told the whole history of Western music as the history of a disintegration. In Greek mousiké verse was already music, because its metre of long and short syllables carried rhythm within the language itself, and language and music were a single reality. When that unity broke, European music was born from the task of setting to music once again a language that no longer carried music within it, the Latin of the Mass, and each epoch was a new way of trying to bring back together what had come apart. That line, from Plato to Aristoxenus and Aristides, from Georgiades to Wagner’s endless melody and to the classroom of my teacher, Salvador Chuliá, is the genealogy of melos in which this essay inscribes itself.

There remains the ontological sense, which is the one that matters most. When song happens, something makes its comparecencia, its appearing in person, the coming-forth of one who answers a summons. I choose the word deliberately. To comparecer is to present oneself when one has been called, as one appears before a judge who has issued a summons, and the Latin verb it comes from, comparescere, carries appearing within it, parere. Comparecencia is presence answering a vocative. That is why I call comparecencia what others call presence, because presence alone may be the presence of a stone, and comparecencia is always that of someone who was summoned and came, in the body, to a place and at an hour. Music appears in person in a body, and in song that body and that comparecencia coincide without remainder, with no intervening instrument, with no mechanism standing between breath and sound. Song is the barest form of embodied comparecencia, and also the most tragic, because the voice is finite, it tires, ages and breaks, and each song happens only once in a body that will one day stop singing. That tragic humanism of embodied comparecencia is the ground of everything this essay proposes, and the lesson that begins by singing is the lesson that begins from it.

And there remains, finally, anthropology. Before understanding a single sentence, every human being has been sung to. The first music almost all of us receive is a voice that rocks us and calls us by our name in a melody of two or three notes, and research on the exchange between infants and caregivers has found in that wordless dialogue pulse, quality and narrative, the rudiments of all music. Human communities sing in order to work, to marry, to bury their dead, to heal and to make war, and in almost all of them song is the first collective activity a child learns, the one that gives the child a place in the chorus and, with it, in the group. Song is, anthropologically, the way a human being enters the community of those who call and answer. When this text says song, then, it says all of this at once. A voice that acts upon what it addresses, a melody articulated as a body is articulated, a voice that stays at the height it has reached, a finite comparecencia, and the gesture by which each of us was received into the world.

I discovered late that the name of this blog already contains the triad, and that Plato had stated it plainly. I have already said that mélos means at once a limb of the body and a song. In the Republic, 398d, Socrates says that melos is composed of three things, lógos, harmonía and rhythmós, word, fitting, movement. Poetry, song, dance. Archaic mousiké named that unity before it was divided into arts, and the Laws, 654a and b, define education itself as choreía (χορεία), singing and dancing together, so that the educated person is the one who has danced in the chorus and the uneducated one is the achóreutos (ἀχόρευτος), the “unchorused.” That is the thesis of this essay in a single word, and it is two and a half thousand years older than the essay.

The loom

On that sentence of Plato’s I have raised, over the years, a figure that this essay carries within it although it has not named it until now, and which must be explained from the beginning. I call it the loom of melos. A loom has vertical threads, the warp, taut and fixed in the frame, and horizontal threads, the weft, which the shuttle passes over and under them. The fabric is born where they cross. Melos, the fabric of song, has three warp threads, and they are Plato’s three with a single correction. Where Plato wrote lógos, I write léxis, following the path Aristides Quintilianus had already opened, because in the Greek that has come down to us lógos ended up naming the said, the proposition, the reason that can be written down and filed away, and what melos needs in that place is the saying itself, the vocative address, the voice that gathers and calls. The first thread, then, is léxis, the saying before the said. The second is harmonía (ἁρμονία), a word that before it named chords named the carpenter’s fitting, the joint that fastens two pieces together, and that in melos is the gravitation of sounds, what sounds at once and draws together, the dissonance that asks for its resolution, the bass that sustains and the leading note that pulls upward. The third is rhythmós (ῥυθμός), the shape of what flows, and its analogues in the body are four, the heartbeat, the stride of one who walks, breathing and dance.

The weft of the loom also has three threads, and they are three strata of being that cross the three warp threads. The lowest stratum is the Flesh, what one has without having chosen it, the face, the breathing, the weight, the timbre of a voice, the length of a breath, the mass of an arm, the gifts nobody chooses and with which each of us has to sing. The middle stratum is the Inclination, intention, gravitation, gesture, the appoggiatura, the instant in which something yields toward something. The highest stratum is the Toward, direction, continuity, pulse, the pure futurity of what has not yet arrived and already pulls at what is sounding. Three threads by three strata give nine crossings, nine cells, and each one names something any musician recognises even if no one has ever given it its name. In léxis, the Flesh is the face of the voice, the timbre that tells who is calling before one knows what is being said, the Inclination is the intention with which the phrase turns toward someone, and the Toward is the direction of that phrase toward its addressee and its end. In harmonía, the Flesh is resonance, the body of the chord, the weight of the bass, the Inclination is the dissonance that leans and yields, and the Toward is the cadential gravitation that draws the harmony toward its rest. In rhythmós, the Flesh is heartbeat and breath, the Inclination is the anacrusis, the foot that lifts, the arsis, and the Toward is the pulse that carries, the stride that is already in the next step.

What is remarkable is that the three strata were already in this text, latent, working without a name. The Flesh is in pneuma (πνεῦμα), breath, which the Greek vocabulary of gesture places at the centre, and it is in the weight of the arm, in that claim on the first page according to which a student who has conducted, walked and sung a phrase arrives at the instrument with the technical problem already solved in the arm. The Inclination is in rhopé (ῥοπή), which the catalogue of gestures defines as “the inclination of a balance, the instant in which it yields,” and rhopé is precisely the Greek name of the Inclination. It is also in the appoggiatura read as an imperative, “lean,” the note that leans on the next one and yields into it. And the Toward is in agōgē (ἀγωγή), conduction, of which the chapter on the tetrads says that it gives music “a where-to.” Breath, balance and conduction. The loom was written before it was drawn. And the Flesh explains, in passing, a distinction that runs through all the work of the hand, that of weight against attack. Attack strikes the instrument from outside, as one knocks on a door with the knuckles. Weight lets the Flesh of the player fall into the sound, the whole arm resting on the key, and that is why it can sustain the sound afterwards. The art born from this I call ars sustinendi, the art of sustaining, and it is the instrumental version of that staying of the voice which Aristoxenus placed at the frontier of song.

Figure 1. The loom of melos. Vertically the three threads of the warp, léxis, harmonía and rhythmós, and horizontally the three strata of the weft, the Flesh below, the Inclination in the middle and the Toward above. Each of the nine cells names what the crossing yields, and to the left of each stratum stands the Greek name it worked under in the text before it was drawn, the pneuma, the rhopé and the agōgē.

There remains the question the loom puts to this essay, and its answer is the newest thing these pages have to say. How do the three lenses, gesture, form and procedure, cross the three threads and the three strata? The temptation is to share them out, to give gesture to rhythmós, form to harmonía and procedure to léxis, one lens per thread, like someone handing out chairs. It must be resisted, because the sharing out mutilates all three. Each lens traverses all nine cells, and what distinguishes them is the direction in which they travel through them. Gesture cuts the fabric vertically. In a single instant it crosses the three strata, from the Flesh to the Inclination and from the Inclination to the Toward, and it does so in all three threads at once. A sigh, gesture G4, is the weight of the first note, which is Flesh, its leaning on the dissonance, which is Inclination, and its release toward the resolution, which is Toward, and in that same instant the word sighs, the harmony leans and the rhythm falls from strong to weak. Procedure runs through the fabric diagonally. It takes what is in one cell and carries it into another, and in that transfer it makes the fabric fertile. Inversion takes a rising Inclination and turns it into a fall, augmentation takes a pulse of the Toward and lets it drop into the Flesh, where it weighs more and breathes more deeply, modal shift keeps the contour of the léxis and changes the gravitation of the harmonía that sustains it. Form, finally, runs through the fabric horizontally, along the Toward. It is what remains when a direction has been sustained across the three threads until it is fulfilled, the beginning, holding, articulating and closing that the chapter on the tetrads calls initium, tenor, mediatio and terminatio. Hence the formula the essay states further on, according to which gesture is the instant, procedure the passage and form the span. What that formula describes without knowing it are three directions of travel through one and the same loom, the vertical, the diagonal and the horizontal.

The pedagogical consequence is immediate, and it is severe with the inherited lesson. A fabric is known by traveling through it in all its directions, and whoever travels through it in only one mistakes one of its faces for the whole. The technique lesson travels through the Flesh and nothing else, weight, posture, muscle, and it forms powerful hands that have never called anyone. The analysis and style lesson travels along the horizontal of forms already fulfilled, names expositions and cadences, and forms ears that recognise what they could never make. The lesson of procedural virtuosity, that of the one who knows how to sequence and vary without ever having sung, runs diagonals through a void and produces ingenuity without a face. The diseases of music teaching are partial journeys through the loom. The three lenses together travel through the whole of it, and the founding order, Call, Song, Gesture, Sound, tells us where to enter it, by the thread of léxis, by the vocative direction that gives everything else someone to address.

Figure 2. Three directions of one loom. Above, gesture cuts the fabric vertically, procedure runs through it diagonally and form horizontally along the Toward, each with its examples. Below, the partial paths of the inherited class, the technique that stays in the Flesh, the analysis that follows only the horizontal of forms already fulfilled and the virtuosity that traces diagonals in the void.

Sing first

So the first and most indispensable practice is to sing. It is almost impossible to stress this enough. Always, every day, even alone, even when no one is listening. To keep the voice alive, to keep the body and the air in conversation. Singing is the place where music has its being, the simplest and at the same time the deepest manifestation of its life. It is through the voice that the hand, the mind and the ear learn to speak the language of sound. And what the instrumental lesson actually does with the voice is almost nothing. When the way learners of an instrument sing to themselves has been studied closely, it has been found that far less singing goes on in the lesson than one might expect, and that singing, when it appears, is rarely used as a tool for reflecting on the music or embodying it, and almost always as an occasional resource for correcting a note or a rhythm. The practice this essay puts in first place is, in the real conservatory, a residual practice.

Figure 3. The founding order and its inversion. Call, Song, Gesture, Sound is the order of sense, and from it springs the pedagogical order, sing first, keyboard second, paper last. The inherited conservatory walks it backwards, begins with paper and reaches song late or never, and the call is left without a place.

I learned this from Salvador Chuliá, with whom I trained from 1993 to 1999, and to whom I owe the centre of everything I defend here. His was the school of song and the arm. The phrase was sung before it was played, always, and the sound was born from the weight of the arm and never from the blow of the fingers. Everything was measured by a single criterion, whether the line sang or did not sing, and his most fearsome verdict, delivered with a half smile in front of a clean and correct passage, was “está perfecto, pero no canta” (it is perfect, but it does not sing). The first recipe in the recipe book further on, R1, “Conduct it before you play it,” comes straight from his classroom, as does the whole order of sing first, keyboard second, paper last. That school also has a genealogy that joins it to the Neapolitan conservatories of a few pages back. Through one of its branches, the one that passes through Ernesto Pastor, Modesto Rebollo, Bartolomé Pérez Casas and Felipe Pedrell, it reaches Emilio Arrieta and, through him, Nicola Vaccai, who wrote a practical method of Italian chamber singing, then Paisiello and Francesco Durante, that is to say the very heart of partimento. The arm that taught me to sing at the piano descended, without anyone in that Valencian classroom knowing it, from the same houses where children learned to compose fugues by singing solfeggi.

To sing, in this sense, leaves out the imitation of a style, the polishing of a technique and performance according to other people’s expectations. It also leaves out the cultivated voice of the professional and any mastery that distances the body from its own impulses. I speak of the voice of the living subject, the student’s own, as it emerges in the body the student inhabits, shaped by breath, memory, gestures, by the student’s very sense of being. Singing is the articulation of the self in sound, a tangible trace of consciousness in time. It is an intimate and ontological practice, a declaration of existence, a way of discovering the world and oneself at once. It is precisely this personal, embodied “I” that music must encounter first, because without it all learning, all technique, all composition remains abstraction, a shadow of life, and music loses its generative pulse.

Music must be in contact with the living streams of oral tradition, with the songs that have passed from mouth to mouth, from village to firelight, from market to festival. Folk music, far from the picturesque, is the primal grammar, the reservoir of human musical sound, the ancestral matrix in which melody, rhythm and narrative are inseparable. To inhabit these traditions is to remember that music is a human act, always communal, always immediate, always engaged in the dialogue between past and present.

This inhabiting of oral culture extends naturally to the word. Poetry recited from memory, declamation learned by heart, the shaping of language through breath and gesture. Far from being ancillary or ornamental, these practices are the same ontological labour that gives music its pulse, the thread of léxis worked on its own. A culture of declamation trains the body to think in sound, to breathe with the phrasing, to inhabit the temporal architecture of meaning and to recognise the intimate relationship between sound and sense. The voice, moving through song or speech, becomes a workshop of human comparecencia.

From this perspective, the classical conception of style collapses. It collapses, that is, as a first principle, and styles remain as dialects of the forms and procedures that follow. Baroque, Classical, Romantic. These labels, borrowed from the plastic arts and from literary periodisations, have little to do with the ontology of music. They impose artificial borders and privilege historical narrative over sonic and musical reality. Music does not advance like a line of progress. Bach is as little “progressive” with respect to Monteverdi as an oak is with respect to a holm oak. Each composer, each culture, each song embodies its own world, its own logic, its own life. The myth of linear artistic progress is a veil over the true condition of music, which is recurrent, endlessly recombining, always alive.

From this spirit arises the approach that follows, which binds itself to no style, to no curriculum of eras and forms, to no hierarchy of the “better” or the “more advanced.” What it does is call, in the strong sense that word has received in these pages, to live in music, to speak it, to create it daily, to learn from what was once sung, danced or spoken, and to let that knowledge guide the hand, the voice and the imagination toward forms that exist only in the moment of their becoming.

III. The three axes

Three axes sustain everything that follows, and each corresponds to one of the three lenses. The first is that of perennial, cross-cultural gestures, the motions of song, dance and poetry from which sound departs before anyone writes it down. The second is that of perennial, cross-cultural form types, the archetypal ordering formulas that recur across history and style, from the lullaby to the suite and from the romance to the blues. The third is that of perennial, cross-cultural compositional procedures, the ancestral operations with which a melody or a motive is worked, stretched, broken, answered, said again. I frame them synchronically and deliberately apart from historicism, as structures and operations that recur regardless of geography, period and idiom, and which can therefore be taught to a student in Valencia, in Graz or in Lahore with the same words and the same voice.

Two words in that sentence ask to be tempered before they are used. To some ears “perennial” sounds like the philosophia perennis of the Traditionalists, a wisdom come down intact from on high without passing through any body, and here it designates exactly the opposite, what recurs because it is made again, the transhistorical that each generation rebuilds with its own breath. Nor should “archetypal” be heard in the Jungian sense, since I renounced universals imposed from above before beginning the catalogue. The Greek týpos (τύπος) is closer, the blow, the stamp, the impression a seal leaves in wax, and archétypon (ἀρχέτυπον) is simply the first impression, the print from which the others are taken, a form carved into matter and never laid up in heaven. Closer still is what cognitive science calls a prototype and what Wittgenstein called family resemblance, the thread that runs through a rope although no single fibre runs through it from end to end. Eleanor Rosch gave that intuition a laboratory. She showed that natural categories are organised around central exemplars and fade toward blurred edges, and that membership of a category comes in degrees. “Rondo” has no essence in that strong sense. It has a centre, the finale of the Pathétique sonata, and an edge that frays toward the song with a refrain and the Vivaldian ritornello, and pieces belong to it more or less according to how closely they resemble that centre. That is what rescues the word and makes it useful in a classroom, because the student is taught the centre and left to discover the edge with the hands.

“Universal” is a word that demands grading, and some entries in the catalogues would not bear its full weight. Retrograde and retrograde inversion are almost absent from oral traditions, because memory runs forward and nobody remembers a song from back to front. Exact intervallic inversion is a literate operation, and the oral world knows the fall that answers a rise, the approximate mirror answer the body gives without measuring, while the mirror measured note by note remains foreign to it. Strict canon is rare outside Europe, and echo imitation and overlapping call and response are its perennial relatives. Sonata form is Classical and Western, and I say so in its entry. The grading is part of the thesis. A grammar that called everything universal would be as useless as a map drawn on a scale of one to one.

The voice and the paper

The distinction that truly orders the catalogues separates the procedures of the voice and the body from the procedures of paper and ink. The first group gathers what human beings do with sound whether or not they can write it, repetition, sequence, augmentation and diminution, ornamentation, drone, call and response, hoquetus, heterophony, parallel doubling, modal shift, fragmentation, extension, elision, acceleration, range expansion. The second group gathers what the first becomes once writing exists, retrograde, mensuration canon, serial permutation, isorhythm, soggetto cavato. Paper does not betray the voice. It lets the voice do things it could not remember on its own, and the order of teaching follows the order of birth, voice first, keyboard second, paper last. Each procedure in the catalogue carries its mark.

Oral traditions do not lack a combinatorics for all that. They have their own, made to the measure of a memory that moves forward. Hindustani pedagogy trains improvisation through memorisation and structured variation, and the student learns palṭā (scale patterns permuted and rotated, sung daily in riyāz) and tān (fast passages first fixed by memory and then unfolded with growing freedom), and is almost never asked to improvise all at once, without a prior store of formulas on which to work. The palṭā permutes, but it permutes forward, a cell of four notes sung in one order and then in another, each row sung from beginning to end like a phrase. That is the exact frontier between the two groups. The voice rotates, reorders and varies everything it can hold in the breath of a single pass. Paper does what no single pass can hold, reading the phrase backwards, measuring the mirror, calculating the series. Improvisation is born in the first group, and the classroom that begins with the second teaches reading before it has taught speech.

Figure 4. The procedures of the voice and those of paper. On the left the fifteen that human beings perform with sound whether or not they can write it, on the right the five they turn into once writing exists. Below, the border between the two, what fits within the breath of a single pass and what no pass can sustain, and above, the order of teaching, the voice first, the keyboard second, paper last.

What the data say

On the universality of the first group there is now empirical evidence that goes beyond the intuition of any teacher. Patrick Savage and his colleagues found in 2015 eighteen statistical universals in a global sample of recordings, among them isochronous beat, phrase repetition, descending contours, small intervals and group performance. In 2018 Samuel Mehr and his colleagues asked listeners from sixty countries to hear brief excerpts of songs from eighty-six societies, most of them small and without writing, and to guess their function. The listeners recognised above chance whether a song was for dancing, for putting a child to sleep, for healing or for love, without understanding a word of the text or knowing anything of the context, and the acoustic features that guided the recognition were those of the body, the lullaby slow, narrow in range and falling in contour, the dance song fast, accented and firmly pulsed. A year later the same group showed, with an ethnography and a discography of worldwide scope, that song appears in every society studied, bound to the same contexts of behaviour, and that the variation within each society exceeds the variation between them. Stephen Malloch and Colwyn Trevarthen documented in Communicative Musicality that pulse, quality and narrative are already present in the vocal exchange between a baby a few weeks old and whoever looks after it. When I speak of voices that have received no training, I speak of the exact place where the data begin.

The data also say why there is recurrence, and they say it in material terms. Nori Jacoby and Josh McDermott asked listeners in the United States and among the Tsimane, a people of the Bolivian Amazon with scant exposure to Western music, to reproduce by tapping a random rhythm of three intervals. Each participant’s reproduction became the stimulus for the next attempt, and after a few iterations the rhythms stopped being random and fell, like marbles into the holes of a board, toward ratios of small whole numbers, one to one, one to two, two to three. Those attractors appeared in every group, and their weights varied from culture to culture, so that what was shared was the body’s tendency to simplify and what belonged to each people was the map of its favorites. This is how oral tradition works. Each singer who inherits a song reproduces it, and in that chain of reproductions whatever memory and the body cannot hold falls away, and whatever they hold takes root. The form that recurs is the sediment of that sifting. Mehr’s experiment teaches the other half of the same fact, for the lullaby resembles itself everywhere because everywhere a child has to be put to sleep with the same apparatus, a voice that descends, an arm that rocks, a rhythm that imitates the heartbeat and the slow breathing of the one who is falling asleep. The embodied function gives the form, and the form recurs where the function recurs. None of this needs an archetype in heaven. Similar bodies doing similar things with the air are enough.

Lenses that leak

Since the three lenses are lenses and in no case boxes, they leak into one another by design. Every form in the catalogue of forms is a procedure from the catalogue of procedures repeated until it has become a habit of listening. Iterated variation becomes theme and variations, a refrain procedure becomes rondo, an ostinato becomes chaconne. If one wants a formula, gesture is the instant, procedure the passage, form the span. Gestures are the inputs, procedures the operations, forms the invariants. Whoever has followed the loom that the introduction has strung will recognise in that formula the strata that cross it, the instant of gesture happens in the Inclination, where something yields toward something, and the passage of procedure runs along the Toward.

That last word, invariant, is taken here literally, because four unrelated traditions say the same thing about the second and third lenses. Kant defines the schema as “the representation of a universal procedure (Verfahren) of the imagination for providing a concept with its image.” A form, in other words, is the rule that generates it. Greek rhetoric had settled the question in its vocabulary. The figures are schḗmata (σχήματα), a single word for the ordering pattern and for the operation that produces it, and that is why the galant schemata that Robert Gjerdingen gave back to the guild belong to both my lists at once, the Prinner being a figure one recognises and a bass motion one carries out. Felix Klein’s Erlangen programme defines a geometry as whatever remains invariant under a group of transformations, and that is exactly the relation that governs here. A form is what survives the procedures. A procedure is what carries you from one instance of a form to another. And the isorhythm of the fourteenth-century motet, a rhythmic talea and a melodic colour of different lengths turning against each other in the tenor until their displacement runs its course and they coincide again, is an ordering formula that consists entirely of an algorithm in motion. Form and procedure are two faces of one thing, seen from outside and from inside, and the student who has turned a talea of seven values against a colour of twelve with their own hands knows forever that the form was the procedure seen from afar.

IV. Two tetrads

A poetics of doing and a syntax of becoming

Before the catalogues there is something more elementary than any of them, and it is the spine of the whole essay. Gestures, forms and procedures are the material. What follows is the order in which that material becomes music in a pair of hands, two series of four ancient words which suffice for an entire lesson and which, stretched across the loom of melos, show why music is made before it is described.

Ab extra and ab intra

There are two ways of coming at music, and almost everything I object to in the inherited teaching follows from the first having swallowed the second.

The curriculum ab extra begins with the finished object and teaches recognition. Here is a phrase. Identify the cadence. Identify the modulation. Identify the form. Its vocabulary is a vocabulary of nouns, chord, motive, phrase, period, exposition, cadence, sonata, and every one of those nouns names something that can only be seen after it has appeared. The student learns to describe what has happened, in the hope that description will one day ripen into competence. That ripening never comes, and anyone who has marked analysis exams in a conservatoire has seen students able to label an entire exposition who could not lead four bars toward a half cadence.

The curriculum ab intra begins before the object exists, and its vocabulary is verbal. It stops asking what a thing is called and asks whether you can make it happen. Begin something. Hold it in the air. Give it an inside. Bring it somewhere. And at the same time, lead it. Weave it with another voice. Move its pieces. Give it tension. Names come afterwards, and they come easily, because by then they name something the hands have already done.

Those two sets of four imperatives have a genealogy. Each is an ancient tetrad, one Greek and one Latin, one born of the theory of melody and the other of the practice of liturgical chant, and between them they compose a grammar of musical making that will not be turned into a template, because its terms are verbs and a verb exists only while it is being conjugated.

The first tetrad. Agōgḗ, plokḗ, petteía, from tonḗ to tónos

The first analogate of compositional procedure

Aristoxenus called composition melopoiía (μελοποιία), “melody-making,” and placed it at the end of the parts of harmonic science, as the use to which everything before it is put. Cleonides, who summarised Aristoxenian doctrine in an Introduction to Harmonics handed down also under the name of Euclid, divides the science into seven parts, notes, intervals, genera, systems, tones, modulation and melopoeia, and lists the four parts of the last, agōgḗ (ἀγωγή), plokḗ (πλοκή), petteía (πεττεία) and tonḗ (τονή). In their strict technical sense they are modest, almost dry. Agōgḗ is the progress of melody through contiguous notes, and Cleonides distinguishes three species, the one that rises, the one that descends retracing its steps, and the one that circles, going up by one path and coming down by another. Plokḗ is progress through notes that are not contiguous, the leap. Petteía is the repeated striking of a single note. Tonḗ is the voice dwelling on one note for a longer time, in a single emission. It is the oldest catalogue of procedures we possess, and even in that dry reading it is remarkable that the four things in which a Greek theorist held melody-making to consist were step, leap, repetition and sustain, four ways of moving or of staying put that any child performs before knowing they exist.

The words, however, are larger than the technical use they were narrowed to, and read from their root they yield an entire poetics of doing. I read the tetrad as a procedural archetype, and that reading finds its firmest ground in the fourth word, where the Greek text says tonḗ and I read tónos (τόνος). The step from one to the other is the best etymological argument in these pages, and it deserves to be spoken slowly and aloud.

Both words come from the same verb, teínō (τείνω), to stretch, to extend, to tense, which goes back to the Indo-European root that linguists reconstruct as *ten-. Both are formed on the same o-grade of the vowel, and they differ only in the suffix. Greek has a whole series of such pairs, and in all of them the feminine form in -ḗ names the action under way and the masculine in -os names what that action leaves behind or what sustains it, tomḗ (τομή), the cut being made, and tómos (τόμος), the slice, the tome, tropḗ (τροπή), the turn, and trópos (τρόπος), the manner, nomḗ (νομή), the sharing out of pasture, and nómos (νόμος), the law, and also, in music, the traditional melody. Tonḗ, then, is the act of keeping the voice stretched, and tónos is the tension itself, and by extension the tensed string, the pitch that tension produces, the register of a scale and, among the grammarians, the accent of the word. A sustained note is a voice stretched as a string is stretched, and Greek acoustics knew from the monochord that the pitch of a sound depends on the tension and the length of what vibrates. To sustain a note is to sustain a tension. The language said it before the theory did, and when I read tónos where Cleonides writes tonḗ I merely pass from the action to its result within a single family of words, the same step that leads from the slice to the cut.

The family is larger still and reaches as far as the body and plainchant. From the same root comes ténōn (τένων), the tendon, the taut string of the body that binds muscle to bone and that every pianist knows in the forearm before knowing it from any book. From it come the Latin tendere, to stretch, and tenere, to hold, and from tenere comes tenor, the reciting string of the psalm tone, the second term of the second tetrad. The family is still alive in tend, tension, tense, tone and tenor, in sustain, which is sub-tenere, and in attention, which is ad-tendere, to stretch toward. The fourth word of the Greek tetrad and the second word of the Latin tetrad are first cousins, and that kinship has consequences. The sustained note of Cleonides and the tenor of psalmody are the same phenomenon named twice, a voice that is held stretched, and the attention of the listener belongs to the same family, because to listen is to stretch the ear toward what is being held. The two tetrads touch at that root like two threads knotted together.

Read in this way, from their root and with the fourth word restored to its tension, the four parts say what follows.

Agōgḗ means to lead, to set in motion, to carry. It is the word of the agōgós, the one who guides, and of the paidagōgós, the slave who took the child to school. Something begins and is carried somewhere. A sound is never simply succeeded by another sound, the first is led toward the second, and in that leading there is already intention, direction, attraction, resistance and continuation. The three species of Cleonides, rising, coming back down and circling, are the three elementary ways of having a course. From here Hugo Riemann took “agogics”, keeping only the inflection of tempo, the small delay and the small haste with which the performer draws the phrase, and even in that reduced version he kept what is essential, that musical time has direction and that direction is felt in the body as a pull or a holding back.

Plokḗ means to interweave, to braid, from plékō (πλέκω), the verb of the braid, the basket and the cloth. What has been set in motion meets another line, and voices become relation. Line against line, consonance turning into dissonance and resolving, imitation, contrary motion, the suspension that lets itself be caught by the neighbouring voice and is released a beat later. It is the primordial contrapuntal operation, and the musician’s task before it is to interweave, long before it is to identify.

Petteía is the play of positions. The word comes from pessoí (πεσσοί), the pieces of a board game the Greeks played on a grid, which Plato uses more than once as an image of calculating thought. Given elements acquire meaning through placement, displacement, opposition, anticipation and response. Transpose, invert, exchange, delay, recombine, answer. Musical intelligence appears as strategic play, and what matters about a configuration is which moves can be made from it, far more than what it is called. That the technical sense of the word should be the repeated note has its own logic, because to repeat is the minimal move, to leave the piece where it stands and strike it again, and from that stroke the whole board comes into view.

Tónos, now restored to its root, means tension, stretching, what is stretched out. It designates the tensile field that gives the whole its direction, resistance, intensity and coherence, far more than the pitch of a note or the “tone” of modern textbooks. A note leans, a dissonance pulls, a register opens, a cadence is held back, an arrival becomes necessary. With tónos music leaves mere succession and mere combination behind and becomes a field of forces.

Compressed almost brutally, lead, weave, play, tense. Said with more ontological weight, movement, relation, disposition, tension. Or, lapidary, agōgḗ gives music a where-to, plokḗ a with-what, petteía a how-among, tónos a stretching-toward.

What fascinates me about the four is that none of them requires the modern concepts of work, form, harmony, thematic development or even composition. They describe operations. Music appears in them as something that is led, interwoven, disposed and stretched, long before it is an object possessing properties. They are four primordial capacities of the maker, and that is why poetics is the right word, since poíēsis (ποίησις) concerns bringing into presence.

The pedagogical consequence is radical. Do not show me that you can identify the sequence, lead me one. Do not identify the counterpoint, weave it. Do not explain the permutation, make the move. Do not circle the tension in the score, create it, sustain it, release it.

The second tetrad. Initium, tenor, mediatio, terminatio, with its flexa

The first analogate of formal ordering

The offices of the psalm tone, which will reappear in form 24 as a reciting formula, go deeper still than the Greek tetrad, because they describe the primordial ordering of musical time, the order in which a doing becomes an utterance, while the first tetrad describes what musical activity does within. They answer another question. What must happen in time for a musical doing to become an intelligible utterance?

A psalm tone is an elastic melodic template that serves to sing any verse of any psalm, whatever its length. The verse is split into two halves, and the chant book marks the cut with an asterisk. The voice enters by a brief intonation formula, the initium, which in the eighth tone rises from G to A and from A to C. It then settles on a single note, the reciting string or tenor, the C of that same eighth tone, and on it says as many syllables as are needed, five or twenty-five, without moving the pitch. On reaching the asterisk, a small formula hooked onto the last accents of the first half, the mediatio, bends the line and leaves it suspended. The second half returns to the tenor without a fresh intonation, and the last formula, the terminatio, carries the voice to its close. That ending has variants, the differentiae, and the cantor chooses the one that links best with the beginning of the antiphon to be sung next, so that the end of each verse is written with an eye on what comes after. In ordinary psalmody the initium is sung only in the first verse, and the others start straight from the tenor. In the Gospel canticles, the Magnificat and the Benedictus, the intonation is repeated in every verse, as though each one began the world again.

And there is a fifth articulation which the inherited tetrad leaves out and which illuminates the other four. When the first half of the verse is too long for a single breath, the book marks with a cross, before the asterisk, a point of flexa. There the voice bends down from the tenor by a whole tone, or by a minor third when the note below lies a semitone away, as happens with the C of the eighth tone, which bends down to A, and on the next syllable it returns to the same reciting string as if nothing had happened. The flexa has no formula of its own, has no cadence, and does not split the verse. It is a minor articulation, a comma within the first half, and it appears only when the text demands it. Its place is exact, inside the tenor and before the mediatio, and from that place it answers the question whether we are facing a fifth function or a fold of the four.

The tetrad subsumes it, and subsumes it in the tenor. A function of the syntax of becoming is necessary to every utterance, and the flexa is contingent, since it depends on how many syllables half a verse has and on how much air fits in a chest. It is born of the flesh and never of syntax. The mediatio divides the utterance into two halves that answer each other, like an antecedent and a consequent, and creates an inside. The flexa divides nothing, it lets the tenor breathe without breaking and returns to the same note, so that the utterance stays whole and the string stays stretched. That is why the flexa belongs to the tenor as the fold belongs to the cloth. And that belonging teaches something decisive about the tenor itself. To sustain was never to stay rigid. A reciting string that could not bend would snap at the first long verse, and the tenor endures because it knows how to bend for an instant and come back. To sustain is to breathe within what is sustained. In the school of song and arm in which I was trained by Salvador Chuliá, a long phrase of Chopin or Schubert was played exactly so, with a minimal lightening of the arm’s weight halfway along, which the phrase registers without stopping, and with the true articulation kept for the point where the phrase bends toward its second half. That is the difference between the caesura of the verse line, gesture G19, which corresponds to the mediatio, and the lesser breath that precedes it and has had a name of its own in psalmody for a thousand years. A student who can tell the flexa from the mediatio in a piano phrase has learned to breathe without cadencing, which is almost everything one needs to know in order to play an adagio.

With the flexa in its place, the four offices say what follows.

Initium, becoming begins. And to begin exceeds the first chronological event. A musician can play the first note without beginning anything, and an anacrusis made of almost nothing can inaugurate a whole world. The initium answers the question of how something ceases to be silence and becomes a happening, and plainchant knows it when it reserves the intonation for the first verse, because the world opens only once.

Tenor, becoming holds. The word comes from tenere, to hold, and beneath tenere lies the same root that stretches the string of tónos. It is the deepest office of the four, because it names the central problem of musical time. If nothing changes, there is scarcely music. If everything changes without retention, intelligible continuity disappears. Something must be held through alteration. A reciting string makes this literally audible, and the principle far exceeds that case. A rhythmic character can be held, or a registral space, a harmonic region, a contrapuntal disposition, an affect, a pulse or simply a direction. The art of music is to a great extent an ars sustinendi, an art of holding, and the tenor with its flexa is its first lesson.

Mediatio, becoming articulates itself. Mere continuation is not enough, and a living utterance must acquire an inside. It bends, breathes, divides, suspends itself, reaches an intermediate place from which continuation becomes possible again. This is crucial. The mediatio has little to do with “the middle.” A ruler has a middle and a duration has a midpoint, and neither of them is a mediatio. The mediatio is the becoming of internal articulation. The initium gives the utterance existence, the tenor gives it continuity, the mediatio gives it interiority.

Terminatio, becoming becomes whole. To end is more than merely to stop. A pianist can stop playing without terminating a musical thought, and a cadence can produce terminatio even when another event follows at once. Terminus is a boundary, the marker stone the Romans planted on the edge of a field. Only in the ending does what began fully reveal what it was that had been happening, and only here does wholeness appear, a wholeness achieved in time and foreign to the spatial object taken in at a glance. The differentiae add a nuance the textbooks usually overlook. The ending of the psalm is chosen according to what comes after, the antiphon that follows it, so that the boundary of the utterance is already looking toward the next one. To close well is to leave the right door open.

So then, begin, hold, articulate, close, or, at depth, emergence, persistence, articulation, fulfilment.

The advantage of this tetrad for everything that follows is that it precedes the taxonomy of phrase, period, sentence, binary and sonata. Those are historical morphologies. Initium, tenor, mediatio and terminatio lie closer to the conditions under which there can be any musical morphology at all. A child singing, Gregorian psalmody, a Renaissance cadence, a chorale phrase, a Neapolitan partimento, a Chopin phrase, an improvised utterance in any tradition, all of them embody the same course, something begins, something holds while breathing, something articulates itself from within, something reaches its end.

The two tetrads on the loom

It is tempting to line the tetrads up term by term, and the temptation must be resisted. Their strength lies in describing two different axes. On the procedural axis, what can be done to the material, agōgḗ, to lead, plokḗ, to weave, petteía, to dispose and play, tónos, to tense. On the axis of ordering, how time becomes an utterance, initium, to begin, tenor, to hold, mediatio, to articulate, terminatio, to delimit. The first is a poietics of doing, the second a syntax of becoming. One names the verbs of generation, the other the conditions of an utterance.

Those two axes find their exact place on the loom of melos that the introduction has set up, the three vertical threads of léxis, harmonía and rhythmós crossed by the three horizontal strata of the Flesh, the Inclination and the Toward. The words of the first tetrad are weavers’ words, and not by chance. Agōgḗ is the Toward of the loom, pure direction, the stratum where music is already going where it has yet to arrive, and that is why the lapidary formula gave it a where-to from the start. It runs through all three threads at once, the word addressed to someone, the fit that pulls toward its rest, the pulse that pushes toward the next beat. Plokḗ is the shuttle itself, the operation that crosses the threads with one another, and its natural territory is harmonía, which in Homer named the joint that fits together the planks of a ship before it named any chord. Petteía is played on the grid of the nine cells, which is a board, and each of its moves carries an element from one cell to another, a gesture of the Flesh turned into a support for the Inclination, a harmonic fit displaced into rhythm, a formula of speech transferred to a pulse.

Tónos has its root in the Inclination and in the tension of weight. The Inclination is the stratum where something yields toward something, and the Greeks had a word for that instant, rhopḗ (ῥοπή), the tipping of the scales at the moment one pan begins to sink. Every musical tension is a balance about to yield, the leading note weighing toward the tonic, the appoggiatura that leans, the dissonance that pulls at its resolution. Yet the balance tips only because there is weight, and weight belongs to the Flesh, to the arm that falls, to the body that gravitates. The Greek loom showed it in plain sight. It was an upright loom, and the warp threads hung from a beam and were kept taut by clay weights tied to their ends. The tension of the fabric came literally from weight. That is how tónos works in a sung or played phrase, a warp stretched by the weight of the body, inclined toward its resolution, without which the shuttle of plokḗ would have nothing to cross. The school of weight against attack, the one that makes sound arise from the fall of the arm and never from the blow of the finger, is the pianist’s way of knowing that tónos hangs from the Flesh.

The second tetrad stretches across the loom in the other direction, along the cloth that keeps coming off it in time. The initium is born in the Flesh, in the breath before the sound that the catalogue calls gesture G1, and it leaves the Flesh as a call. The tenor is sustained weight, the Flesh held in the Inclination without being allowed to fall, and its flexa is the Flesh breathing within what is sustained. The mediatio is the Inclination become form, the point where the utterance bends and yields toward its second half. The terminatio is the Toward fulfilled, and the differentiae show that its fulfilment leaves another Toward open, because the end of the verse is already looking at the antiphon. For the last gesture weavers have the same word as flamenco, the remate, the knot that secures the selvedge so that the cloth does not unravel and that allows it to be cut whole from the loom.

That is why they cross everywhere instead of running in parallel, as the hand passing the shuttle and the advancing cloth cross on a loom. I can use agōgḗ to produce an initium, and equally to carry a tenor or to drive toward a terminatio. Plokḗ can work within an initium, across a mediatio, or to intensify a terminatio. Petteía can transform what the tenor established, or make the mediatio possible. Tónos can charge the initium from its first instant, sustain the tenor, make the mediatio necessary and generate the demand for terminatio. And at one point the two axes knot together, in the root that tónos and tenor share, the stretched voice that the first tetrad names as an operation and the second as an office. There tension and holding are the same thing seen from the hand and seen from time.

Sixteen questions

So between the tetrads there are no diagonal arrows, and there is something better, a generative field of four by four and sixteen questions of musical making.

Agōgḗ asks, facing the initium, how I lead something into being, facing the tenor, how I carry it forward, facing the mediatio, how I lead through an articulation, and facing the terminatio, how I lead toward a boundary. Plokḗ asks how relation begins, how it is sustained, how the weave articulates itself and how it closes. Petteía asks what opening disposition generates possibilities, which moves preserve the game, which move changes its state and which move makes further movement unnecessary. Tónos asks how tension is born, how it is maintained, how it is redistributed and how it is fulfilled or released.

Table 1. The generative field. The four parts of melopoeia, with tonḗ given back to tónos, crossed with the four offices of the psalm tone yield sixteen questions of musical making, and none of them asks what something is called. It can be read by rows, what each operation asks of each office, or by columns, what each office demands of the four operations.

Parts and offices	initium, to begin	tenor, to hold	mediatio, to articulate	terminatio, to close
agōgḗ, to lead	How do I lead something into being?	How do I carry it forward?	How do I lead through an articulation?	How do I lead toward a boundary?
plokḗ, to weave	How does relation begin?	How is it sustained?	How does the weave articulate itself?	How does it close?
petteía, to play	What opening disposition generates possibilities?	Which moves preserve the game?	Which move changes its state?	Which move makes further moving unnecessary?
tónos, to tense, from tonḗ back to tónos	How is tension born?	How is it maintained?	How is it redistributed?	How is it fulfilled or released?

The first square of the field deserves a pause, because the sense of all the others depends on it. To lead something into being, agōgḗ facing the initium, is to call. The first act of the Toward upon silence has the figure of gesture G2, the leap rising to a held note projected to be heard at a distance, the shepherd’s call, the street cry, the horn fifth. Before saying anything, music addresses someone. That is the vocative thesis the introduction has founded, music calls before it represents, as the vocative case in grammar calls someone by name without predicating anything of them, and here it enters the tetrad by the main door, because the square that opens the field is a call. The founding order, the call before the song, the song before the gesture, the gesture before the sound, is recognised from within the field. The sixteen questions make up the grammar of a saying, of a léxis, the saying before the said, and at no point the grammar of an object said. That is why the most accomplished terminatio of any utterance is the one that answers its initium, and that is why the last square of the field, tónos fulfilled or released, almost always sounds like an answer.

None of those sixteen questions asks the student what something is called. Every one of them asks whether the student can make it happen. Any of them fills a lesson, several fill a year. The catalogues that follow, gestures, forms, procedures, are the material with which the sixteen are answered, and the recipes are answers tested in the classroom. The questions come first.

A possible lesson on a single question

A possible lesson devoted entirely to one of the sixteen begins like this. The question is that of petteía facing the terminatio, which move makes further movement unnecessary. Imagine a seventeen-year-old student who arrives with the melody of the day, eight bars in D Dorian that he sang that morning in the kitchen and wrote down on the bus. The opening motive has four notes, D, F, E, A, with a leap of a fourth at the end that sounds like a question. The teacher writes those four notes on four cards and sets them on the music stand side by side, like pieces on a board. He asks the student to sing the whole melody and to stop in the last bar without finishing it.

For the first half hour the student moves the pieces. He tries ending with the four notes in their original order, and the melody stays open, because the leap to A asks the question again. He tries the retrograde, A, E, F, D, and the teacher points out to him, without yet saying the word, that he has just answered his own beginning, that he has come down from where the first phrase went up. He tries liquidating the motive, removing first the leap, then one note, then another, until only the D struck twice remains, petteía in its driest technical sense, the stroke on a single note, and he discovers that this repetition closes more firmly than any textbook cadence. He tries ending on A, ending on F, ending with a silence. Each time he sings the whole eight bars from the beginning, because an ending can only be judged with everything before it in the body, and each time the teacher asks the same question, whether after that move another one would be needed.

At the half hour the teacher moves the student, sits him at the piano and asks him to try the four best endings with the right hand while the left sustains a drone on D and A. Now the pieces weigh differently, because the drone has its own tónos, and some moves that closed in the voice are left floating over the fifth. The boy chooses one, writes it down, and writes beneath it, in his own words, why nothing more needs to move. What he writes usually resembles this, that the last move returned the pieces to a position from which any further movement would repeat what had already been said. That sentence, written by a boy who has never read Cleonides, is a definition of terminatio as good as that of any treatise. At the end of the hour the teacher shows him four endings from the repertoire, the last phrase of a Chopin mazurka, the close of a sung verse of jota, the ending of the eighth psalm tone, the last bar of a two-part invention by Bach, and the student recognises in all four the same move he has been looking for with his cards. Then, and only then, the teacher says the word cadence, and the word comes easily because it names something the hands have already done.

The act before the thing

A poietics of doing precedes a theory of things, and a syntax of becoming precedes a taxonomy of forms. Together they say that music is first an ordered becoming brought into presence through acts, and only afterwards, for whoever looks at it from outside, an arrangement of things in time. The poietics of doing names the acts. The syntax of becoming names the order by which those acts become an utterance. Form, in the later textbook sense, is the trace left behind when a particular doing has completed a particular becoming, the cloth cut from the loom with its remate on the selvedge. Whoever knows only the cloth can describe it thread by thread and still not know how to weave. Whoever has stretched the warp with the weight of his own arm, has passed the shuttle and has decided where to finish it off, looks at any cloth and still sees the hands that were making it, and hears in every ending the call it answers.

V. Perennial gestures

Song, dance, poetry

Gesture resists catalogues, and it is right to resist them. The objection that a list kills the thing it lists applies equally to forms and to procedures, and I make those lists anyway, because a student cannot practise what has no name. With gesture the danger is smaller still, because what receives a name here is motion, the few dozen things the voice and the body do with sound before anyone has decided what they mean. A named feeling cools. A named motion can be repeated, and in the repeating it grows warm.

The triad I have called the ontological nucleus of music, song, dance and poetry, gives the catalogue its structure. Gestures of song are what the voice does. Gestures of dance are what the body does with pulse and weight. Gestures of poetry are what the breath does with words, the figures of speech that every melody inherits. The three families overlap constantly, and the truth of the matter lies in that overlap. A sigh is at once a vocal gesture, a falling motion and the shape of a certain kind of sentence.

The words of gesture

Greek is unusually rich here, and each word teaches something. Kínesis (κίνησις) is movement, enérgeia (ἐνέργεια) being-at-work, hexis (ἕξις) the embodied disposition that Latin renders as habitus, and schêma (σχῆμα), before it meant scheme, meant posture, bearing, a figure of dance. Four other words do more than teach. Read together they draw, without anyone having planned it, the loom of melos I set out in chapter II, and they draw it precisely from the side of gesture. I recall its figure here for the reader who arrives without it. Three vertical threads, léxis (λέξις), the saying addressed to someone before anything has been said, harmonía (ἁρμονία), the fitting by which some sounds gravitate toward others and draw them near, and rhythmós (ῥυθμός), the shape of what flows, cross three horizontal strata. Below lies the Flesh, the given that no one chooses, the face, the breathing, the weight. In the middle lies the Inclination, the instant in which something yields toward something. Above lies the Toward, direction, continuity, the pure futurity of what has not yet arrived. Nine crossings, nine cells. And the Greek vocabulary of gesture was already a map of those three strata, drawn two thousand years before I gave them names.

The Flesh has two words in Greek. Pneuma (πνεῦμα), from pnéō, to blow, is breath, and it is at once the wind and, much later, the spirit, so that the language already knew that the highest thing it would come to name began in the lungs. And báros (βάρος) is weight, whose adjective, barýs, gave Greek prosody its grave accent and gave our voices the baritone. Breath and weight are what the body brings to music without having decided to, the air in the chest and the arm hanging from the shoulder. The school of song and arm in which I was formed with Salvador Chuliá rested entirely on this stratum, the phrase is sung before it is played and the sound is born of the weight of the arm rather than the force of the finger, and when Rudolf Laban wanted to give human movement a working vocabulary he placed weight among his four factors, alongside space, time and flow. The Flesh is what there is before anything moves.

The Inclination has an exact name in Greek, and that name is rhopé (ῥοπή). It comes from rhépō (ῥέπω), said of the pan of a balance as it dips, and it names the instant in which the balance yields. Homer left the primal scene of that word. Before the last combat Zeus holds out his golden scales, sets a fate of death in each pan, lifts them by the middle, and the fatal day of Hector sinks and goes down toward Hades. The verb with which Zeus holds out the scales belongs to the family of teínō (τείνω), to stretch, the same family from which tónos comes, and the verb with which the pan goes down is the verb of rhopé. Tension and inclination thus appear in a single line, the string drawn taut and the instant in which it yields. Greek physics also gave the name rhopé to the tendency of a body toward its place, the moment in which weight stops being a given and begins to be a going. Rhopé is the Inclination of the loom under its Greek name. It has weight and still lacks a fulfilled direction, it is the hinge between the Flesh and the Toward, and no musical gesture exists without passing through it. The appoggiatura that leans, the sigh that lets its weight fall on the first note, the anacrusis that rises before it settles, are rhopaí, inclinations of the balance of sound.

The Toward has two more words in Greek. Hormé (ὁρμή) is the Stoic word for impulse, and the Stoics defined it as a movement of the soul toward something, phorà psychês epí ti (φορὰ ψυχῆς ἐπί τι), with a preposition, epí, that is literally the Toward. By a near-homophony I cannot resist, hórmos (ὅρμος) is a harbour, so that the harbour of motion is the impulse finding its anchorage. And agōgē (ἀγωγή), leading, the first of the four parts of melopoeia we saw in chapter IV, is also the word with which Aristides Quintilianus names the quickness or slowness of time, the tempo. Agōgē gives music a whither, I said there, and it can now be added that it gives it in both senses the word allows, where the music goes and at what pace.

Among these words runs a pair that crosses the three strata in a single stroke. Arsis (ἄρσις) and thesis (θέσις) meant the raising and the setting down of the foot, and Aristides Quintilianus still defines them as movements of a part of the body, the one upward and the other downward. Rhythm was named from the body before anyone noticed. And the pair contains the whole loom. Thesis is the Flesh, the weight that reaches the ground. Arsis is the Toward, the foot that lifts to go somewhere. And between them, at the highest point of the lifted foot, when the weight begins to decide where to fall, lies rhopé.

There remains cheironomía (χειρονομία), the art of drawing the melody in the air with the hand, which brings a historical reward to this essay, because the oldest neumes, those without a staff, are still called cheironomic. Notation began as the fossil of a gesture. “Sing first, keyboard second, paper last” has its documentary proof in that word, and the order that sustains it, deeper than any workshop preference, I set out shortly when I come to the call.

If the vocabulary is a map, the catalogue that follows is the inhabited territory, and the loom works in it in two ways. The first is vertical. The three families of the catalogue are the three threads. Plato said in the Republic that melos is composed of lógos, harmonía and rhythmós, and I have radicalised his lógos into léxis, the saying before the said. The gestures of poetry are léxis become breath, the line, the caesura, the accent, the curve with which a sentence asks or affirms. The gestures of song are harmonía become voice, the sound that reaches out, holds and falls toward another sound. The gestures of dance are rhythmós become foot. The second way is horizontal, and it is the one that defines gesture as a lens. A gesture is the whole passage from the Flesh to the Toward through the Inclination, accomplished in an instant. That is why I said in chapter III that gesture is the instant, procedure the trajectory and form the extent. Procedure runs through the fabric along a thread, form takes it in as cloth, and gesture crosses it from bottom to top in a single beat. Every gesture in the catalogue has its home in one of the nine cells, and no cell is left empty. The step, G10, and the stamp, G13, live in the Flesh of rhythmós, the sway, G11, and the swing, G12, in its Inclination, the run, G16, and the leap, G14, in its Toward. The held tone, G6, is the Flesh of harmonía, the sigh, G4, and the lament, G3, its Inclination, the swell, G5, its Toward. The line, G18, is the Flesh of léxis, because it measures how long a breath lasts, the caesura, G19, and the accent, G22, its Inclination, the declamation curve, G24, and the rhyme that promises to return, G21, its Toward. That twenty-four gestures gathered from traditions with no contact between them should fill the nine cells without leaving a single one deserted is for me the best argument that the loom describes something that was already there.

Latin and the workshop add gestus, actio, the fifth canon of rhetoric, the discourse delivered by voice and body, ductus, which in palaeography is the manner of drawing the stroke and in rhetoric the course of a discourse, impetus, conatus, affectus, the German Anschlag, the pianist’s touch, literally a striking, the French toucher, and our own attack, anacrusis, agogics, inflection. In spectromorphology Denis Smalley technically opposes gesture to texture, gesture as a trajectory of energy and motion that drives the sound forward, texture as sound lingering within its own interior. Robert Hatten treats musical gesture as an embodied unit of meaning, an energetic shape the listener recognises because the listener’s own body already knows it. Empirical research in recent years has given that intuition a laboratory. The volume Rolf Inge Godøy and Marc Leman assembled in 2010 studies musical gesture as the link that binds sound, movement and meaning, and it distinguishes the movements that produce sound from those that accompany it, which are the same movements the listener’s body sketches without noticing. And Arnie Cox has formulated what he calls the mimetic hypothesis, according to which we understand music in large part by imitating inwardly, in a motor imagery that is almost always covert, the actions that produce it, so that to hear a phrase is already, in the body, to rehearse singing it. This is the experimental description of what a lesson in song and arm took for granted. The listener too has Flesh, and listens with it.

And at the far end, where the word stops being technical, appears Warburg’s Pathosformel, the formula of pathos, the gesture that survives across the centuries in its Nachleben, its afterlife, which is precisely The Pattern That Remembers Us, filed under Form in my epithets, and rightly so, because the Pathosformel is the gesture that has become form and carries memory. There is Agamben’s gesture as pure mediality, which exhibits the medium itself without any end, and that is what I mean when I ask that music flow as action. There are Merleau-Ponty’s flesh and chiasm, touching and being touched, which the pianist knows better than anyone, because the key under the finger returns the pianist’s own weight in the same instant. There is Husserl’s distinction between Leib and Körper, the body lived from within and the body as a thing that can be measured from without, and the Flesh of my loom is Leib through and through, weight that feels itself weigh. There is Brecht’s Gestus, gesture as the attitude of one person toward another, the social gesture, a gesture always addressed and therefore akin to the call. There is the Gebärde of Benjamin, who read the work of Kafka as a codex of gestures whose meaning is never fixed, gestures prior to the decision about what they mean, which is exactly what this catalogue tries to gather. And there is Focillon’s praise of the hand, the hand that thinks by making.

The call

One of the twenty-four gestures has a dignity the others lack, and it has it because it founds them. It is the call, G2. It keeps its number, because in the order in which the voice is traversed it comes after the breath that makes it possible, and because other chapters of this book look for it under that code. Yet it is first in dignity, and everything that follows in this chapter, and much of what follows in the book, depends on it.

Ancient grammar knew a case that calls without predicating. Dionysius Thrax lists five cases of the Greek noun, and the fifth is the klētikḗ ptōsis (κλητικὴ πτῶσις), the case of calling, from kaléō (καλέω), to call, which Latin translated as vocativus, from vocare. The vocative has a property no other case has. It lies inside the declension and outside the sentence. A noun in the nominative can be a subject, in the accusative an object, in the genitive it can possess, and in the vocative it can occupy no place at all in what is said. “María!” asserts nothing about María. It does not describe her, does not classify her, does not make her the topic of a statement. It calls her, and in calling her it opens the relation within which anything said afterwards can be said. Recent linguistic typology confirms this with a precision that moves me, for it finds that the vocative markers of very different languages mark the noun as incompatible with the argument positions of the sentence, and that what they encode, besides the call, is the kind of bond between the one who calls and the one who is called and the physical distance that separates them. The vocative measures distance and crosses it. That is what music does before it does anything else.

That is the vocative thesis, and this is its place. Music is vocative before it is representational. It calls before it says anything. It may afterwards paint, narrate, imitate water or the storm, build cathedrals of tonal relations, yet all of that happens within a relation the call opened first, just as all the cases of the sentence happen within a conversation that someone began by saying a name. That is why I call what this book proposes a deep grammar. A grammar of operations is the grammar of a saying, and a saying has an addressee before it has an object. The léxis of the loom, the thread I have set where Plato set lógos, names that saying before the said, and the call is the only gesture in the catalogue in which léxis appears naked, without words, in the pure voice.

Most astonishing of all, speech itself, when it truly calls, turns into song. Phonologists describe in many languages an intonation proper to calling at a distance, the contour the literature names the vocative chant or calling contour, in which speech becomes stylised and ceases to speak. In the Ladin of the Badia valley, for instance, the melody of the call consists of a low stretch, a rise to the high register on the stressed syllable, a held plateau and a considerable lengthening of the nucleus of the final syllable. A rising leap to a held high note. It is the definition of G2 written by linguists who were thinking of anything but music. The place where language turns into song is the vocative, and the border between speaking and singing runs exactly through someone’s name spoken from afar.

From this follows the order that founds everything else. Call, Song, Gesture, Sound. First someone is called, and the voice addresses itself before it knows what it will say. Then the call is sustained, tuned, finds its fitting and its fall, and becomes song. Then song passes into the body, into the arm that draws it and the foot that walks it, and becomes gesture. And only at the end is gesture entrusted to an instrument, to a string or a hammer, and becomes sound. That order is the ontological reason for a watchword that until now might have seemed a matter of workshop taste. “Sing first” covers the call and the song, “keyboard second” covers gesture and sound, and paper comes last because it is the fossil of everything before it, as the cheironomic neumes are. The order also explains an apparent paradox in this catalogue. The call appears in it as a gesture of the voice, numbered among the others, and yet in the founding order it precedes gesture. The same holds for the vocative, which stands among the cases and outside the sentence. The call belongs to the catalogue as its threshold.

Read with the loom, the call is the only gesture that occupies the three strata with equal intensity. It is Flesh, because it demands the whole air of the lungs and the whole body behind the voice, as the Swedish herdswoman knows when she sends her kulning across a valley. It is Inclination, because the leap of a fourth or a fifth is the instant in which the voice leans toward the one it calls, the rhopé of the balance turned into an interval. And it is Toward in its pure state, because the held note stays in the air waiting, and that waiting is already the time of the answer. A call without an answer is still a call, and for that reason it comes before the conversation it founds. From it come call and response, form 12, the period of antecedent and consequent, procedure 45, which is the call interiorised, and recipe R7, which turns it into daily exercise. The school of song and arm measured everything by whether the line sings. The call adds to that measure its precondition. A line sings when it is addressed to someone.

A possible lesson

Imagine a fifteen-year-old student who brings “Träumerei”, the seventh of Schumann’s Kinderszenen. She plays it well. The fingers are in place, the pedal clean, the tempo reasonable, and the piece sounds the way it almost always sounds in conservatoires, like a lullaby that has fallen asleep, a lukewarm surface with nobody inside. The opening is an upbeat on C that rises a fourth to F, and in her hands that fourth does not exist. It is one more step, like the ones that come after it.

The teacher could correct her, ask for more weight on the F, point to the hairpin. A possible lesson does something else. It asks her to go out into the corridor, to walk to the far end, and from there to call by name a classmate waiting in the room, without shouting, the way one calls someone in from the fields for supper. The student laughs, is a little embarrassed, and calls. And in the call something happens that no remark about the score would have produced. Her voice starts on a comfortable low note, leaps upward on the stressed syllable of the name and stays there, held, lengthened, waiting. She comes back into the room without yet knowing what she has done.

Then the teacher asks her to sing the first two notes of “Träumerei” as she has just sung that name, addressed to someone far away. The C is the intake of breath and the start, the F is the syllable that rises and holds. She sings it once, shyly, then again with more air, and by the third time the fourth has become a call, G2, and the arpeggio that afterwards climbs to the high F stops being a figure for the right hand and becomes the voice still seeking the one it has called. Then she conducts the phrase with her arm, recipe R1, and the arm discovers by itself that the F needs to fall with the full weight of the shoulder and stay, which is Flesh, that the rise is an inclination toward someone, which is rhopé, and that the whole phrase lives in the expectation of an answer, which is Toward. Only at the end does she return to the piano. The first note is the same, the F is the same, the fingering has not changed. Yet now the piece speaks to someone, and what sounded like a dream without a dreamer sounds like what Schumann put in the title, a reverie, which is always someone’s reverie and turned toward someone. Call, song, gesture, sound, in that order and in twenty minutes. Nobody has told the student that music is vocative. She has discovered it in the corridor.

A. Gestures of song. The voice

G1. The breath before sound. The audible intake, the preparatory silence, the zero gesture from which all the others depart, pure Flesh before the threads separate. Flamenco knows it as the temple, the wordless “ay” with which the cantaor tempers the voice and settles the mode before the first syllable, and every conductor’s upbeat is its translation into the arm. It lives in every tradition that sings, in cantillation, in flamenco, in the operatic attacca, in the entry of the jazz singer, and flamenco also has names for the other two positions of the arc, the llamada, which opens or summons, and the remate, which closes. It is heard in the temple of a soleá, in the silence the pianist holds before the singer’s first note in a Lied, in the raised bow before the first note of a quartet.

G2. The call. A rising leap, usually of a fourth or a fifth, to a held high note, projected to be heard at a distance. It is the oldest shape of melody and the ancestor of the fanfare, the theme, the hook, and the first in dignity of the whole catalogue, for the reasons I have just set out. It lives in herding calls, such as the Swedish kulning, in the adhān, in street cries, in the yodel, in the bugle, in the gospel shout. It is heard in the opening of Mahler’s Third, in the pregón that opens a rumba, in the horn fifths of every hunting call.

G3. The cry and the lament. The voice breaking under weight. The ululation, the dirge, the quejío, the held high note that cracks and falls. Its cultivated descendants are the pianto, the descending minor second of Renaissance and Baroque grief, and the chromatic descent of the lament bass. It lives in Irish keening, in the Greek moirológia, in flamenco, in the Romanian doina, in the blues moan, in Monteverdi’s Lamento della ninfa, in Purcell’s Dido. It is heard in the “ay” of a siguiriya, in the passus duriusculus, in the descending fourth in the bass of “When I am laid in earth”.

G4. The sigh. A two-note fall, strong to weak, with the weight on the first, the appoggiatura, the Seufzer, the leaning note. It is the smallest expressive gesture in Western music and the most frequent, and it is the Inclination of the loom reduced to its least expression, a weight yielding toward the next note. It lives wherever a voice leans into a note and lets it go, in Mozart’s slow movements, in the Mannheim “sigh”, in the slide of the gamaka into the pitch. It is heard in the opening of the Adagio of Mozart’s K 488, in the appoggiaturas of any Bellini cavatina, in the slur that falls onto the final note of a cante.

G5. The swell. A single tone that grows and fades, the messa di voce, the foundation of bel canto teaching and of every dynamic hairpin we argue about. In the body it is the arm opening and closing. It lives in the Italian schools, in the single tone of the shakuhachi, in the long note of the dhrupad singer that grows and fades, in the brass chorale. It is heard in the long notes of “Casta diva”, in the prelude to Lohengrin, which is a swell four minutes long, in any note sung on one breath to its end.

G6. The held tone. The voice become a floor for other voices, the tenor of the psalm tone, the ison of Byzantine chant, the bass of the Sardinian tenores, the tanpura. A gesture of not moving that makes all the others audible, because upon it harmonía becomes literal and every sound that moves above it is measured by its gravitation toward what remains. It lives in drone traditions everywhere, in the bagpipe, in the hurdy-gurdy, in the organ pedal. It is heard in the isokratima beneath a Byzantine hymn, in the tonic pedal of the first bars of Das Rheingold, in the dastgāh singer’s return to the shāhed.

G7. The melisma. Many notes on one syllable. The voice leaving the word to travel on its own breath. It lives in the Gregorian jubilus on “alleluia”, in Qur’anic tajwīd, in the gamaka, in gospel runs, in flamenco, in the doina, in the Persian tahrir. It is heard in the “alleluia” of any gradual, in the cadenza of a Handel aria, in the “ay” that opens a malagueña.

G8. The cantillation. One note per syllable, the melody led by the text, elastic in length and almost without ornament, the opposite of the melisma and its partner. It lives in the cantillation of the Torah, in psalmody, in Vedic recitation, in the epic line of the guslar, in the romance sung to a formula, in rap. It is heard in a psalm tone, in the Evangelist of a Bach Passion, in the blind singer’s romance de ciego.

G9. The rock. The lullaby’s rocking inside the voice, a narrow range, a third or a fourth that swings, a slow pulse in two, soft and descending. The data of Mehr and his colleagues place the lullaby among the song types that listeners from very different cultures recognise most accurately from their sound features alone. It is also the first melody almost all of us hear, and the first call we receive, because every lullaby is addressed to someone who does not yet know how to answer. It lives in every cradle. It is heard in the “Nana” of Falla’s Siete canciones populares españolas, in Brahms’s “Wiegenlied”, in the Basque lo, lo, which is at once word and rocking.

B. Gestures of dance. The body

This whole group descends from the pair we have already seen, the lifting and the setting down of the foot, and each of the categories that follow is a way of lifting and setting down, of transferring the weight, holding it, throwing it, striking with it, leaving the ground or refusing to move. Metrical theory inherited the pair and forgot the feet. The lesson gives them back. Émile Jaques-Dalcroze built an entire pedagogy on that restitution, and research on his eurhythmics, read precisely through Merleau-Ponty’s phenomenology of the body, describes bodily movement as a way of knowing music that comes before any illustration of it. Marja-Leena Juntunen and Leena Hyvönen showed how, in eurhythmics lessons, the student understands in movement what the student could not yet put into words, and how that embodied knowing precedes conceptualisation and makes it possible. The foot knows before the head, and in the order of the call this has a name, gesture comes before sound.

G10. The step. Weight transferred from one foot to the other at walking pace, the procession, the march, the pavane, the paso, the walking bass, the andante, “going”. It is the gesture beneath almost all music in duple metre, and the Flesh of rhythmós in its plainest form. It lives in processions, funerals, weddings and armies, in the pasodoble, in the passacaglia, in the “passing along the street”. It is heard in the funeral march of the Eroica, in the bass of a Bach gavotte, in the tread of a Holy Week processional march.

G11. The sway. Weight moving from side to side without leaving the ground, the barcarolle, the siciliana, the habanera, the lilt of 6/8 and 12/8. The rocking of the lullaby settled in the hips, an inclination that always returns to its centre. It lives in boats and cradles, in the left hand of a Chopin nocturne, in the cunita of the tango. It is heard in the accompaniment of Chopin’s Nocturne op. 9 no. 2, in the “Barcarolle” from Les Contes d’Hoffmann, in a siciliana by Scarlatti.

G12. The swing. The pendulum with a push. The jig, the tarantella, the jota, the swung quaver, the upbeat that throws the weight forward. Where the sway stays, the swing goes, and the difference between them is exactly the one that separates an inclination that returns from an inclination that turns into Toward. It lives in 6/8 dances everywhere, in the Irish jig, in the tarantella, in the muiñeira, in the jota, in jazz swing. It is heard in the gigue of Bach’s French Suite no. 5, in the “Tarantella napoletana”, in any Basie shout chorus.

G13. The stamp. The foot that strikes the ground, the accent as a bodily event. Its instrumental relatives are the sforzando, the golpe, the pesante, the martellato. It lives in the zapateado, in the heelwork of the verbunkos, in the accent of the Basque zortziko, in the bourrée, in Beethoven’s sforzando. It is heard in the golpe on the top of the flamenco guitar, in the stamping of Stravinsky’s “Danses des adolescentes”, in the accent of a csárdás.

G14. The leap and the fall. Leaving the ground and landing. The saltarello, the octave leap, the caída of flamenco dance. Melodically, the upward leap followed by stepwise descent is one of the most common phrase shapes on earth, and it is the call that, instead of staying held and waiting, descends to seek its own answer. It lives in leaping dances, in the saltarello, in the Highland fling, in the leaps of the Basque aurresku, in the arched vocal phrase. It is heard in the opening leap of “Over the Rainbow”, in the saltarello finale of Mendelssohn’s “Italian”, in the rise and fall of a jota copla.

G15. The spin. The body turning on itself. The turn of the waltz, the sema of the dervishes, the trill as a spin in miniature, the whirl of a fast finale. It lives in couple dances and whirling rituals, in the Baroque circulatio, in the Viennese waltz. It is heard in the Mevlevi ayin, in the circulatio figures of Baroque rhetoric, a word that is Kircher’s, in the chains of trills that bring back the theme in Chopin’s Nocturne op. 62 no. 1.

G16. The run. The flight. The scale passage, the presto, the jhālā, the fugue, whose name means flight, the chase, the hands of the toccata running one after the other. It is the Toward of rhythmós unleashed, direction that no longer stops to incline. It lives in finales, in tarantelle, in the jhālā of a raga, in the carrerilla of the bailaora, in the bebop line. It is heard in the last movement of Chopin’s Sonata in B flat minor, in a jhālā by Ravi Shankar, in the final pages of a Bach toccata.

G17. The stillness. Not moving as a gesture. The held pose, the ma of the Japanese arts, the fermata, the general pause, the tenuto, the silence after the last chord. The body remains engaged, and that distinguishes stillness from stopping, because in stillness the Flesh goes on weighing and the Toward stays stretched out even though nothing sounds. It lives in nō, in the remate of flamenco dance, in the Classical general pause, in the sustained final chord. It is heard in the silences between the last pizzicato chords of the Coriolan Overture, in the last bar of Winterreise, in the dancer’s stop on the tenth beat of the compás, which the body carries on to twelve.

The dance gestures run on a small number of rhythmic grounds that recur across the world and belong to this lens before they belong to the forms, the perennial metres and timelines. There is the plain pulse in two and in three. There is the tresillo, 3+3+2, which is the habanera, the tango, the son and half of West Africa. There is the sesquiáltera, 6/8 against 3/4, which is the jota, the huapango, the joropo, the chacona and the zarabanda. There are the aksak or limping metres, 2+3, 2+2+3, 2+2+2+3, with the Bulgarian râchenitsa in 7, the kopanitsa in 11, the Turkish karşılama in 9 and the Greek kalamatianós in 7. There are the twelve-pulse bell pattern of West Africa and the Cuban clave, timelines against which everything else is measured.

Then come the long cycles, the Hindustani tāla, with the 16 of tintāl, the 10 of jhaptāl and the 7 of rūpak, the Arabic īqāʿ, with maqsūm and samāʿī thaqīl, the flamenco compás of twelve with its accents on 3, 6, 8, 10 and 12, the Javanese gongan. And there is the free rhythm of the doina, of the ālāp, of the taqsīm, of plainchant, where the pulse stays alive as breathing, the body that has stopped walking and breathes. A student who can walk, clap or rock each of these grounds possesses more of the world’s rhythm than any treatise can give.

C. Gestures of poetry. The breath and the word

The Greek word for accent was prosōidía (προσῳδία), “the song sung alongside” speech. Poetry was never added to music. It was the same gesture heard as words, the léxis of the loom in its most recognisable form, the saying that still keeps its breath.

G18. The line. The line of verse as a unit of breath and therefore of phrase, the octosyllable of the romance, the hendecasyllable, the alexandrine, the tercio of the cante, the Arabic bayt. The length of a melodic phrase is usually the length of a line in disguise, because both measure the same thing, how long the air in the chest lasts. It is heard in the octosyllables beneath any romance melody and in the four-bar phrase, which is the hendecasyllable of music.

G19. The caesura. The cut within the line. The hemistich, the comma, the breath mark, Koch’s Einschnitt. The place where the line breathes without ending, an inclination that pauses for an instant without falling. It is heard in the breath between “Freude, schöner Götterfunken” and “Tochter aus Elysium”, and in the comma that splits a seguidilla.

G20. The foot. The smallest rhythmic cell of verse, iamb, trochee, dactyl, anapaest, spondee. The medieval rhythmic modes were these feet under other names, the first mode trochaic, the second iambic, the third dactylic, and the Arabic ʿarūḍ and the Sanskrit chandas are their cousins. A rhythmic motive is a foot that has forgotten its words. It is heard in the first rhythmic mode, the trochaic, of a Notre-Dame clausula, in the dactyls of the Allegretto of Beethoven’s Seventh, in the anapaests of a tarantella.

G21. The rhyme and the refrain. The return of a sound as a promise kept. Rhyme is cadence in words, the refrain is rhyme at the scale of the stanza, and the ritornello and the hook descend from it. Every rhyme opens a Toward, because from the first line the ear awaits the return. It is heard in the vuelta of a villancico that comes back to the rhyme of the estribillo, and in the chorus of any song.

G22. The accent. The stressed syllable as strong beat, the ictus, and a rule that every language keeps. A line ending on a stressed syllable, aguda, produces a masculine cadence, and one ending on an unstressed syllable, llana, a feminine cadence. Half of phrasing consists in knowing which of the two a melody wants, whether the fall of the weight coincides with the end or leans one syllable further still. It is heard in the feminine endings of a Chopin mazurka, in the masculine endings of a march, in the Italian verso tronco under a final cadence.

G23. The stanza. The stanza as the seed of form, the quatrain, the copla, the seguidilla in 7-5-7-5, the redondilla, the couplets of the ghazal, the stanza of the Minnesang that gave the Bar form its Stollen and its Abgesang. Here gesture settles into sediment and the catalogue of forms begins. It is heard in the AAB of a Minnesinger stanza and in the four-line copla beneath a jota.

G24. The declamation curve. The intonation of a sentence. Rising for the question, falling for the statement, the arch of the exclamation, the flat line of the list. Janáček transcribed these curves from speech overheard in passing and called them nápěvky mluvy, Mussorgsky built his recitative from them, and the Greek rhapsode and the Andalusian cantaor never needed to transcribe them. Among all these curves, the curve of the call is the one that escapes speech and becomes song, and that is why G24 and G2 are the two banks of a single border. It is heard in the question and answer of an antecedent and a consequent, in the speech melody of Jenůfa, in the way a saeta follows the sentence of its text.

D. The words of performance as a gestural lexicon

The vocabulary we already use at the instrument is a catalogue of gestures that nobody taught us to read as such. Appoggiatura comes from appoggiare, to lean, acciaccatura from acciaccare, to crush, mordente from mordere, to bite, portamento from portare, to carry, glissando is sliding, legato bound, staccato detached, tenuto held, sforzato forced, rubato stolen, sospirando sighing, martellato hammered, tremolo trembling, vibrato shaken, slancio a surge, scorrevole flowing, pesante heavy, leggiero light, stringendo tightening, allargando broadening, morendo dying, calando falling, crescendo growing, attacca attack. Every one of them is a verb of the body.

And each has its stratum in the loom. Pesante, tenuto, leggiero and martellato speak of the Flesh, of how much the sound weighs and how it settles. Portamento, slancio, stringendo, scorrevole and attacca speak of the Toward, of where the sound is going and in what haste. And the appoggiatura, with sospirando, calando and morendo, speaks of the Inclination. The appoggiatura read as “lean” is exactly the Inclination of the loom, rhopé written into a score, the instant in which the weight of one note yields toward the next and the balance dips. A student who reads “appoggiatura” as lean, instead of reading it as ornament, has already changed the way that note will sound, because the student has stopped adding something to it and has begun to let the weight of the arm fall upon it.

VI. Perennial forms. Archetypal ordering formulas

These forms recur in the learned traditions, in folk musics, in ritual chants, in jazz standards, in urban popular song and in the ceremonial or functional musics of the whole world. By a form I mean an archetypal ordering formula, the slots and their order, the paradigm with its cells still empty. What this chapter catalogues are ways of disposing time that the body recognises before it knows how to name them, and their governing word, which will be grounded further on with all its philological weight, is rhythmós (ῥυθμός), the form of what flows.

Form and genre

A word I used loosely a few pages back has to be tightened here, when I said that music had baptised three genres after the three lenses. Toccata, ricercar and sonata belong to another order than the lullaby, the Mass or reggaeton, and the distance between the one and the other is measured in order and never in degree.

A form is a mode of internal ordering. It is said of the work from within, and it names the rule by which the time of that work is disposed, in the Kantian sense I have already cited, the procedure that gives the concept its image. A genre is a mode of external classification. It is said of the work in its relation to everything around it, its function, its occasion, its social destination, its place, its performers, its public, its market and its name. Form answers the question of how this thing is made. Genre answers four others, what for, for whom, where and under what name. Almost everything else follows from this.

Form is exercised and genre is predicated. A piece has its form even if nobody names it. A child’s song is AAB before the word Bar exists, and it would go on being so if the word were lost. Nothing, on the other hand, becomes a nocturne, a motet or a bulería until a tradition calls it so. Form is a fact of constitution, genre a fact of naming and of use. That is why forms are discovered and genres are founded.

A possible lesson teaches this better than any definition. Picture a girl of seven, perched on the edge of the piano bench, whom nobody has yet told what a form is. The teacher asks her to sing something about what she saw on her way in, a dog waiting in a doorway. The girl invents a four-bar phrase that rises a fourth, lingers an instant on the high note and comes down without quite ending, “the dog was waiting at the door of the bar”. Because she likes the phrase she repeats it, now with other words, “the door had a pane of glass”, and in the repetition the voice already knows where it is going, it leans with more weight on the high note, it breathes earlier in the same place. Then something happens that nobody has asked of her. The third phrase comes out different and longer, it begins higher, descends by step for six bars and settles on the note it set out from, “and nobody came out for him”. The girl laughs, because she has felt that it was over. The teacher still says no technical word. She asks her to sing it again standing up, marking with her hand where she breathes, and the girl’s hand draws two equal arches and a third that stretches out and falls. Then she asks her to find it at the piano, with a single finger, and the third phrase costs her more because it is the one that does not repeat. Only at the end, when the song is already in the body and in the key, does the teacher write on a card two German words that come from the Mastersingers of Nuremberg, Stollen and Abgesang, the two equal feet of the stanza and the song that moves away, and tell her that Wagner gave a whole scene to teaching a young man to do what she has just done without anyone’s leave. The form was exercised before it was named. The name came to gather what the voice had already ordered, in the order this grammar defends, sing first, keyboard second, paper last.

Form exists distributively and genre attributively. A form is whole in each piece that realises it and nowhere outside them. A genre is a historical totality whose parts are joined by real relations, transmission, imitation, commission, market, canon, school, and none of its pieces contains it whole.

The criterion of identity differs in each case. A form is identical with itself by invariance, it is what survives a group of transformations, according to the definition I took from Klein. A genre is identical with itself by continuity, by a chain of works that quote, imitate and correct one another, and by a name that is inherited. The first is geometry, the second genealogy.

And that is why their temporality differs. Genres have a date of birth, a map and often an obituary, the madrigal, opera seria, ragtime. Forms have no birth, and what they do is recur. This whole chapter is staked on that claim.

The two categories are, moreover, independent of each other, as one sees the moment one crosses them. A single form serves many genres. The refrain principle is the finale of a concerto, a Marian cantiga, a children’s song and a rap track. A single genre admits many forms. The tango can be strophic, ternary or verse and refrain without ceasing for a single bar to be tango. If the one and the other were the same kind of thing, such crossings would be impossible.

Hence the error that the catalogue below avoids. The manuals call the sonata a form, and the sonata is a genre that crystallised a form. They call the fugue a form, and the fugue belongs wholly to another lens, that of procedure, imitation upon a subject whose unfolding produces a different piece each time. That is why nobody has ever managed to draw its scheme without lying. They call the concerto a form, and the concerto is at once a genre, a work for soloist and ensemble, a form, the ritornello, and an institution, a place on the programme and in the market. That confusion goes beyond lexical carelessness. It records a real fact, namely that genres form by sedimentation around forms and procedures, and end by lending them their name. Genre is the sediment, form what was sedimented.

And from there, at last, the pedagogical consequence, which makes this distinction something far more serious than a luxury. Genre is the ab extra category par excellence. It names the piece from outside, from the side of whoever consumes it, programmes it, catalogues it or sells it. The three lenses of this essay are ab intra, and that is why genre is missing from among them, quite deliberately. Nobody can be taught to make a genre. One can be taught to make forms, with procedures, starting from gestures. Genre is what the world decides to call the result. A curriculum made of genres and styles teaches the part of music the student cannot make.

None of this degrades genre. It is as real as a guild, and its reality is of the same kind. Genre brings with it the horizon of expectation without which there would be no surprise, no irony and no parody, it brings the tacit contract between the one who plays and the one who listens, it brings éthos, occasion and decorum, almost everything that makes a music mean something to someone in some place. I only say where it lives. If forms are the language and styles its dialects, genres are its speech situations, the places where one is required to speak in a certain way. They are learned by going to them, and a grammar, which is what these pages are building, concerns itself with the language.

Table 2. Form and genre. The six criteria by which I separate the two categories, preceded by the place from which each is said. One column holds what the work exercises from within, the other what the world predicates of it from without, and that is why crossings between them are possible.

Criterion	Form	Genre
Where it is said from	From inside the work, as a mode of internal ordering. It answers how this is made	From outside, as a mode of external classification. It answers what for, for whom, where and under what name
Exercised or predicated	Exercised. A child’s song is AAB before the word Bar exists	Predicated. Nothing becomes a nocturne, a motet or a bulería until a tradition calls it so
Constitution or naming	A fact of constitution. Forms are discovered	A fact of naming and of use. Genres are founded
Distributive or attributive	Whole in every piece that realises it and nowhere outside them	A historical totality bound by transmission, imitation, commission, market, canon and school, which no single piece contains whole
Invariance or continuity	Identical with itself by invariance, what survives a group of transformations. Geometry	Identical with itself by continuity, a chain of works and an inherited name. Genealogy
Temporality	It has no birth and it recurs	It has a birth date, a map and often an obituary, the madrigal, opera seria, ragtime
Ab intra or ab extra	Ab intra, like the three lenses. One can be taught to make it	Ab extra par excellence. It is what the world decides to call the result, and nobody can be taught to make one

Form or institution

Against the word form there stands a serious objection, and a Spanish one, and it has to be met here and outside any note. From the philosophical materialism of Gustavo Bueno, and above all in the philosophy of music that this school has developed, the course Bueno gave in Oviedo in 2007, and later Vicente Chuliá’s Manual of 2018 and his Tratado of 2022, the category of musical form looks suspect of idealism, and in its place the proposal is to treat the sonata, the fugue, the motet or the concerto as musical institutions, whose essence is analysed with the theory of generic essence, nucleus, body and course. The objection has two edges, and both of them cut.

The first is that form imports a visual model into music. Morphé (μορφή) is figure, silhouette, the outline of something that stands there before us and can be taken in at a glance. Yet a piece of music is a totality whose parts are never given simul sumptae, all together at once. When the last bar sounds, the first exists only in memory. To speak of the form of a sonata as one speaks of the form of a vase is to spatialise what exists only by happening. In the vocabulary of that school, music is a joreomatic totality, and the adjective does precisely that work.

The second edge is historical. The classical sonata form was never a mould waiting for someone to fill it. It was a late product, recomposed out of earlier materials, the rounded binary, the ritornello of the concerto, the galant schemata, the habit of recapitulation, and consolidated, as an institution with a name and a doctrine, in treatises that arrived after the works they claimed to describe. What really exists are pieces, performers, orchestras, publishers, professorships, programmes and manuals, a body of realisations and a historical course around a nucleus of relations. That has an exact name, and the name is institution.

Does this align with what I hold here? Only in part, and one can say in which part, because the agreement is greater than it seems and the disagreement cleaner than it seems.

I agree with everything the objection denies. Heaven holds no moulds. I have already written that a form was never a container into which a piece is poured, that archétypon is the first impress and in no case a figure laid up on high, and that form is only the trace left behind when a given doing has completed a given becoming. I renounced universals imposed from above before beginning the catalogue, and I say of the sonata, in its own entry, that it is the only one that lacks any cross-cultural title. When I affirm that the sonata stands outside the perennial forms and that school affirms that the sonata is an institution, we are saying the same thing in two vocabularies. The critique, carried to its proper end, leaves musical forms standing and concludes something finer, that the sonata was never one of them.

I agree too with the argument from non-simultaneity, and I believe moreover that it favours me. It withdraws morphé and confirms rhythmós. The word that governs this catalogue leaves figure and silhouette behind and takes up the one Benveniste rescued from the pre-Socratics, the form of what moves, in the instant in which the moving thing assumes it. A form that does without simultaneity, that escapes the glance, that exists only while something is taking it on, is exactly what is needed here, and it is the reason why the epithet of this lens is the contour of becoming and never the contour pure and simple. Against form understood as a vase, the objection is decisive. Against form understood as rhythmós, it finds nothing to bite on.

Where I part company is over the extension of the concept. Institution is a magnificent category, and it is the exact category for the sonata, the fugue, the Mass, the concerto and the recital, for everything that someone founded, someone named, someone taught and someone preserves. What this chapter catalogues, however, lies beyond its reach. Nobody founded the rocking of the lullaby on a descending third. Nobody legislated that a refrain should come back, or convened the congress at which it was decided that a line stated twice should be followed by a third that differs. There are no professorships of AAB and no market in call and response. And yet they recur, and they recur where there was never any contact. An institution explains the sonata. It leaves unexplained why a Bulgarian mother and a Japanese mother rock their children on a descending third. If every musical ordering were an institution, the resemblances in this catalogue would be diffusions to be documented one by one, or mirages of the observer. And there are empirical reasons, those of Savage and those of Mehr, for thinking they are something other than either. Institution is a category historically fertile and comparatively sterile. I need one that admits, as Owen wished, both homology and analogy.

And I part company too over the direction of the concept, which is the deeper difference. Institution is, by construction, an ab extra category. It names music from the side of objective culture, of the social body that sustains it, of the norm that is handed on. It is, in the vocabulary I have just fixed, the fine theory of genre, and form falls outside its jurisdiction. What I need from the word form is the opposite, the view from inside the one who makes, the schema in the Kantian sense, the rule that generates the image, what remains invariant under a group of operations. A sociology of music needs institutions. A grammar of making needs forms. The two live side by side without competing. They describe the same thing from its two sides, and this book is written from only one of them.

The practical consequence is the usual one. One enters an institution, one exercises a form. A student can be taught to make a form in an afternoon, and in a whole lifetime nobody will manage to teach that student to make an institution, because that never depends on the student. If the sonata is an institution, and it is, then a sonata class is a corporate initiation. If the rotational principle is a form, and it is, then it is a capacity. This book is about capacities.

I concede, all the same, one thing that the objection obliges me to say better. What recurs lacks the standing of a thing. When I say perennial I deny that there exists an object called “refrain form” subsisting above its cases. I affirm a fact of recurrence, and that fact calls for a material explanation, never for an entity. The explanation is close at hand and it is humble. Breath lasts as long as it lasts, and that is why there are lines of verse. Memory runs forward, and that is why there is repetition and no retrograde. Bodies walk in twos, and that is why there is duple metre. A taut string gives octave, fifth and fourth before anything else. There are two hands, and there is one who sings and one who answers. Forms recur because bodies and materials are the same. The science of comparative song has begun to measure that humility. When people from widely separated cultures are asked to reproduce a random rhythm, and then to reproduce their own reproduction, and so on several times over, the rhythms drift towards ratios of small whole numbers, one to one, one to two, two to one, which is to say that memory and the body pull time towards the step and the double step, though each culture weights differently the ratios it tends towards. And when listeners from all over the world hear short excerpts of songs from eighty-six societies, they recognise above chance whether they serve to rock a child, to dance or to heal, without understanding a word, because function has left its trace in form. That is a materialism, and being one does not trouble me.

So I keep the word. I annex it, and I give it its place. Gesture, procedure, form, institution. A movement of the body sediments into an operation, the operation repeated until it becomes a habit of listening sediments into a form, the form named, taught, programmed and defended sediments into an institution. It is a single arc, and it runs from the diaphragm to the conservatory. My complaint against the inherited classical lesson then fits in one sentence, that it begins with the fourth term. And Latin has the irony ready, because instituere means at once to found and to teach, and Quintilian’s Institutio oratoria was a treatise on education, so that the word holds at once what I write against and what I do. A conservatory used to conserve children. An institution instituted students. Names know what they are doing, it is we who forget it.

Figure 5. From the diaphragm to the conservatory. Gesture, procedure, form and institution trace a single arc, and each term is the previous one sedimented. The three lenses read the first three from within, the institution is named from without, and the inherited classical class begins with the fourth term.

The words of form

Táxis (τάξις) is the cleanest Greek term for ordering, typos (τύπος) is the stamp or the mould, parádeigma (παράδειγμα) is the model the craftsman looks at in the Timaeus, and in grammar the paradigm is the inflection table, a formula with empty cells, which is exactly what AAB or ABACA are. Schêma (σχῆμα) is the word the trade already uses, by way of Gjerdingen. Diáthesis and oikonomía name the arrangement and the internal economy of a work, and sýstema, in Greek harmonic theory, is the stacking of tetrachords, an ordering formula for the modes. Latin adds formula, the diminutive of forma, a fixed pattern in law and in rite, clausula, for cadential formulas, modulus, the common root of mould, model and module, matrix, the matrix, the womb. And harmonía, in Homer, still designates the joint that fastens the timbers of Odysseus’s raft, long before anyone heard it as a chord.

But the word that governs this whole catalogue is rhythmós. Benveniste showed that in the pre-Socratics it meant something very different from what we call rhythm. The word comes from rhéō (ῥέω), to flow, and school etymology wanted to see in it the to and fro of the waves. Benveniste showed that the waves never appear in the texts, and that what appears is form. When Aristotle sums up Leucippus and Democritus, he says that atoms differ in three things, rhysmós, diathigé and tropé, and he at once translates them into his own vocabulary, the rhysmós is the schêma, the diathigé is the táxis, the tropé is the thésis. In a single line of the Metaphysics there stand, stitched by the same needle, the word that names this lens and the word that governs it. Yet rhythmós is set apart from schêma by one decisive trait. Schêma is fixed form, set there like an object, and rhythmós is form in the instant in which what moves assumes it, the mobile, the fluid, the form of what lacks organic consistency, the disposition of a humour, the bearing of a body passing by, the figure of a letter as it is traced. It was Plato who narrowed the word towards our sense, when in the Laws he called rhythm the order of movement, kinḗseōs táxis (κινήσεως τάξις). And in that definition, which Benveniste reads as the moment when rhythm becomes number and the measure of the dancing body, táxis appears once more. Rhythm is the táxis of movement, and táxis, when it moves, is called rhythm. That is why these forms are figures that hold sound without fixing it, the contour of becoming.

Around it gathers a small family of thinkers who said the same thing in other words. Goethe preferred Bildung to Gestalt because Gestalt abstracts from motion and fixes what is only a moment, whereas Bildung names at once the product and the producing. Pareyson called art formatività, a doing that, while it does, invents its own way of doing. Simondon replaced the imposition of form upon matter, the old hylomorphism, with a prise de forme, a taking of form that emerges from the operation itself, as the brick takes form in the mould because clay and mould adjust to each other in one and the same operation of energy, and that is what I mean by forms that exist only in the instant of their becoming. And Benjamin’s constellation is the figure of a universal that is a configuration and never a mould, ideas are to phenomena as constellations are to stars, which is exactly what I mean by patterns that stubbornly re-emerge in place of universals imposed from above.

Form on the loom

That crossing between Benveniste and the lens of form has a precise place on the loom of melos that chapter II unfolds from its root. Let me recall the essentials. Melos, which in Greek is at once a limb of the body and song, is woven from three vertical threads, léxis (λέξις), the saying that calls before it says anything, harmonía (ἁρμονία), the fitting together and the gravitation of sounds that sound together and draw one another, and rhythmós (ῥυθμός), the form of what flows, the pulse, the stride, the heartbeat, the breath, the dance. Those three threads are crossed by three horizontal strata, the Flesh, which is the face, the breath and the weight, the gifts nobody chooses, the Inclination, which is the instant in which something yields towards something, the rhopé (ῥοπή) of the scales, the appoggiatura that leans, and the Toward, which is direction, continuity, pulse as pure futurity. Nine crossings, nine cells. Now it becomes visible that the thread of rhythm and the lens of form are the same word seen from two sides. Benveniste’s rhythmós, form in the instant in which the mobile assumes it, is literally the name of the thread, and the lens of form is the way of travelling through the fabric along that thread from bottom to top.

That journey passes through the three strata. In the Flesh, the thread of rhythm is the length of the breath and the cadence of the feet, and from there comes the material explanation of recurrence I have just given, lines last as long as an exhalation, duple metre is the stride. In the Inclination, the thread of rhythm is the place in the phrase where something yields, the caesura, the mid-cadence, the feminine ending that leans and lets itself fall, and there live the mediatio of the psalm tone and the hinge of every binary. Form does its chief work, though, in the stratum of the Toward. A form is a promise about what is to come. The refrain is an expected return, the new verse is an expectation fulfilled in another way, the Abgesang is the direction the stanza takes once it has spent its two equal feet, jo-ha-kyū is the whole futurity of a piece disposed as acceleration. If gesture is the lens that reads the Flesh and the Inclination, the instant in which the body rises and leans, form is the lens that reads the Toward, and it reads it with the name of the third thread. The cell where rhythm crosses the Toward is its home.

The other two threads pass through that home as well. Léxis crosses the Toward in the text-driven forms, where it is the saying that disposes time, and in responsorial form, which is what the call engenders when someone answers it, so that the founding gesture of this essay, the call, has its direct descendants in the catalogue of forms. Harmonía crosses the Toward in cadential plans and in ostinato cycles, in the chaconne bass that comes round again and in the bridge that strays harmonically in order to return. What the catalogue orders, then, are ways of knotting the Toward, and the thread that gives all of them their name is rhythm.

Scales, families and ways of standing

The catalogue mixes three scales, and each has to be named for what it is, typos for types of whole piece, such as the rondo, the arch or the sonata, schêma for phrase-level models, such as the Prinner, the sentence or the twelve-bar blues, formula or clausula for cadences and recitation patterns, such as the psalm tone or the clausula cantizans.

It also contains two families, and German theory names the split the catalogue in fact contains. Reihungsform, form by stringing together, gathers the strophic forms, the rondo, variations, the additive and cyclic forms, the vast majority of the world’s music. Entwicklungsform, form by development, is essentially the sonata. The first is what humanity does. The second is a local and magnificent specialisation.

There are, besides, four ways in which a piece may stand towards its archetype, and all of them start from the fact that a form was never a container into which a piece is poured. Hepokoski and Darcy’s terms serve anywhere, rotation, the cyclic return through a referential ordering, which is the principle shared by the strophe, the rondo, variations, ostinato and the pairing of exposition and recapitulation, the default, the archetype understood as a hierarchy of expectable options and never as a rule, deformation, the piece’s departure from it, and dialogic form, the piece heard as a conversation with the archetype and in no case as obedience to it. That default has the structure Eleanor Rosch found in the categories of ordinary speech, a centre of examples better than others, a bird that is more of a bird than the penguin, and an edge that fades by degrees, so that a piece belongs to a form as a sparrow belongs to the birds, more or less, and that gradation is what saves the word archetype. Caplin’s formal functions, beginning, middle, end, are the other useful abstraction, because what recurs across cultures are the functions and scarcely the letters.

When I say that Purcell’s ground and the Gnawa riff are relatives, I add together two claims that Richard Owen, when he coined the word archetype for the vertebrate skeleton in 1848, took care to keep apart, homology, likeness by common descent, and analogy, likeness by convergence. Some of the resemblances in this catalogue are homologies. The zéjel really did travel from Baghdad to Paris, and the Iberian pasacalle, the Italian passacaglia and the French passacaille really are a single word. Others are analogies. Nobody was taught to sing lullabies in descending thirds. The forms are relatives in both senses, and since it matters which, I try to say which.

The nearest thing to this catalogue in another art is Propp’s Morphology of the Folktale, thirty-one functions in invariant order, drawn from folk material, variable in their content. Focillon and Kubler add what I most want to keep. Forms have their own time, their families and their migrations, and that time runs in a different channel from the history of styles. Kubler spoke of formal sequences that stay open for centuries and resume when someone takes up the problem again, and Focillon of a life of forms that passes from the hand to the material and from the material to another hand. Each entry that follows carries its name, its scheme, its regions and traditions, its types of piece and its examples, and every one of them can be sung before it is read.

A. One-part forms. Monostrophic, unitary, continuous

1. AAA, strophic, single-idea. A single strophe or a single module is repeated as many times as the text has verses or for as long as the rite lasts. It is universal, and it is found in Europe, the Middle East, Africa, India, China and the Americas, in folk song, liturgical chant, romances and ballads, urban popular song and ritual incantations. Its types of piece are the hymn, the romance and the strophic song. It can be heard in Gregorian hymns such as Veni Creator Spiritus, in the psalm tones, in European ballads such as “Barbara Allen”, in the strophic structures of the blues and in Bob Dylan’s “Blowin’ in the Wind”.

2. Through-composed, or continuous. ABCDE… Here all repetition is absent, and the music unfolds like a story that moves forward without turning its head. It lives in Western art music, in many maqām genres and in the ālāp of the Indian raga, and it yields types of piece such as the art song, the symphonic poem and the music-drama scene. Its examples are Schubert’s “Erlkönig”, the Wagnerian scenes and the Hindustani ālāp as continuous elaboration.

B. Two-part forms

3. AB, simple binary. A and then B, one half that proposes and another that answers. It lives in Europe, the Middle East and Asia, in Baroque dance movements, in folk dances and in the pairing of verse and refrain. It can be heard in the Baroque allemande and courante, in the structure of the Irish reel and in modern verse and chorus songs.

4. AAB, or Bar form. Two equal Stollen, A and A, and a different Abgesang, B, which gathers what the feet have prepared and carries it to its end. Its name comes from medieval Germany, but the form is found all over the world, in Minnesang, among the Mastersingers and in folk song. The canonical example is Die Meistersinger von Nürnberg, whose third act shows Sachs teaching Walther to make a Bar out of his morning dream, Stollen, Stollen, Abgesang, a gesture turned into a form by a procedure, a composition lesson staged as an opera. In the English folk tradition many ballads come close to AAB, and it is the form that the girl in the lesson imagined above found without looking for it.

5. Rounded or circular binary. Two halves, each repeated, A repeated and then B with A′ repeated together. The second half moves away and comes back to the opening material, almost always shortened. It is the commonest small form in the Western repertoire and the seed of the minuet, the scherzo, the variation theme and, enlarged, the sonata. It is often loosely called ternary, and the name betrays it, because the return happens inside the second half and never as a third section. It lives in Baroque and Classical dances, in the themes of almost every set of variations and in countless folk tunes with a turn that comes home. It can be heard in the theme of Mozart’s K 331 and in the minuets of Haydn’s quartets, and the Aria of the Goldberg Variations is its simple binary cousin.

C. Three-part forms

6. ABA, ternary. A, B and A, with the return as a complete section. It is universal, and it lives in art music, in the minuet with trio, in the da capo aria and in some forms of the raga. It can be heard in Chopin’s nocturnes, in the Baroque da capo aria and in many Indian gat forms with a return.

7. ABC, successive contrast. Three sections, each of them new, and none of them coming back. It is universal, and it can be heard in some urban popular song, such as “Happiness Is a Warm Gun”, and in Romantic piano pieces in three sections, such as Mendelssohn’s Songs without Words.

D. Cyclic or refrain forms

8. Rondo. ABACA, ABACABA. A recurring refrain A alternates with contrasting episodes. It lives chiefly in Western art music, but also in refrain dances the world over. It can be heard in the finales of Beethoven’s sonatas op. 2 no. 2 and op. 13, and in urban popular song with a recurring hook and contrasting bridges.

9. Verse and refrain. AxAyAz… A stable refrain and changing verses, so that what returns is the music and what moves forward is the story. It lives in Europe, the Middle East and Africa, and in epic traditions. It can be heard in Neapolitan song and in flamenco cante with a recurring refrain.

E. Additive, modular, iterative forms

10. ABACAD…, rotating modules. Modules that rotate, frequent in oral cultures, where the piece grows by turns rather than by development. It lives in Africa, in the cyclic forms, in Asia, in minimalism and in electronic dance music. It can be heard in the sectional forms of the gamelan, the gendhing with merong and minggah, and in the drum cycles of West Africa with their recurring timeline pattern.

11. Theme and variations. A, A1, A2, A3 and so on, the same theme coming back each time transformed. It is global, and it lives in Europe, in India, in the Arabic taqsīm and in jazz choruses. It can be heard in the Goldberg Variations, in improvisation on a fixed bandish and in the successive choruses of jazz.

F. Call and response forms

12. Responsorial and antiphonal. Responsorial form sets a soloist against a chorus, with call A and response B, often in a cycle. Antiphonal form sets group against group, two choirs answering each other. It is the form that is born when the call, the first gesture of the voice, meets someone who answers, and that is why in it the thread of léxis orders the time of the whole community. It lives in Africa, in the African diaspora of the Americas, in Indigenous America and in the medieval and Renaissance liturgy of the West. Gospel call and response and the coro and pregón of the Cuban rumba are responsorial, and the Gregorian antiphons and the Venetian coro spezzato are antiphonal.

G. Forms over ostinato

13. Ground bass, chaconne, passacaglia. A bass that repeats and variations that rise above it. It lives in Europe, with analogous patterns all over the world. The names are Iberian and they remember their origin. The pasacalle is pasar la calle, to pass along the street, the guitarist’s ritornello between the verses of a song, an episode that was already walking the street before it became a form. It can be heard in Purcell’s lament for Dido, in Bach’s Chaconne in D minor and in the ostinatos of flamenco.

14. Loop forms, in pop and electronic music. Layers of a repeated loop over which a texture evolves. Today it is universal, and it can be heard in the loops of hip-hop and in the additive build-ups of electronic dance music.

H. Large-scale architectures

15. Sonata principle. Exposition, development, recapitulation. Two themes contrast, and a harmonic tension opens the distance that the return closes. It lives in Western art music, in Mozart, Beethoven and Brahms. It is the only entry in the catalogue that lacks any cross-cultural title. What is perennial in it is rotation, statement, departure and return, and the dependence of the development on the procedures, and that is why I keep it.

16. Arch form. ABCBA. A palindromic symmetry, in which the piece retraces its steps from a centre. It lives in modern art music and also in ritual musics. It can be heard in Bartók’s Fourth Quartet and in many ritual forms with a symmetrical sequence.

I. Forms of paired repetition and of refrain

17. Paired, or progressive, repetition. Aa bb cc dd… Each new idea is stated twice, often with an open and a closed ending, the ouvert and clos of the estampie, ancestors of our first and second time bars, and then abandoned for the next pair. It lives in the medieval sequence and lai, in the estampie and the ductia, and in many fiddle and pipe repertoires whose strains are played twice before passing to the next. It can be heard in Victimae paschali laudes, in the Dies irae, in the estampies of the Chansonnier du Roi and in the paired stanzas of folk ballads.

18. Ritornello form. R S₁ R′ S₂ R″ … R. A tutti refrain returns, often in different keys and shortened, between solo episodes. It is the Baroque parent of the rondo, and a principle older than either. It lives in the Baroque concerto and aria, in the Ottoman peşrev, with hane and teslim, where the teslim is the refrain, in the mukhṛā that comes back in a khyal after each excursion and in the refrain of the qawwālī. It can be heard in any fast movement by Vivaldi, in the ritornellos of the da capo aria and in the teslim of a peşrev by Tanburi Cemil Bey.

19. The zéjel family. AA bbb a AA, estribillo, mudanza and vuelta. A refrain, a stanza of three lines on a new rhyme, the mudanza, a turning line, the vuelta, which recovers the rhyme and the music of the refrain, and the refrain once more. It lives in the zéjel and the moaxaja of al-Andalus, in the Cantigas de Santa María, in the Castilian villancico, in the Italian ballata and lauda, in the French virelai and in the Galician-Portuguese cantiga de refram. It is a form that travelled from Baghdad to Córdoba, to Toledo, to Florence and to Paris, and the best argument I know for the migration of forms. It can be heard in a zéjel by Ibn Quzmān, in Cantiga 100, “Santa Maria, strela do dia”, in the villancicos of Encina, in the ballate of Landini and in the virelais of Machaut.

J. Cycles and preludes

20. The suite, or the ordered cycle. A succession of movements in fixed or customary order, almost always on one mode or key, and almost always ordered by a perennial logic, from the unmeasured to the measured, from slow to fast, from grave to light. It lives in the Andalusi nūba, with five mīzān in fixed rhythmic order in the Moroccan āla, in the Ottoman fasıl, with peşrev, beste, ağır semai, şarkı, yürük semai and saz semaisi, in the performance of the Persian dastgāh, with darāmad, the gūsheh and the forūd, in the Hindustani concert, with ālāp, jor and jhālā and then the gat in slow and fast tāla, in the Baroque suite, with allemande, courante, sarabande and gigue, in the Ordinary of the Mass, in the song cycle and in a DJ’s set. It can be heard in the nūba al-Māya, in a fasıl in makam Hicaz, in Bach’s partitas and in Winterreise.

21. The free-rhythm prelude. An unmeasured exploration of the mode, which precedes the measured music, establishes the world of pitches, the characteristic intervals and the register, and ends on the final. It lives in the ālāp, the taqsīm and the vocal layālī, in the Persian āvāz, the Turkish gazel, the Romanian doina, the Renaissance intonazione, tiento and toccata, the unmeasured prelude, the cadenza, the rubato “verse” that precedes the chorus in the American song and the flamenco temple. It can be heard in the unmeasured preludes of Louis Couperin, in a Hindustani ālāp in Yaman, in the taqsīm that opens a samāʿī and in the verse of “Stardust”.

22. The acceleration form. The same material or the same mode passes from free rhythm to a slow pulse and then to a fast one, or a slow dance gives way to its fast partner. It is acceleration as architecture, and as rite. It lives in ālāp, jor and jhālā, in the Hungarian lassú and friss, in lassan and friska in Liszt’s rhapsodies, in the doina followed by a hora or a sârba, in the pavane and the galliard, in the passamezzo and the saltarello, in the last khāna of an Arabic samāʿī, which breaks into 6/8, in the flamenco fin de fiesta, where everything ends por bulerías, in the Sufi dhikr, in the Gnawa līla and in the tarantella. It can be heard in Liszt’s Hungarian Rhapsody no. 2, in a doina and a hora by Taraf de Haïdouks, and in the jor and jhālā of any sitar recital. A possible lesson teaches it without a single word. Four students stand in a ring, one sings a doina without pulse on a mode with the augmented second, the other three hold the final softly, and when the singer so decides, a foot strikes the floor. From that stamp onward the others walk in twos, slowly at first, then faster, and the melody that was floating has to learn to fit into the steps. After five minutes the ring is turning and the phrase has become a hora. Nobody has explained what an acceleration form is, and all of them have exercised it with the body, which is where form learns to remember.

23. Closed, then open. A closed first part, strophic and composed, followed by an open second part, cyclic and improvised over a vamp or a cycle, the form that turns a song into an event. It lives in the Cuban son, with largo or canto and then montuno, in jazz, with head, solos over the changes and head, in the Hindustani bandish followed by vistār and tān, in gospel, with the song and then the vamp, in flamenco, with the letras and then the falsetas and the escobilla, and in the Baroque aria with its cadenza. It can be heard in “El manisero”, in “So What”, in a bandish in Bhairav and in the closing vamp of a gospel service.

K. Text-driven forms and song schemata

24. The recitation formula, or the litany. An elastic melodic template whose length is set by the text, with its intonation, its reciting tone, its mid-cadence and its termination, the initium, the tenor, the mediatio and the terminatio of the psalm tone, with the flexa as the lesser articulation that chapter IV places before the mediatio when the first half-verse runs long, and with its differentiae for the endings, or else a chain of short formulas fastened to the accents of the text. It is the purest archetypal ordering formula in Western music, applied to many thousands of texts, and its offices are the second tetrad above, so that everything said there holds here, in its historical home. In it the saying disposes time, and léxis governs the Toward of the piece verse by verse. The technique of assembling a whole chant out of stock formulas has a name of its own, centonization, from cento, a patchwork cloak. Leo Treitler showed that the word describes poorly what the singer did, because plainchant was handed down for centuries as Milman Parry and Albert Lord had seen the epic of the Balkan guslari handed down, through a system of formulas the singer knew how to remake on each occasion, closer to the improviser than to the copyist. The recitation formula is thus the form in which oral memory becomes grammar. It lives in psalmody, in Qur’anic tartīl, in Vedic chant with its three accents, in Torah cantillation, where each sign stands for a formula, in the epic recitation of the guslar and of the byliny, in the litany and the rosary, in the auctioneer and in the pregón. It can be heard in psalm tone 8 with its differentiae, in a sura recited in tajwīd and in a blind singer’s romance sung to a single formula for two hundred lines.

25. The cumulative song. Each stanza repeats all the earlier elements and adds one, form as an exercise of memory and the oldest of the additive processes. It lives in children’s and ritual song everywhere. It can be heard in “Ḥad Gadya” and “Eḥad Mi Yodea”, in “The Twelve Days of Christmas”, in “Alouette” and in “Estaba la rana cantando debajo del agua”, and the additive process of Philip Glass is this form without the words.

26. The 32-bar song form, AABA. Four eight-bar phrases, of which the third, the bridge, strays harmonically and comes back. It is the most used form of the twentieth century and, in its own right, a schema for improvising. It lives in Tin Pan Alley, in jazz and in early rock. It can be heard in “I Got Rhythm”, whose changes, the rhythm changes, are the basis of dozens of contrafacts, in “Over the Rainbow” and in “Body and Soul”.

27. The twelve-bar blues. Three four-bar phrases over I IV I V IV I, with their variants, which usually carry an AAB lyric, statement, repeated statement and answer, the same ordering that the girl in the imagined lesson found on her own. It is a harmonic and formal schema as fixed as any romanesca, and as generative. It lives in the blues and in everything descended from it. It can be heard in “Sweet Home Chicago”, in “Now’s the Time” and in “Hound Dog”.

L. Forms of energy

28. Jo-ha-kyū. Beginning, break and rush, a slow opening, a middle that intensifies and a rapid close. It disposes energy before it disposes sections, and Zeami applied it to the single phrase, to the whole play and to the order of an entire day’s programme. It is the contour archetype, procedure 38, raised to a principle, and the form that most clearly dwells in the cell where rhythm crosses the Toward, because it orders a pure futurity. It lives in nō, in gagaku, in the tea ceremony, in the martial arts and, unnamed, in almost all the ritual music of the world. It can be heard in a nō play, in a gagaku suite and in the three-part arc of a taqsīm.

VII. Perennial compositional procedures. Work on motive and melody

The Greek word for composing was melopoiía (μελοποιία), and Spanish inherited it as melopea, which the dictionaries still record as the art of producing melody before they record it as a fit of drunkenness, an irony I rather enjoy. It has two roots. Poieîn (ποιεῖν) is to make, to fashion, to bring something into presence, and mélos (μέλος) is at once the limb of the body and the song. Yet melos, as I set it out in chapter II when I unfolded its loom, is woven from three threads. There is léxis (λέξις), the saying before the said, the vocative direction of a voice that turns towards someone. There is harmonía (ἁρμονία), the fitting and the gravitation of sounds that attract one another. And there is rhythmós (ῥυθμός), the shape of what flows. From this follows the thesis of the present chapter, and I give it whole before the catalogues begin. Melopoeia is a making that speaks. When a procedure works a motive it works a saying, and what it transforms is a direction of speech before it is a sonic object. The proof is simple and fits in anyone’s throat. A rising leap of a fourth to a held note is a call, gesture G2, the oldest figure in melody. Invert it, procedure 6, and the same two notes at the same distance fall instead of rising. They no longer call, they answer. No pitch has changed its nature, and yet who is speaking, and to whom, has changed. An operation that looks like pure geometry on paper reorganises in the air the relation between a voice and the one it addresses, and that is why the grammar of operations I propose is the grammar of a saying. The second thread the procedure works is harmonía, and here the word keeps its Homeric sense, the joint that fits together the planks of a ship. To transpose is to sail the whole ship into other waters without touching its joints. To change the mode is to change the timber beneath the same joints. To invert is to turn the hull upside down and discover that it floats in another way. The third thread, rhythmós, is worked above all by the transformations of time, and in each section below I say which thread bears the weight. The procedures, moreover, live mainly in two of the three strata of the loom. They inhabit the Inclination, the instant in which something yields towards something, the appoggiatura that leans, the cadence that is put off, and they inhabit the Toward, the direction and continuity that make a succession into a journey. The Flesh, the breath and the weight that nobody chooses, is the ground on which they rest, and from that ground comes the distinction that follows.

The procedures of this chapter are archetypal operations that recur wherever there is melodic craft, from ancient chant to jazz, from the song to the symphony. Each one carries a mark. Those of the voice are what human beings do with sound whether or not they can write it, what a body can carry in its memory while memory runs forward. Those of paper are what the first group becomes once writing exists, operations that require seeing the whole melody at a glance, spread out in the space of the page. Some belong to both domains, and I say so. The mark respects an order that the Flesh imposes and that this essay makes its own, voice first, keyboard second, paper last.

The words of procedure

Méthodos is metá plus hodós, the road one follows. Póros is a passage or a ford, and aporía is its absence, which is the exact description of the work I call the hardest of all, since an episode is the póros, the crossing opened between A and B. Téchne is for Aristotle the reasoned disposition for making, and Plato’s Gorgias opposes it to tribé and empeiría, the knack and the routine that cannot give an account of themselves. This matters for the polemic of my opening pages. What I called the tyranny of technique is tribé, and what I defend is téchne, so the complaint was never against craft. Mêtis is the cunning practical intelligence of the navigator, the hunter and the weaver, and kairós the opportune instant, and between them they name what improvisation truly uses. Kanón means rule, and it carries a twist worth savouring. In the fifteenth century the word “canon” named the verbal rule from which the second voice was to be derived, and the resulting piece came afterwards. Tinctoris defines it as “a rule showing the composer’s intention under a certain obscurity”, and it was the performer who resolved it. The word I use pejoratively when I say “not as a canon” once meant precisely a compositional algorithm. And éphodos (ἔφοδος) was Archimedes’ word for his Method, the way that finds a result before it can prove it, the original sense of heuristic.

Two ancient taxonomies anticipate mine. Cleonides classifies metabolé, change, into change by génos, by sýstema, by tónos and by melopoiía, an ancient taxonomy of exactly the pivots I describe under modal mutation, and génos, synaphé and diázeuxis, the conjunct and disjunct tetrachords, are the native terms for what I call the exchange of tetrachords, just as jins and ajnās are in the theory of maqām. Augmentation and diminution, for their part, were for two centuries literally analogy, in the Greek sense of proportion. Mensural notation wrote them as fractions, proportio dupla, tripla, sesquialtera, so procedures 1, 2 and 4 existed as notational algorithms long before they existed as expressive gestures.

The procedure books

The idea of a catalogue like this one has a long genealogy, and I acknowledge it gladly because it proves me right. Ganassi in 1535 and Ortiz in 1553 printed diminution tables, lookup tables that give, for each interval, a menu of ways to divide it. Spanish has the native names for the two operations, glosa and diferencias, and glosa already stands on this blog’s masthead. The regole of the partimento are the same idea applied to harmony, because given this motion of the bass they prescribe this realisation. Mattheson’s loci topici of invention, from 1739, list repetition, inversion, augmentation, diminution, transposition and fragmentation as sources of ideas, and not merely as ways of developing them, which is precisely my thesis. Vasili Byros has shown that in that same circle the partimento served as a bridge towards free composition, because realising a given bass was at once the exercise and the quarry of inventiones, and Mattheson’s topics and the practice of the Neapolitan bass describe from two sides a single workshop in which the musical idea is found by operating. Kircher’s Arca musarithmica, from 1650, was a physical box of combinable slats for setting any text to music, and the dice game attributed to Mozart is its parlour descendant. Behind both stands the ars combinatoria of Ramon Llull, and behind my own claim that few elements yield constellations.

And above all there is the Figurenlehre of musica poetica, from Burmeister to Kircher, Bernhard, Vogt and Scheibe, which codified almost all of this catalogue centuries ago under rhetorical names. That they were names from rhetoric, the art of discourse addressed to someone, confirms what I said at the opening of the chapter about the thread of léxis. Epizeuxis, the immediate repetition of a word, is procedure 43. Polyptoton, the same word declined in different cases, is the same motive at another pitch, the transposition and the sequence of procedures 5 and 24. Gradatio or climax, the staircase of rising clauses, is the rising sequence of procedure 24. Anadiplosis, the end of one line turned into the beginning of the next, is the elision of procedure 14. Hyperbaton, the word taken out of its place, is the displacement of procedure 3. Parenthesis, the internal insertion, is procedure 12. Synonymia, saying the same thing in other words, is the paraphrase of procedure 15. Ellipsis, the omission that lets one hear what is missing, is the fragmentation of procedure 11. Aposiopesis, the discourse that breaks off and falls silent, is the general pause as transition within the episode writing of procedure 23. Anabasis and catabasis, ascent and descent, are the registral shifts of procedure 36. And circulatio, the figure that turns upon itself, is gesture G15.

Symmetries

There is a modern reading of all this that carries the thesis of perenniality to its strongest form. Babbitt observed that prime, inversion, retrograde and retrograde inversion form the Klein four-group, and that transposition and inversion generate a dihedral group. These procedures recur because they are the symmetries of pitch and of time, and no culture invents a symmetry, every culture finds it. The vocabulary that follows from this is useful in the classroom. A generator is an operation from which, together with a few others, the whole group arises, and that says formally what I was saying with few procedures and endless combinations. An orbit is everything reachable from a motive by means of the operations, and it offers a rigorous definition of that motive’s identity. Closure, the inverse and the involution describe operations that undo themselves, and the retrograde is its own inverse. The composition of operations is my chains of procedures. And isomorphism allows the repertoires of operations of two cultures to be compared without reducing one to the other. David Lewin’s transformational attitude states the whole pedagogy in one sentence, and it uses the word with which this essay opens. “If I am at s and wish to get to t, what characteristic gesture should I perform in order to arrive there?” Lewin explicitly opposes that question to the stance of the outside observer, to what I have called the museum and the laboratory. Chomsky’s transformational rules of 1957 were elementary operations on structures, permutation, deletion, insertion, copying, which are the syntactic counterparts of retrograde, fragmentation, internal expansion and repetition, so that “deep grammar” can mean exactly what I want it to mean. The ordering formulas generate the skeleton, the procedures work the material. Aristid Lindenmayer’s L-systems, rewriting rules that make the shapes of plants grow, fuse grammar and growth in a single device. Nicolas Ruwet’s paradigmatic analysis, which aligns the variants of a unit in columns, is the analytic mirror of this catalogue and the way to discover which operations a given tradition really uses. And D’Arcy Wentworth Thompson’s theory of transformations, the outline of one species projected onto another by deforming a grid, is the intervallic recomposition of procedure 41 drawn as geometry. All of this, however, describes harmonía and rhythmós with precision and leaves léxis out. The Klein group knows that the inversion of a call is its mirror, and it does not know that it is an answer. Only the one who sings it knows the second thing.

Algorithm and heuristic

Most of the recipes in this book ask for judgement at every step, they say “adjust by ear”, and Pólya’s word for that is heuristic. A few are strictly mechanical, retrograde, exact inversion, augmentation by a fixed ratio and permutation, and those are algorithms in the full sense, an effective procedure in the phrase of Church and Turing. One has to know which of the two things one holds in one’s hands, because algorithms are executed and heuristics need mêtis. Jeff Pressing described the improviser in just this way, as someone who works upon a referent, a melody, a harmonic scheme, a form or a repertoire of learned figures, and who at each instant chooses between continuing associatively what has just been played and breaking it off, supported by a knowledge base that practice has made automatic. Pressing’s referent is my melody of the day, and the knowledge base is this catalogue once it has come down from the paper into the hands. Aaron Berkowitz, studying pianists who improvise in the Classical style, arrived at the same figure from cognitive science, a repertoire of learned formulas recombined in real time as the words of a mother tongue are recombined. A procedure that no longer has to be thought has become what the Greeks called héxis, an embodied disposition, and only then is mêtis left free for kairós.

The other traditions have better names for all this than ours does. Turkish calls the path of a makam its seyir, with a word that means journey. Hindustani music calls the gait of a raga its chalan and its growth through elaboration its baḍhat. The tihāī is a phrase played three times and calculated to land on the sam, an arithmetic cadential algorithm that any tabla player executes in real time. The paltā and the alaṅkār are permutational scale patterns, practice understood as combinatorics. The layakārī is the play of proportions, the proportio once again. Flamenco has the falseta, and jazz has substitution, the turnaround, the riff and the vamp. Each entry that follows gives the name of the procedure, its description, its mark and its examples.

A. Transformations of time

These four operations work above all the thread of rhythmós, yet they touch léxis more than one might think. A phrase stretched to double length becomes a proclamation, and a phrase compressed to half becomes haste or a confidence.

1. Augmentation. It consists in stretching the rhythmic values while keeping the order of the pitches. It belongs to the voice, because any singer knows how to lengthen a melody she knows, and tradition made it a foundation when it turned the Renaissance cantus firmus into a voice that sustains, in long values, the word the other voices gloss. It can be heard in Bach’s fugues, where the subject returns in doubled values as if someone deeper were saying it, in the cantus firmus of the Masses and in the slowed-down versions of a theme in jazz.

2. Diminution. It consists in compressing the rhythmic values. It belongs to the voice, and it is the operation that Baroque ornamentation and Indian layakārī carry to the extreme, when the same line is said at twice, three times or four times the speed without losing its profile.

3. Rhythmic displacement. It consists in shifting the melody forward or backward within the bar without changing its durations, so that what fell on the strong beat now falls off the beat. It belongs to the voice. Rhetoric called it hyperbaton, the word taken out of its place, and it produces the same effect, because the displaced accent forces us to hear afresh what we thought we knew. It is shown by the first bars of Beethoven’s Third, where the metre staggers beneath the theme, and by the syncopations of hard bop.

4. Proportional and irrational changes. They consist in altering the temporal proportions between the parts, with relations of three against two or five against four, or with the rubato that steals time from one note to give it to another. They belong to the voice, and they live in Ligeti, in the African traditions of polyrhythm and in flamenco.

B. Transformations of interval and melodic profile

Here harmonía bears the weight, and it is in this section that léxis reveals most clearly that it was there all along. To transpose keeps the saying, to invert turns it inside out, to retrograde makes it illegible to the ear and legible to the eye.

5. Transposition. It consists in carrying the whole melody to another pitch while keeping its intervals. It belongs to the voice, and its universality is complete, in folk music, in the raga, in plainchant and in art music. It is the operation performed by anyone who starts a song lower because the voice will not reach, and that is why it is the clearest example of a procedure the Flesh decides before theory does.

6. Inversion. It consists in reflecting the intervals about an axis, so that what rose now falls and what fell now rises. It belongs to both domains, and the double mark keeps a fine distinction. The fall that answers a rise is oral, and every tradition of call and response knows it. The exact mirror, interval by interval, is literate, because it requires seeing the whole line and measuring it. The oral operation works léxis and turns a call into an answer. The literate operation works harmonía, and sometimes it uncovers in the mode a degree that the original melody had never touched. Bach took it to the limit in The Art of Fugue, and twentieth-century serialism made it the norm.

7. Retrograde. It consists in playing the melody backwards, from the last note to the first. It belongs to paper, because memory runs forward and almost no oral tradition practises it. It lives in the puzzle canons of the Renaissance, whose verbal canones sometimes asked for the voice to be read from the end, and in the twentieth-century classics.

8. Retrograde inversion. It consists in applying inversion and retrograde at once, and the order in which they are applied makes no difference. It belongs to paper, and it is the fourth element of the Klein group that Babbitt made visible.

9. Modal mutation. It consists in keeping the contour and altering the context of the scale, so that the same figure sings in another mode. It belongs to the voice. Greek theory calls the whole family metabolé. My word “mutation” has a second lineage in the Guidonian mutatio, the change of hexachord, and a beautiful cousin in the inganno described by Artusi, which keeps the solmization syllables and changes the hexachord beneath them, an algorithm of modal mutation performed entirely inside the singer’s head. It is harmonía in its pure state, because the joints stay in place and the timber changes. It is shown by the medieval commixtio modorum and by the flamenco alteration that moves from playing por arriba to playing por medio.

10. Contour elaboration, or fioritura. It consists in adorning the tones of the skeleton with passing notes, neighbour notes, appoggiaturas and turns. It belongs to the voice. It is the procedure in which the Inclination of the loom becomes audible note by note, because each ornament turns out to be a sound that leans towards the next. The Indian gamakas, Baroque diminution and Arabic ornamentation live in it, three dialects of one operation that nobody confuses once they have sung them.

C. Fragmentation and development

These operations work the syntax of the saying, and therefore léxis. To break a phrase, to insert something into its middle, to prolong its end or to overlap two phrases are things that speech does every day.

11. Motive fragmentation. It consists in taking a short segment of the melody, from two to five notes, and developing it as if it were a single word repeated until it acquires a meaning of its own. It belongs to the voice. Rhetoric called it ellipsis, and Beethoven’s Fifth is its canonical example, four notes that suffice for a symphony.

12. Internal expansion. It consists in inserting new material into the middle of a melody, like an aside that opens within a sentence. It belongs to the voice, and it is the parenthesis of the rhetoricians. Lisztian thematic transformation practises it, and so does the filigree of Chopin’s nocturnes, which opens the phrase from within without breaking it.

13. Extension, or the lengthening of the phrase end. It consists in adding bars at the cadences, delaying the arrival. It belongs to the voice. The phrase expansions of the Classical style know it, and so do the turnarounds of jazz, which lengthen the ending so that the next chorus has somewhere to start from.

14. Elision. It consists in overlapping the end of one phrase with the beginning of the next, so that a single bar ends and begins at once. It belongs to the voice, and it is the anadiplosis of rhetoric. Classical development sections use it to quicken the momentum, and bluegrass fiddle tunes use it so as not to let the dance draw breath.

15. Melodic paraphrase. It consists in keeping the idea and rewriting it freely, saying the same thing in other words, which is synonymia. It belongs to the voice, and it is practised by the reharmonisation of a jazz ballad and by the chorale preludes that paraphrase the hymn until it becomes fantasy.

D. Types of variation

Each type of variation isolates one thread of the loom and works it while leaving the others still, and that is why this section is the most pedagogical of the catalogue.

16. Melodic variations. They are the ornamented, the simplified, the paraphrased, the skeletal and the glossed variation, five ways of touching the profile of pitches. They belong to the voice, and Spanish has known them since the sixteenth century under the name of diferencias.

17. Harmonic variations. They keep the melody and change its chords, so that the same saying changes its ground. They belong to paper, because they demand a vertical thinking that the voice alone cannot sustain. Jazz reharmonisation and the Baroque passacaglia practise them.

18. Rhythmic variations. They alter the syncopation, the augmentation or the diminution of the melody while keeping its profile of pitches. They belong to the voice.

19. Textural variations. They present the melody in homophonic or contrapuntal texture, in broken chords or arpeggiated. They belong to the voice, in so far as a group of singers knows how to make them without writing them down.

20. Timbre variations. They change the instrumentation or the orchestration, and with them the body that says the melody. They belong to both domains. Their textbook example is Ravel’s orchestration of Mussorgsky’s Pictures at an Exhibition.

21. Structural variations. They change the order or the length of the phrases. They belong to the voice.

22. Modal or scalar variations. They place the same melody in different modes or ragas. They belong to the voice, and they are the mutation of procedure 9 turned into the principle of a series.

E. Episodic and modular techniques

These are the operations of the Toward, the ones that give music a journey between two places, and harmonía governs them, because a sequence or a pedal is a field of gravitation.

23. Episode writing between two melodies. It gathers the chains of sequence, the modulating bridge, the ostinato interludes, the transitions made of texture alone, the expansion of a rhythmic ostinato and the general pause that rhetoric called aposiopesis. It belongs to the voice. The episode is the póros I spoke of above, the crossing opened between A and B, and it is where composition properly so called begins. It is shown by the episodes of Beethoven’s rondos and by the bridges of urban popular song.

24. Sequence. It consists in repeating a motive at successive pitches, until the repetition generates its own gravity. It belongs to the voice. It is the polyptoton of rhetoric and, when it rises, its gradatio. Baroque sequences live in it, and so do the rising sequences with which popular song prepares its chorus.

25. Pedal-point transitions. They hold a static pitch while the melody moves above it. They belong to the voice. The pedal is the held note of gesture G6 placed at the service of a passage.

26. Layered additive construction. It raises the piece from ostinatos laid one upon another. It belongs to the voice, and it is the way of building of the gamelan, of African polyrhythm and of minimalism.

F. Polyphonic and contrapuntal operations

Here harmonía returns to its literal sense of a fitting between pieces, and léxis appears as dialogue, because to imitate is to answer in the other’s words.

27. Canon. It is strict imitation at a fixed distance. It belongs to paper. Strict canon is largely a European and literate practice, and its perennial relatives are the round, echo imitation and overlapping call and response. For the hoquetus, see procedure 28.

28. Hoquetus. It consists in interlocking several voices that share out a single line among them, each with its sounds and its silences. It belongs to the voice. It is practised by the polyphony of the Central African forests, by medieval motets and by the Andean panpipes, where each musician holds only a few notes of a melody that nobody plays whole.

29. Countermelody creation. It consists in inventing a second melody compatible with the first, one that answers it or accompanies it. It belongs to the voice, and it is the first form of descant.

30. Free imitation. It consists in imitating a fragment at flexible intervals and rhythms, giving cohesion without the discipline of canon. It belongs to the voice.

31. Invertible, or double, counterpoint. It makes two lines exchange their registers, so that the upper becomes the lower and the fit still holds. It belongs to paper. It must be told apart from voice exchange, in which two voices swap their pitches over a short span.

G. Harmonic and modal procedures

This section is harmonía understood as gravitation, the field of forces in which one note leans upon another.

32. Drone-based elaboration. It builds the melody over a drone that does not move. It belongs to the voice. It is the oldest texture in the world, and it lives in India, in Scotland, in Eastern Europe and in medieval Europe.

33. Modal pivoting. It passes into a parallel or neighbouring mode through a shared note or chord. It belongs to the voice, and it is the harmonic face of procedure 9.

34. Reduction to the harmonic skeleton. It draws out of the melody its harmonic skeleton in order to build new ideas upon it. It belongs to the voice, in so far as the experienced singer hears beneath any coloratura the tones that hold it up, and it is the operation that teaches the hand most about where to lean.

35. Ground-bass rewriting. It sets a melody over a new ostinato, or a new melody over the same ostinato. It belongs to the voice.

H. Gestural and expressive procedures

These three operations come out of the Flesh and return to it. They work register, density and curve, what the body feels before it knows which note is sounding.

36. Registral shifts. They present the same idea in different strata of octave. They belong to the voice. Rhetoric called them anabasis and catabasis, and loaded them with meaning, the ascent towards the heights and the descent towards the depths.

37. Density shaping. It carries the music from thin texture to thick, or the other way round. It belongs to the voice, and it is universal in ritual musics, where the assembly enters little by little until the whole people is singing.

38. Contour and dynamic archetypes. They shape the piece after figures of the wave, the terrace or the spiral. They belong to the voice, and jo-ha-kyū, form 28, is this procedure raised to a principle.

I. Transformational and thematic procedures

To transform the character of a theme is to change who says it, and that is why this section belongs to léxis before any other thread.

39. Thematic transformation, or the Lisztian archetype. It transforms the melody in its character, heroic, lyrical, demonic, until the same theme seems spoken by different persons. It belongs to both domains. This is the path of transformation, and Lewin’s question is the one to put to it. If I am here and wish to be there, what gesture takes me?

40. Motivic saturation. It builds a whole piece from a single cell. It belongs to the voice. Beethoven practised it, and so does the Indian pakad, the cell that pervades a raga and makes it recognizable from the first phrase.

41. Intervallic recomposition. It keeps the intervallic relations and creates a new rhythm and contour, as if the melody’s DNA were expressed in another body. It belongs to paper, and it is what D’Arcy Thompson drew on his grid.

42. Hybridisation or grafting. It combines parts of two melodies into a new one. It belongs to the voice, and the seams between the two teach more than either of them alone.

J. Phrase-building procedures

Eighteen further operations follow, several of them more basic than any of the foregoing. The first six are the very syntax of musical saying, the way a phrase repeats itself, states, asks, answers, dissolves, spins itself out and refuses to end, and in them léxis can be heard more clearly than anywhere else in the catalogue.

43. Repetition, the zero degree. Exact repetition is an operation in its own right and the ground of all the others. Cleonides called the repetition of a note petteía, rhetoric calls the repetition of a word epizeuxis, and the ostinato is repetition that has become a floor. The ear never hears the same thing twice, because the second hearing is already variation from the moment attention has moved. It belongs to the voice. It is shown by Ravel’s Boléro, two melodies repeated again and again with only the timbre changing, by the letras of a cante repeated until they mean something else, by Steve Reich’s essay on music as a gradual process and by the mantra.

44. The sentence, 2 + 2 + 4. A basic idea of two bars is stated and repeated, exactly, varied or transposed to the dominant, and then a continuation fragments it, accelerates the harmonic rhythm, often sequences and drives towards a cadence. It is Classical in its theory, that of Schoenberg and of Caplin, and far older in its instinct, because it is the way anyone insists twice before saying what they meant to say. It belongs to both domains. It is shown by the opening theme of Beethoven’s op. 2 no. 1, by “Happy Birthday”, which behaves like a sentence, and by the first eight bars of countless folk tunes and song verses.

45. The period, antecedent and consequent. It is question and answer at the scale of the phrase, an opening phrase that ends on a weak cadence and is answered by the same beginning, which this time ends on the final. It is call and response interiorised by a single voice that answers itself. It belongs to the voice. It is shown by the first eight bars of the Ode to Joy, by the opening of Mozart’s K. 331 and by the two halves of a copla.

46. Liquidation. The term comes from Schoenberg. It consists in stripping the motive, repetition by repetition, of its characteristic features until only a conventional remnant is left, a scale fragment, a neighbour note, a repeated note, which then dissolves into the cadence or into the next section. It is the decrescendo of the motive’s identity, a word said ever more softly until it is left as breath, and the most elegant way to build a transition. It belongs to both domains. It is shown by bars 5 to 7 of Beethoven’s op. 2 no. 1, by the end of almost every Classical continuation and by the way a falseta thins down to a single repeated note before the cante comes back in.

47. Fortspinnung, or spinning out. It is the Baroque principle of continuation. An opening idea, the Vordersatz, is continued by spinning out its tail through sequence, the Fortspinnung, as far as a cadential epilogue, the Epilog. It is what I described earlier as spinning sequences until they generate their own gravity, and its way of speaking resembles that of someone who links one clause to the next without stopping to answer. It belongs to both domains. It is shown by the ritornelli of the Brandenburg Concertos, by any opening of Vivaldi, by the sequential descent of a taqsīm and by a bebop line spun through the changes.

48. Cadential deferral. It consists in arriving at the cadence and refusing it, with the deceptive cadence, the evaded cadence, the cadential phrase begun again “one more time”, the abandoned cadence, the dominant prolonged by its trill or its pedal, Gjerdingen’s indugio. My opening pages say that tension seeks resolution and defers it, and this is the deferral. It is the Inclination of the loom sustained to the limit, the instant in which something yields towards something, stretched over several bars. Its opposite is the tihāī, which calculates the arrival to the exact beat. It belongs to the voice as deferral and to paper as harmonic vocabulary. It is shown by the coda of Chopin’s Nocturne op. 9 no. 2, by the endings of Beethoven’s first movements, by the remate the dancer holds back and by the gospel choir’s third repetition of the final phrase.

K. Textural procedures

The two operations of this section work harmonía in the loosest and in the tightest fit known to music sung in company.

49. Heterophony. Several performers render the same melody at once, each with his own ornamentation, rhythm or register. It lies halfway between unison and counterpoint, and it is the most widespread texture on Earth. It belongs to the voice. It is shown by the gamelan’s layers over one melody, the Arab takht, the Chinese sizhu ensembles, the lined-out psalms of Gaelic Scotland, the New Orleans front line and Britten’s Curlew River.

50. Parallel doubling. It doubles the melody at a fixed interval, at the fourth or fifth in organum, in sixth chords in fauxbourdon, in thirds and sixths in half the world’s folk polyphony, in seconds in Bulgarian diaphony, in whole chords in Debussy’s planing, in jazz block chords and in the guitarist’s barre. It belongs to the voice. It is shown by the Musica enchiriadis, Dufay’s fauxbourdon, the parallel thirds of a huapango or of an Italian canto a due, and “La cathédrale engloutie”.

L. Cyclic and combinatorial procedures

Here rhythmós becomes arithmetic and the operation passes onto the page, even though its effect remains the body’s.

51. Isorhythm, talea and colour. A rhythmic pattern, the talea, and a pattern of pitches, the colour, of different lengths, turn together so that their alignment drifts apart and returns. The name is medieval and the mechanism perennial, the same as that of a melody of seven beats over a cycle of sixteen or of a timeline against a phrase. It belongs to paper, though its effect is the body’s. It is shown by Machaut’s motets, by Messiaen’s “Liturgie de cristal”, where the piano turns a cycle of 29 chords against a rhythm of 17 values, by a bandish phrase crossing the bar of the tāla and by Reich’s phase pieces.

52. Permutation and rotation. It reorders the notes of a cell, and that is permutation, or starts it from another note, and that is rotation. English change-ringing has done this with bells since the seventeenth century, as the Tintinnalogia of 1668 shows, written by Richard Duckworth and printed by Fabian Stedman. Each row differs from the one before by a single swap, and the whole is group theory rung by village neighbours. The Hindustani paltā does it with scale patterns, and the pedagogy of that tradition trains improvisation in precisely this way, by memorising paltās and tāns and varying them with method, almost never by asking for improvisation all at once. The timelines of West Africa are rotations of one another. Full permutation belongs to paper and rotation to the voice. It is shown by Plain Bob on six bells, the paltā exercises of a vocal riyaz, the rotational arrays of late Stravinsky and the bell pattern begun from its third stroke.

M. Procedures of interval, range and time

The last five operations of construction cross harmonía and rhythmós, the width of the intervals and the speed of time.

53. Interval expansion and contraction. With the contour kept, the intervals widen or narrow, and a pentatonic cell is stretched into leaps or compressed into chromaticism. It is Bartók’s habitual procedure and the mechanism behind much thematic transformation. It belongs to both domains. It is shown by the chromatic compressions and diatonic expansions of Mikrokosmos, by the widening of a blues shout and by the chromatic cell of Bartók’s Fourth Quartet with its diatonic expansion in the finale.

54. Range expansion, or baḍhat. It unfolds the material register by register from the tonic outward. Each phrase adds a degree above or below, the octave is reached near the climax and the range contracts in order to close. The Hindustani ālāp calls this baḍhat, growth, the taqsīm climbs through the ajnās, and the Classical aria keeps its highest note for a single moment. It is the Toward made space, direction turned into a territory to be conquered. It belongs to the voice. It is shown by any ālāp, by a taqsīm in Bayātī rising from the qarār to the octave, by the doina and by “Casta diva”, whose highest note comes only once.

55. Hemiola, or sesquiáltera. It sets three against two at the level of the bar, two bars of 3/4 heard as three of 2/4, or 6/8 regrouped as 3/4. It is the Iberian and Latin American rhythmic signature of the jota, the huapango, the joropo, the chacarera, the bambuco, the chacona and the zarabanda, the Baroque pre-cadential gesture and the Ewe bell against the dancers’ feet. It belongs to the voice and to the body. It is shown by “America” from West Side Story, the cadences of a Handel courante, the Valencian jota and Brahms everywhere.

56. Compression and expansion of harmonic rhythm. It makes the chords of the same progression change faster or slower. The acceleration of harmonic rhythm is the engine of almost every drive to the cadence, and its deceleration the engine of almost every coda. It belongs to paper, with a bodily effect. It is shown by the continuation phase of any Classical sentence, the doubled changes of a turnaround, the rush of one chord per beat at the end of a gospel number and the long tonic pedal that closes a Beethoven coda.

57. Metric modulation. A subdivision of the old pulse becomes the new pulse, so that the tempo changes by an exact ratio and without a break. Elliott Carter made it a system, and criticism gave it its name in writing about his music. Jazz calls it double time, Hindustani layakārī plays at once and a half, twice and four times, and Balkan dancers pass from 7/8 to 2/4 on the same feet. It belongs to both domains. It is shown by Carter’s Cello Sonata of 1948, a bebop head going into double time and the drut that follows a vilambit gat.

N. Borrowing and derivation

The last three operations write on top of what already exists or draw music from outside music. They are the most openly lexical in the catalogue, because in them the melody speaks over someone else’s words, or is literally born from a word.

58. Trope, quotation, contrafact. They are three ways of writing on top of what already exists. The trope inserts new words or music within an old chant, and in Spain the glosa expands a borrowed verse line by line. The quotation embeds another melody as a sign, as the jazz quote does, and Ives, and Berio’s Sinfonia, and signifyin(g) in Henry Louis Gates’s sense, as Samuel Floyd applied it to jazz. The contrafact keeps the harmonic skeleton and writes a new melody, as “Ornithology” does over “How High the Moon”, and the contrafactum keeps the melody and gives it a new text, as when “Innsbruck, ich muss dich lassen” became “O Welt, ich muss dich lassen”. At the largest scale the same operation is the parody Mass, which takes a whole polyphonic model apart and rebuilds it, the grafting of procedure 42 with an entire motet as the graft. It belongs to both domains.

59. The ornamented repeat. It is the return varied by increasing ornament. The Baroque double knows it, and so do the ornamented da capo, the returns of a Chopin nocturne, of which in the case of op. 9 no. 2 his own handwritten variants survive in his pupils’ copies, the ladder of the piobaireachd, with urlar, siubhal, taorluath and crunluath, each variation a denser species of ornament, and the bandish that returns with ever longer tāns. The variation of procedure 16 and the ornamentation of procedure 10 fuse here into a formal principle, the refrain that never comes back the same, which is the way someone repeats a promise each time with greater conviction. It belongs to the voice. It is shown by the doubles of Bach’s English Suites, a da capo aria as Farinelli would have returned it, “MacCrimmon’s Lament” through its variations and the A sections of Chopin’s op. 9 no. 2.

60. Soggetto cavato and other derivations from outside music. It derives a motive from something foreign to music. The vowels of a name become solmization syllables, as in Josquin’s Hercules Dux Ferrariae, re, ut, re, ut, re, fa, mi, re, what Zarlino called soggetto cavato dalle vocali. Letters become note names, as in B-A-C-H, in Schumann’s A-S-C-H or in Ravel’s minuet on the name of Haydn. A line of verse becomes a talea, and a birdsong, a melody of speech or a skyline of mountains becomes a line. It is the procedure that lets a student begin when nothing comes to mind, and it is also the most literal proof that melos is born from léxis, because here the melody comes out of a name, out of the way someone is called. It belongs to paper, and to play. It is shown by the Missa Hercules Dux Ferrariae, the last subject of The Art of Fugue, Carnaval, Messiaen’s birds and Janáček’s speech melodies.

A possible lesson

Let us imagine a fifteen-year-old student who arrives at her lesson with the melody of the day that she sang yesterday, transcribed by ear and brought along noted down on a folded sheet of paper. It is in D Dorian and very short. It begins with a low A as an upbeat that leaps a fourth to D and stays there, held, then descends by step, F, E, D, C, and ends on E and D, settling onto the final like someone sitting down. It is a call followed by a descent, gesture G2 and a chain of small sighs, and she does not know it yet. A possible lesson begins without touching the paper. The teacher asks her to sing it again, standing, with her free hand drawing the leap in the air, and the student discovers that her arm rises of its own accord before the D. Then he proposes a procedure, number 6, inversion around D. The student does not write it down first. She sings it, slowly, correcting herself. Where there was an A rising to D, a G now falls to D. Where the descent passed through F, E, D, C, the line now climbs through B, C, D, E, and the ending settles onto D from C, from below. There is a moment of silence in which the student listens to what she has just sung. The B natural, the Dorian sixth that the original melody had never touched, has appeared of its own accord, and the whole mode suddenly sounds clearer, like a room in which a window has been opened. That is harmonía at work. But what the student says aloud is something else. She says the new melody seems to be answering. The teacher corrects nothing. He asks her to sing the two one after the other, the original and the inverted, and what sounds is a call and its answer, recipe R7, and at the scale of the phrase a period, procedure 45, even though nobody has yet spoken the word. The pitches are the same, the intervals are the same, and the direction of the saying has turned around. Then comes the second procedure, liquidation, number 46. The student repeats the answer three times, and each time she takes something away. The first time it loses the opening fall. The second time it loses the B and is left with C, D, E, D. The third time it is left with C and D, repeated, ever more softly. In the end only a held D remains, gesture G6, the note that does not move and makes audible everything that moved before it. Only now does she go to the piano. The right hand plays the call, the left hand answers it with the inversion two octaves lower, and the liquidation falls onto the low D like a conversation dying away. At the end, and only at the end, the student writes it down. She has composed sixteen bars in twenty minutes with three operations that an algorithm could execute, and yet no algorithm would have framed the question she takes home with her. She wants to know whether the answer she found was already hidden in her melody, waiting for someone to turn it around, or whether she invented it by singing it.

Figure 6. The lists in compact form, gestures and forms. The twenty-four gestures spread over the three families of song, dance and poetry, with their codes, and the twenty-eight forms in their twelve families, with the number each bears in the catalogue. The call stands out because it is first in dignity.

Figure 7. The lists in compact form, procedures. The sixty operations in their fourteen sections, with the number each bears in the catalogue. The circle marks those that belong to the voice, the square those that belong to paper, and the two together those that live in both domains.

VIII. The recipe book

Here grammar comes down into the hands. What follows are executable, repeatable practices for the gestures of the catalogue, and the next chapter will do the same for each of the procedures. Each recipe works as a small workshop with its bench and its tools. It pursues a goal, gathers its ingredients, which are what one needs to have at hand, a melody, a metre, paper, advances by exact steps, is illustrated by a short example and leaves the student an exercise for the week. The order in which they appear climbs from breath to direction, and a lesson may run through it from beginning to end or enter by whichever bench the day’s phrase asks for, as one enters a workshop by the trade that presses.

The nearest literary model for this way of working is Queneau’s Exercices de style, one banal anecdote passed through ninety-nine procedures, until the anecdote is effaced and the work is left made of procedures. The Oulipo called the generative restriction a contrainte and the deliberate swerve away from it a clinamen, and called the literature it made potential, which in Greek is simply dýnamis (δύναμις). A student who has taken an eight-bar melody through forty operations has understood something about music that no analysis delivers, and has also learned the deeper lesson of the Oulipo. Far from limiting invention, the constraint causes it.

Step zero

All the recipes share a prior step which I no longer repeat in each of them, and which governs them all. Sing it before you write it, and write only what you can already sing. The rule looks like hygiene and is ontology. It brings into the lesson the founding order I set out in chapter II, Call, Song, Gesture, Sound, according to which music first calls, then sings, then becomes the movement of a body, and only at the end settles into an instrumental sound and, later still, into a written sign. Paper comes last because it is the last to be, and whoever writes a melody his own throat does not know has turned the ladder upside down, beginning with the track and only afterwards looking for the animal that left it.

This rule reached me the way a craft is received. I studied with Salvador Chuliá, born in 1944 and dead in 2025, from 1993 until 1999, and his school was that of song and the arm. The phrase was sung before it was played, the sound was born of the weight of the arm, and everything, fingering, pedal, tempo, dynamics, was measured by a single question, whether the line sang. His most dreaded verdict, está perfecto, pero no canta (it is perfect, but it does not sing), summed up an entire hierarchy, because it declared that complete correctness could still amount to nothing. That school came from far away. One of its lines rises, through Manuel Palau and Manuel Massotti, to the Paris Conservatoire of Guiraud, Gedalge and Koechlin, and another, through Ernesto Pastor, to Rebollo, Pérez Casas, Pedrell and Arrieta. What these pages take apart into numbered steps, song first, the arm after, the keyboard at the end, was there a single undivided demand, and step zero is the shortest form I have found of giving it back that unity.

Empirical research confirms from the side of deficit what that school knew from the side of practice. Amalia Casas-Mas and her colleagues studied the private singing of instrumentalists, the humming a musician addresses to himself while practising, and found that far less singing happens in the lesson than one would expect and that, when there is singing, it is almost never used as a reflective or embodied tool, as a means for the student to think the phrase with his own body. Song survives in the classroom as the teacher’s illustration, a hum that shows how it ought to go, and disappears as the student’s own work. Step zero reverses that economy. The one who sings is the one who learns, and what he sings is his way of thinking the phrase before the instrument imposes its easy ways on him.

A possible lesson makes it visible. Imagine a twenty-year-old composition student who brings to class a sixteen-bar melody written with care, with its slurs, its hairpins and a leap of a ninth in bar eleven of which he is secretly proud. The teacher neither plays it nor reads it aloud. He asks him to sing it. The student begins well, the first phrase comes out, the second falters and, on reaching bar eleven, he stops, tries the leap, misses it, tries again and ends up singing a seventh. Nobody says anything for a few seconds. Then the teacher asks him to sing the whole phrase once more, this time without looking at the paper, letting the voice go wherever it wants to go. The voice, consulting no one, resolves the leap through a seventh and precedes it with a passing note the paper did not have. The student writes it down. What he has discovered in those four minutes is worth a semester of harmony, because he has seen that his melody had two authors, one who heard it and another who drew it, and that only the first knew how to sing.

Recipes for gesture

What the body does is the object of these pages, and technique is taught in them though the word does not appear. What we call technique is sedimented gesture, and each of these recipes returns the sediment to its original movement. Their reach is better understood if they are read on the loom of melos I set out in chapter II, the fabric whose vertical threads are the léxis (λέξις), the saying that calls, the harmonía (ἁρμονία), the fitting together of what sounds at once and attracts, and the rhythmós (ῥυθμός), the shape of what flows, and whose horizontal strata are the Flesh, the Inclination and the Toward. The recipes for gesture work these three strata one by one and then together. The Flesh is here breath and weight, the pneuma (πνεῦμα) taken before the anacrusis and the gravity of the arm falling onto the key, and it is worked above all by R4, R5, R6 and R8. The Inclination is support and yielding, the rhopé (ῥοπή), the instant in which the balance gives, the appoggiatura read as “lean”, the sigh that lets itself fall onto its second note, and it is worked by R6, R8, R9 and R10. The Toward is direction, the phrase that goes somewhere, the foot that throws the weight toward the next step, the call that awaits an answer, and it is worked by R1, R2, R3, R7 and R11.

That distribution is approximate, because no gesture lives in a single stratum, and the approximation itself teaches something the inherited piano technique cannot name. Almost every fault a lesson corrects is an empty cell of the loom. Attack is Inclination without Flesh, a yielding that has no weight to yield and therefore strikes, and against it weight is the Flesh that inclines. The metronomic phrase is Toward without Inclination, pure direction advancing without leaning on anything, and so it sounds like a formality. The beautiful, stagnant sound is Flesh without Toward, weight that goes nowhere. A good teacher diagnoses by ear which of the three strata is missing, and chooses the recipe that restores it. Hence their inner order, which almost always begins with the Flesh, song, breath, continues through the Inclination, the support the arm finds as it shapes, and ends in the Toward, the whole phrase thrown toward its close, because direction that is not born of weight is the empty direction of the metronome.

R1. Conduct it before you play it. This recipe looks in the arm for the energy shape of the phrase before the fingers touch it, and to practise it any phrase from the repertoire or the melody of the day will do, with a free arm. First the phrase is sung. Then it is beaten plainly in its metre, as a conductor would beat it who wanted only to hold the orchestra together, the arm falling on every beat with the same indifference. Then that beating is abandoned and the phrase is shaped, and the arm draws its dynamic curve, the swell, the fall, the breath. Then comes the instrument, and the phrase is played with one hand while the other goes on conducting. Finally it is played with both hands on the keyboard and the conducting arm remembered, present in the shoulder though it no longer moves in the air. The canonical example is the opening phrase of a Chopin nocturne conducted as one long exhalation, with a lift before the leap. The exercise asks the student to conduct the same phrase in three characters, prayer, dance and argument, then to play it in each of them, and to record the three versions and compare them.

The steps of R1 travel the loom from bottom to top and back again. Song lays down the Flesh. The plain beat is a Toward without a body, metre in its skeletal state, and it is worth doing deliberately in order to hear how poor it sounds. Shaping restores the Inclination, because the arm that draws the swell has to decide where it leans and where it yields, and only then is direction turned from beating into phrase. Of all the recipes, this is the one that most directly translates the school of song and the arm in which I was formed. There the arm was the place where song became sound, and the keyboard was played with the phrase already known in the shoulder.

Imagine a possible scene. A nineteen-year-old student brings Schubert’s Impromptu in G-flat major, D 899 no. 3, and plays it with impeccable fingers and a melody that moves like a tram, stop by stop, each long note of the tune set in its place and abandoned as soon as the next one arrives. The teacher asks her to get up from the bench. She sings the first phrase, with some embarrassment, and the voice, which knows nothing of keys, already binds what the fingers kept apart. Then she beats time with her right arm, and does it well, with the punctuality of a clock, and the teacher asks her to sing while she beats, so that she hears the beating and the song pulling in different directions. The third step comes, and that is where the lesson changes temperature. As she shapes, her arm rises on the third note, which nobody had pointed out, and falls slowly to the fifth, and she laughs because she has just discovered the shape of a phrase she had been playing for months. She sits down. She plays the melody with the right hand while the left, in the air, goes on drawing the curve, and the figuration of the accompaniment, which used to push, begins to rock beneath it. At the end she plays with both hands. The tram has become a boat, and nobody has said a word about fingering.

R2. Draw the line, or cheironomy. This recipe turns the contour of a melody into a gesture of the hand, as the first neumes were, and it needs nothing more than a melody and air. The melody is sung while the hand traces its contour in the air, height for pitch and horizontal distance for time. It is repeated with eyes closed, so that the hand stops copying what it sees and begins to feel what it hears. At the instrument, the free hand traces while the other plays. Then the process is reversed, and a curve is drawn first, in the air or on paper, so that a melody may then be sung to fill it, and composition begins in gesture. The Greeks called this art of the hand that draws the song cheironomía (χειρονομία), and unstaffed neumes are still called cheironomic because they were the trace of that hand before they were signs. The example is the rising and falling arch of “Over the Rainbow” drawn in a single stroke, followed by a new melody composed on another stroke. The exercise consists in drawing five curves, singing five melodies, notating the one you like and applying to it a procedure from the next chapter. On the loom, R2 is an exercise of the Toward, the phrase as trajectory, yet its final reversal uncovers something finer, that the curve drawn before singing is already an inclination of the body toward a song that does not yet exist.

R3. Step the metre. This recipe puts the pulse and the timeline in the feet before the hands, and it requires a metre or a timeline from the catalogue of gestures and a floor. The pulse is walked. Then only the strong beats are stepped and the rest is clapped. Then the timeline itself is walked, the twelve-pulse bell pattern, the flamenco compás of twelve, an aksak with one long step and short steps. Then one sits at the instrument and plays while the feet go on marking quietly. At the end the feet stop and the marking is kept inside. The example is a bulería compás stepped on 3, 6, 8, 10 and 12 before a single note is played, or a Bulgarian seven stepped long, short, short. The exercise asks the student to improvise a melody over each of four walked grounds, the plain pulse, the tresillo, the sesquiáltera and the aksak, and to observe how the melody changes when the feet change.

R3 is the recipe closest to the eurhythmics of Émile Jaques-Dalcroze, who made the body in movement the musician’s first instrument, and what research has observed in his classrooms describes exactly what is sought here. Marja-Leena Juntunen and Leena Hyvönen showed that in Dalcroze eurhythmics bodily movement, far from illustrating what has already been understood, becomes the very place where musical knowledge is formed, a knowing that belongs first to the body and only afterwards turns into concept. On the loom, stepping the metre sets the rhythmós in its bodily analogues, the stride, the heartbeat, the dance, and forces the three strata to meet, because the foot that treads has weight, which is Flesh, yields that weight to the floor, which is Inclination, and throws it toward the next step, which is Toward.

Imagine another possible scene, this time with a group. Four students of thirteen and fourteen walk in a circle around the piano while the teacher marks a Bulgarian seven with his hand on the lid, long, short, short. Three of them catch it at once. The fourth, a tall boy who plays Clementi very well, goes on stepping in four out of sheer inertia, and every time the long step comes he trips over himself and laughs, irritated. The teacher does not correct his foot. He asks him to sing the pattern in syllables as he walks, ta-a ta ta, ta-a ta ta, and by the third cycle the voice has dragged the body along and the long step appears. Then they all sit down, and each improvises eight bars over a drone on D while the feet go on marking quietly. The tall boy’s melody, which before the walking would have been a scale in quavers, now has a long note every seven pulses, as though it limped with elegance. He does not know it yet, but he has just composed his first melody in aksak.

R4. Breathe the anacrusis. This recipe wants every beginning to be an intake of breath and understands the anacrusis as gesture, and it works with a phrase that begins on an upbeat and then with one that does not. The phrase is sung with an audible intake of breath before it. The hand lifts with the inhalation, and that lifting is the anacrusis. The first note is played as the landing of that lift. Then five different intakes are tried, slow, quick, a gasp, a sigh, a silent one, and one listens to how the first note changes with each of them. The example is the upbeat of the Ode to Joy, or the silent breath before the first chord of a Schubert song. The exercise asks the student to take a phrase that begins on the downbeat and find its hidden anacrusis, beginning to breathe one beat early and playing from that breath. It is the most purely carnal recipe in the book, because it works the pneuma, the zero gesture from which all the others set out, and it discovers that the first note of a phrase receives its character from something that happened before it sounded.

R5. Vowel, syllable, word. This recipe uncovers what the voice knows of legato, of colour and of accent before the instrument does, and it gathers a phrase, some vowels, solfège and a text, real or invented. The phrase is sung on “u” and then on “a”. It is sung in solfège. It is sung to nonsense syllables, like the flamenco tiriti tran or a scat. It is sung to words, one’s own if none exist. At the end it is played keeping the vowel. The example is the theme of a Mozart slow movement sung on “u”, where the legato is found, then to an invented text, where the accents are found, and then played. The exercise consists in speaking the phrase as a statement, as a question and as an exclamation, and playing each, which is also the shortest introduction to recitative. Every vowel is a shape of the mouth and therefore a shape of the breath, and the closed “u” teaches a continuity that the open “a” turns into radiance, so that the hand that plays keeping the vowel plays with the Flesh of a voice that no longer sounds.

R6. The arm before the hand. The swell. This recipe works the messa di voce as the root of dynamics, and one tone and eight slow counts are enough for it. A tone is sung from nothing to fullness and from fullness to nothing in a single breath, over eight counts. At the instrument the same is done on a repeated note, with the arm opening and closing while the fingers merely follow. Then the same across a whole phrase, a single swell for the entire phrase. Then two swells in one phrase, and afterwards the opposite, a fall followed by a rise. The examples are the long notes of “Casta diva” and any hairpin in a Brahms intermezzo. The exercise asks the student to play the melody of the day with a single swell, then with one in every bar, then with none, and to decide which the melody wants. On the piano, where every note begins to die as soon as it is born, the swell can only be made with the weight the arm keeps giving and withdrawing along the phrase, and that is why R6 teaches better than any other the lesson of weight against attack. The Flesh gives the weight and the Inclination administers it, note by note, like someone paying out rope.

R7. The call and the answer. This recipe takes the oldest pair of gestures as the basis of phrase-making, and it needs two people, or one person and two registers. First calls are improvised, an ascending leap of a fourth or a fifth to a held note, gesture G2 of the catalogue. The partner answers with a fall to the final. Then the roles are exchanged. Alone, one calls in the treble and answers in the bass, and then the other way round. At the end a call and its answer are notated, and what remains on paper is an antecedent and a consequent, the period, procedure 45. The examples are the pregón and the coro of a rumba, or the horn call and the strings’ reply in a Bruckner opening. The exercise consists in recording four calls and four answers, in four modes, in two minutes. Since the call is the founding gesture, the one that opens the order of Call, Song, Gesture and Sound, this recipe stands at the centre of the book. The call is the Toward in its nascent state, a phrase launched without yet knowing who will answer, and the answer teaches the student that a musical phrase is completed in another, just as the vocative is fulfilled only when someone turns round.

R8. The cry. This recipe works weight and fall, and the lament as a figure, and a descending second and breath are enough for it. A descending minor second is sung with the weight on the first note, three times, each time heavier. It is sequenced downward by step until it forms a lament of four sighs. A chromatic descent is placed beneath it in the bass, the lament bass. Over that bass a quejío is improvised, a held note that breaks and falls. The examples are Dido’s lament and a siguiriya. The exercise asks the student to compose a four-bar lament from a single sequenced sigh, and then its opposite, a four-bar call from a single leap. In R8 the Inclination appears in its barest form, because the descending minor second is literally a balance that gives way, and the student who loads it three times with weight learns that musical grief consists in a support that cannot hold.

R9. Silence as gesture. This recipe keeps the body engaged through the rests, so that silence is held instead of being dropped, and it works with a phrase that has them. The phrase is conducted including its rests, and the arm, far from stopping in them, sustains them. Then it is played with all the rests doubled, without letting go of the tension. Then with all the rests halved. At the end it is played as written, and the rests have become gestures. The examples are the silences in the first movement of Beethoven’s Fifth, or the remate of a bulería, which ends on a stop the body continues. The exercise consists in improvising for one minute in which the rests last longer than the notes. A held silence is an Inclination without sound, a support sustained in the air, and it is also the Toward at its severest test, because the direction that survives the absence of notes proves that it never depended on them.

R10. Laban’s four questions. This recipe gives a vocabulary for the character of any phrase and a way of changing it, and it works with a phrase and the four factors of movement, weight, space, time and flow. One decides the weight, space, time and flow of the phrase, and names its effort, glide, press, flick and the rest. It is played in that effort, exaggerated. Then it is played in the opposite effort, a glide turned into a punch, a float turned into a press. On returning to the first, that first will have changed. The example is a Dorian melody played as glide, then as punch, then as glide again. The exercise asks the student to record the same two-bar motive in all eight efforts and to choose two for a piece in which the motive changes character halfway through, which is procedure 39, thematic transformation, reached by way of the body. Laban’s four factors distribute themselves naturally over the strata of the loom, weight belonging to the Flesh, flow, bound or free, measuring how much the body yields and so belonging to the Inclination, and space and time, direct or flexible, sudden or sustained, giving shape to the Toward.

R11. Speak it. This recipe finds the accent and the phrase from the sentence, and it works with a phrase that has a text, or with a phrase and an invented text. The text is said as one speaks, naturally, several times. Its rhythm and its curve of declamation are notated, gesture G24. It is compared with the melody, asking where the melody obeys it and where the melody resists it. Then the phrase is played following the speech, and afterwards following the resistance. The examples are the opening of “Der Lindenbaum” spoken and then sung, or the text of a saeta first said and then hurled. The exercise asks the student to take the melody of the day, write a sentence beneath it and revise the melody until the sentence can be spoken in its rhythm. With R11 the recipes for gesture return to the léxis, to the saying that calls before it signifies, and close the circle that step zero opened, because the spoken phrase, the sung phrase and the played phrase turn out to be three bodies of a single saying, and the lesson that runs through them in that order has given back to the instrument the voice it came from.

IX. Compositional recipes. How making transforms

The sixty procedures of the catalogue return here under their own numbers, and each brings what a workshop asks for, a purpose, materials, a sequence of gestures, an example and a task for the student. All of them start from the same prior step that already governed the recipes of the body. The melody is sung before it is written, and only what one already knows how to sing gets written down. The rule looks obvious and lessons break it almost every time. Amalia Casas-Mas, Guadalupe López-Íñiguez, Juan Ignacio Pozo and Ignacio Montero watched instrumentalists closely while they learned, and found that singing appeared in practice and in the lesson far less than one would expect, and hardly ever as a tool for thinking the phrase or for feeling it in the body. A procedure applied to a melody nobody has sung transforms signs on paper. Applied to a melody that has passed through the throat it transforms a voice, and the student hears in their own breath what the line has gained and what it has lost. That difference is the whole reason these recipes are sung first, played at the keyboard second and set on paper last.

1. Augmentation. Augmentation seeks to make the melody feel slower and weightier by lengthening its values without touching the order of the pitches, and all it needs is the original melody with its rhythm and metre notated. One begins by choosing a factor of augmentation, which may be double, triple or one and a half, and is nearly always double. Then every value is multiplied by that factor, so that the quarter note becomes a half note and the eighth a quarter. Once this is done the proportions of the phrase need watching, because a lengthened phrase easily runs out of air, and if it stretches too far one opens breathing points in it or subdivides the beat with sustaining accompanimental textures. The tempo asks for a decision of its own. You can keep it the same, and then the piece grows longer, or change it so that the augmented melody fits the duration you wanted. Long durations often call for a harmony to hold them up, pedal points, sustained chords, passing harmonies, and finally one notates the dynamics and articulation that keep the shape of the phrase despite the slowness. A four-bar melody in eighth notes thus becomes eight bars of quarter notes, and an organ pedal under sustained chords gives it ground. The student’s task is to take an eight-bar folk song, augment it by two and compose a four-bar accompaniment that keeps the interest alive beneath the lengthened melody.

The loom of melos, as it was strung at the beginning of these pages, crosses three threads, léxis (λέξις), the saying that calls before it says anything, harmonía (ἁρμονία), the fitting together and the gravitation of sounds, and rhythmós (ῥυθμός), the shape of what flows, with three strata, the Flesh, which is breath, weight and the gifts nobody chooses, the Inclination, the instant in which something gives way toward something, and the Toward, pure direction. Augmentation looks like an operation of rhythmós and nothing more, and yet it is paid for in the Flesh. The breath that sufficed for four bars does not suffice for eight, and whoever sings the augmented melody discovers in the diaphragm that to lengthen a phrase is to ask the body for air it did not have. That is why the breathing points belong to the procedure itself and are no mere retouching of it. On paper augmentation is a multiplication. In the voice it is a trial of the Flesh, and what survives the trial is what truly held the phrase up.

A possible lesson shows this better than any rule. Picture a fifteen-year-old student singing a song from her village with the haste of someone who knows it too well, eight bars in 2/4 dispatched in twelve seconds, with no note weighing more than another. She is asked to sing it again with every value doubled, changing nothing else. Halfway through the third bar she runs out of air, and to reach the end she has to breathe where the song lets her, which turns out to be just before the note that falls by step onto the final of the first line. That note, trampled in the fast version, becomes in the slow one an appoggiatura that leans and yields. The student then returns to the original tempo and sings the song again. She can no longer trample that note. The augmentation has vanished from the surface and has left inside the melody a breath and a weight that were not there before, and that had belonged to the song from the start.

2. Diminution. Diminution wants the opposite, for the melody to feel faster and more urgent through shortened values, and its only ingredient is the original melody. First a ratio of diminution is chosen, a half, a third or two thirds, and the usual one is a half. Then each value is replaced by the next shorter one, the quarter note by the eighth. The new line has to fit the metric rhythm and the harmonic rhythm, and if the harmony was slow it receives passing chords or a more active accompaniment. It remains to decide whether the accompaniment follows the melody, more active, or stays static, setting cross-rhythms against it. Finally the articulation is added, staccato, accents, which lets the line be understood at speed. A chorale line in quarter notes becomes in this way a virtuoso run of eighths, harmonised with passing diminished chords. The exercise asks for a hymn tune diminished by half, with a two-bar ostinato written beneath it that contrasts with the speed.

3. Rhythmic displacement. The aim is to shift the melody in time without changing its durations, to create syncopation or metric ambiguity, and it needs a melody with clear barlines. First the amount of displacement is chosen, a beat, an offbeat, half a beat. Then the whole melody is moved forward or backward by that amount relative to the downbeat. Where notes fall across the barline the bars must be rewritten so that the phrase boundaries make musical sense, with ties across the bar. The harmonic support is then reconsidered, either shifting the chord changes along with the melody or keeping the harmonic rhythm fixed to create tension between the two, and at the end one adds the accents that clarify the new metric emphasis. A melody that began on the first beat thus begins on the “and” of two. The student takes a four-bar phrase and makes three displaced versions, a quarter note forward, a quarter note back and an eighth, notates them and plays them against the original progression.

The loom makes clear why this procedure, so small on paper, changes the character so much. Displacement touches neither a pitch nor a duration, and what it moves is the place where the melody leans, so that it works at the crossing of rhythmós with the Inclination. Each note remains the same, yet it yields toward another place, and an appoggiatura that fell on a strong beat now falls in the air, suspended, with no ground to rest on. The ear feels it as syncopation. The body feels it as a foot that looks for the floor and fails to find it where it expected.

4. Proportional and irrational changes. This recipe alters the proportional relationship between the parts to create a complex rhythmic interlocking, and it asks for a melody and an accompaniment or a second voice. First a proportional scheme is decided, three against two, five against four, seven against eight. The main melody is notated in its original metre, and the altered part with tuplet brackets that show the ratio. The exact durations are calculated before playing, so that in 4/4 with a proportion of three against two you will write triplets spanning two beats while the other part moves in duplets. It is rehearsed slowly, with a click, until the alignment points are secure, and periodic alignment points, every two to eight bars, are used so that the listener can anchor. A vocal line in 4/4 can thus run while the piano plays a repeating figure in a proportion of five against four. The exercise is to compose eight bars in which melody A repeats every bar and melody B completes its cycle every five quarter notes at the same tempo, marking the bars of alignment.

Those anchoring points now have an empirical foundation. Nori Jacoby and Josh McDermott asked listeners from very different cultures to reproduce random rhythms, and then to reproduce their own reproduction, again and again. Within a few rounds the rhythms drifted toward simple integer ratios, and although each culture preferred a different set of ratios, all of them pulled toward the simple proportion. The irrational proportion works against that gravity of the ear, which is why it needs the alignment points. Without them the listener cannot hear two cycles crossing and hears only disorder, and the interlocking dissolves into noise.

5. Transposition. Moving the melody intact to another pitch level asks for the melody and the key or centre of arrival. The interval of transposition is chosen and added to each pitch, thinking in pitch classes or in intervallic relations. The ranges are then reconsidered, because the new pitches have to be playable and singable, and if necessary the octave is changed. The accompaniment is adjusted to the new key. If what you seek is a change of colour, consider modal transposition, which keeps the accidentals and so changes the character. A folk melody in G transposed up a minor third to B flat settles into another range. The student takes a short melody, writes three transpositions, a second up, a fourth down and a minor sixth up, and plays each with a different timbre.

6. Inversion. Inversion mirrors the intervals, so that ascending ones become descending and the reverse, and it asks for the melody in its scale context. First an axis is determined, nearly always the first note or the tonic, and the direction of each interval is inverted around it. For a strict inversion the exact size of the intervals is kept, and for modal colour changes of quality are allowed by ear. The coherence of the contour is checked afterwards, smoothing large leaps with changes of octave. Finally the harmony is adjusted, because the inverted melody may call for reharmonisation or for a modal reinterpretation. C and E, a rising major third, inverted around C give C and A flat, a falling major third. The task asks for a four-bar theme inverted around its first note, and then for the inverted line to be reharmonised.

7. Retrograde. Writing or playing the melody backwards requires the complete melody in notation, because memory runs forward and the voice alone hardly knows how to run the other way. The notes are written in their order and the order is reversed, so that the last pitch becomes the first, keeping the durations in the correspondingly reversed order. Then the punctuation of the phrase is checked, because retrograde often creates awkward cadences, and link bars are added or durations adjusted. Stretches where the harmonic motion no longer fits are reharmonised. A, B, C, D becomes D, C, B, A. The exercise takes a chorale phrase, retrogrades it and glues it to the original, so that it reads forward and backward, and then reharmonises the retrograde.

8. Retrograde inversion. This recipe combines the two previous operations on the melody. Inversion and retrograde are carried out in whichever order one likes, because the result is the same, and one obtains the pitch series inverted and at the same time turned backwards in time. The rhythms may be reversed too, or keep their original order for contrast, and the student states which was chosen. Finally the harmony and the register are reworked so that the result is playable. The exercise asks for a short fugue subject, its retrograde inversion, and the use of that retrograde inversion as the answering voice.

9. Modal mutation. Mutation keeps the melodic contour and changes the modal surroundings, and it asks for the melody and a list of possible modal frames. First the degrees on which the melody leans are identified and the target mode is chosen. Pitches that clash with it are adjusted, preserving the contour as far as possible. Cadences and leading notes have to be reinterpreted, because some modes lack a leading note and their cadential gestures must be rethought from within. When reharmonising for the mode, drones and modal harmonies nearly always work better than functional progressions. A folk melody in the major is resettled in Dorian simply by lowering the third. The student rewrites a simple melody in three modes, Dorian, Phrygian and Aeolian, and observes how the character changes.

Another possible lesson. A twelve-year-old boy, asked for a song he knows, sings a children’s melody in the major that climbs by step to the third and stays there, content. He is asked to sing it again with that third lowered a semitone, and nothing more. At first he sings out of tune, because the throat looks for the usual note, and the second time he finds it. He expected the song to turn sad. It has turned old instead, as though it had stepped back several centuries, and the note that was a place of arrival has become a note that asks to go on. He himself, without anyone suggesting it, lengthens the lowered third and lets it fall to the second. That gesture, which nobody taught him, is exactly what distinguishes one mode from another, the note where the melody yields. The boy has learned Dorian in the only place where it is truly learned, at the precise point of his own song where the mode changed the gravity.

10. Contour elaboration, or fioritura. Fioritura adds ornaments, turns and passing notes to adorn a skeletal melody, and it asks for the skeletal line with its chord tones marked. First the structural tones are identified, the strong beats and the cadences. Between them the ornaments are inserted, passing notes, appoggiaturas, neighbour notes, mordents, trills, grace notes. The dialect is respected, because Baroque diminution and the bebop approach note belong to different dialects even when they perform the same operation. The logic of the phrase is preserved, since the ornament is there to clarify the structure, and the structure is covered over as soon as the ornament forgets it. Everything is notated clearly, with standard symbols or with small notes. C, E, G thus becomes C, D, E, D, E, G, with passing notes and a turn. The student creates three ornamented variants of a two-bar theme, one Baroque, one Romantic and one in jazz style.

The tables of Ganassi and of Ortiz, which offered for each interval a menu of ways to divide it, are this recipe printed almost five hundred years ago. And the loom says something those tables leave unsaid. The ornament works at the crossing of léxis with the Inclination. An appoggiatura heard as the imperative hidden in its name, lean, is a way of addressing the next note, a saying before the said, and so the well-made ornament sounds like the voice leaning toward the note that matters and naming it as it leans on it, with nothing in it heard as decoration laid on top.

11. Motive fragmentation. The aim is to extract a small cell, of two to five notes, and use it as a brick, and the ingredient is the original melody. First the motives are identified, short recurring patterns or intervallic cells, and the shortest useful cell is extracted. Then variants are created by repeating it, sequencing it, inverting it, augmenting it, shortening it. The cell can serve as ostinato, as accompaniment figure or as generator of new lines, and with it alone one builds episodes that unify the piece. Beethoven’s Fifth opens with a four-note cell used everywhere. The exercise takes a two-note cell from a melody and writes an eight-bar development using only that cell, varied in rhythm, register and harmony.

12. Internal expansion. Internal expansion lengthens the melody by adding material inside it and leaving its ends intact, and it asks for a melody with a clear midpoint. A logical point of insertion is identified and material is created that follows the melodic logic while increasing complexity, a sequence, a contrasting episode, a modulation. That material is inserted with transitions, pivot chords, linking motives, elisions. The form is then rebalanced, and if the insertion breaks the symmetry the later sections are adjusted. The connective tissue, slurs and dynamics, is rehearsed until it runs smooth. A four-bar phrase thus receives in its middle a two-bar insert of sequenced fragments. The task asks for a two-bar sequence inserted in the middle of a four-bar theme, so that the new phrase has six, and for the linking harmony to be notated and played.

13. Extension. Extension lengthens a phrase by adding bars at the end, and its ingredient is a phrase with a cadence. First the type of extension is decided, prolongation, extension with modulation or cadential elaboration. Then cells derived from the end of the phrase are added, repeating the final motive, sequencing it or setting an ostinato beneath it. Tension and resolution call for care, with a deferred cadence or with a final cadence stronger than the first. The phrasing is rebalanced so that the extension feels earned, and the instrumentation can bring it forward. A two-bar cadence becomes four by repeating the last bar with an added chromatic bass line. The exercise extends the final phrase of a short melody by four bars using sequential diminution.

14. Elision. Elision overlaps the end of phrase A with the beginning of B to achieve seamless continuity, and it asks for two adjacent phrases. The end of A and the beginning of B are identified and the length of the overlap is decided, a beat, a bar. B begins before A ends, tying or sustaining what is needed, and the harmony is planned so that the overlap is coherent. Elision serves to quicken momentum or to disguise cuts in the form. The singer begins phrase B on the last syllable of A while the accompaniment holds the harmony of A. The student creates a two-phrase song in which the second begins two beats before the first ends, notates the elision and performs it. In the loom elision is the Toward in its pure state, a phrase that starts to go forward before it has finished arriving, and that is why ancient rhetoric called it anadiplosis, the ending that turns into a beginning with no pause between the two.

15. Melodic paraphrase. Paraphrase rewrites the melody keeping its identity and changing the details freely, starting from the original melody. First one finds its core identity, contour, characteristic intervals, rhythm. Then the surface elements are changed, rhythms, ornaments, a few pitches, while the contour is kept, and enough reference points are left, such as the opening interval or the cadence, for the melody to be recognised. The result is reharmonised and reorchestrated for its new context, and the student decides the degree of freedom, from light paraphrase to free. A hymn tune can be recast in this way until its melody becomes an instrumental fantasia. The exercise paraphrases a well-known lullaby until it turns into a sixteen-bar piano interlude with new harmonies.

This recipe is older than the writing that describes it. Leo Treitler showed that plainchant was handed down for centuries the way Homeric verse was, by the reworking of formulas that kept the identity of each chant and let its details move in every mouth. A singer who paraphrases does what every singer did before the score promised that a melody could stand still.

16. Melodic variations. Here a series of variations is created, each underlining a different parameter, and the theme is enough. A parameter is chosen for each variation, melody, rhythm, harmony, texture, timbre, so that the first variation works on ornamentation, the second on a rhythmic reworking, the third on a reharmonisation, the fourth on a change of texture and the fifth on a change of timbre. Phrase lengths are kept comparable, or deliberately altered for contrast. A unifying element, a bass ostinato or a recurring interval, runs through them all, and the series ends with a variation that restores the theme or transforms it decisively. The exercise asks for four eight-bar variations on a simple melody, each centred on a different parameter.

17. Harmonic variations. These variations keep the melody and change the harmony, and they ask for the melody and its chord map. First the original progression is aligned with the notes of the melody. For each chord possible substitutes are considered, diatonic substitutions, secondary dominants, modal interchange, tritone substitution, quartal harmony. If needed, passing chords are added to support the new voice leading. One must check that the melody notes still fit, or that they clash on purpose and resolve, and the cadences are revised because the new plan needs its own cadential logic. I IV V thus becomes I ♭VII IV V, by modal interchange, or a jazz I vi ii V. The student reharmonises an eight-bar melody in four ways, diatonic, jazz with ii V, with modal interchange and with chromatic mediants.

18. Rhythmic variations. These variations change the character of the melody by altering its rhythm and keeping its pitch profile. A strategy is decided, syncopation, augmentation, diminution, hemiola, and it is applied across the whole melody, tying notes or changing the groupings where the phrasing suffers. If the melody is syncopated, the offbeats are accented and one considers syncopating the accompaniment as well. The notation is handled with care, with ties and tuplets, and the prosody is weighed at the end, because rhythmic changes must respect the text if there is one. The exercise creates a purely rhythmic variation of a four-bar melody using only triplets and syncopations.

19. Textural variations. What changes here is the way the melody is presented in relation to its accompaniment, and one needs the melody and several accompaniment options. Textures are chosen, melody with block chords, melody with counterpoint, melody embedded in arpeggios. Accompanying parts are created that follow the melody or contrast with it rhythmically. If the texture is contrapuntal, at least one countervoice is written that complements it and avoids parallel fifths and octaves, except where the dialect wants them. Density is controlled through orchestration, and changes of texture serve to mark off sections or underline climaxes. A copla can be presented as solo voice with guitar and its refrain in four parts with a countermelody. For a sixteen-bar melody the student writes three versions, with arpeggiated accompaniment, in two-part counterpoint and in a dense texture of clusters.

20. Timbre variations. Presenting the melody again with other instruments reframes its meaning, and for this one needs the melody and a list of instruments. The instrument that carries the melody in each variation is chosen and the register is adapted to that instrument’s best tone, which sometimes forces a transposition. Articulation and dynamics are adjusted to the timbre, and contrasting accompaniments set it off. With electronic timbres one designs filters and envelopes that support the phrasing. The same melody sounds intimate on a solo soprano saxophone, heroic in a brass fanfare, ambient on a synthesizer pad. The exercise arranges a sixteen-bar melody for three different ensembles and notes how the character changes.

21. Structural variations. These variations change the macroform by reordering sections or phrases, and their material is the sections A, B, C and whatever others there are. The sections and their functions are identified and new orders are proposed, ABA, AAB, ABCBA, or everything is broken into shorter cells. Linking devices are created, modulations, bridging motives, so that the reordering seems natural. The listener’s expectation counts, because reordering can surprise, and that surprise serves narrative turns. The transitions are notated and rehearsed until the flow is confirmed. The student takes a thirty-two-bar song, produces three different formal plans, strophic, rondo and arch, and realises one of them.

22. Modal or scalar variations. Here the melody is expressed anew in other scale systems, and one needs the melody and the target scales or modes. The new scale is chosen, pentatonic, whole-tone, from the family of a raga. The core degrees of the melody are projected onto it, choosing the nearest ones to preserve the contour. Where notes fall outside the scale they are replaced, or kept as expressive passing notes foreign to it. The ornamentation is adjusted to the new scalar grammar, and if there is harmonic support the melody is reharmonised. The exercise turns an eight-bar major melody into whole-tone and pentatonic versions and observes which intervals change most.

23. Writing episodes between two melodies. This is the recipe that creates connective material to link two different melodies or sections, A and B. First the harmonic and pitch relationship between them is identified, and the function of the episode is decided, to modulate, to contrast or to pass across by sequence. The techniques are several. A fragment of A can be sequenced while the material of B is gradually introduced, an ostinato can be laid under changing harmonies, an interlude of pure texture can be opened, or a pedal that eases the change of key. The length is kept in proportion, and the episode ends on a pivot chord or a common tone that prepares B cleanly. A four-bar sequence of A can thus climb by diatonic seconds until it reaches the centre of B. The task asks for a six-bar episode that modulates from C major to A minor, using a fragment of A gradually transformed into the opening interval of B.

24. Sequence. Sequence repeats a motive at successive pitch levels, and it asks for the motive and a sequence scheme. The type is chosen, tonal, which stays within the scale, real, which transposes the intervals exactly, or rhythmic. The interval of each step and the number of iterations are decided. In tonal sequences the accidentals are adapted, and in real ones the intervals are kept and the harmony altered accordingly. The harmonic support may demand chromatic or modulating chords, and the culmination of the sequence serves as a point of arrival or as a means of modulation. The exercise creates a four-iteration sequence of a two-bar motive that modulates from G major to B minor.

25. Pedal-point transitions. A sustained pitch anchors the music and makes modulations or unifications of texture possible, and the ingredient is the pitch chosen as pedal. You choose the note you will sustain, tonic, dominant or common tone, and hold it in the bass or in an inner voice through the changing harmonies. Above it you compose harmonies that create tension and colour while the pedal stays constant. The pedal also works as a pivot, the common note reinterpreted as a different degree in the new key, and at the end it is released with a cadential gesture. The student writes an eight-bar passage that uses a pedal on G to travel from C major to E minor.

26. Layered additive construction. A piece is raised by adding layers little by little over a foundational cell, which is an ostinato. First a short ostinato is created, of one to four bars. One starts with that single layer and adds a new one every one to four bars, varying orchestration and register to keep clarity. Subtraction belongs to the procedure, and taking layers away gives relief. The long-range points of arrival are calculated in advance to avoid monotony. In the manner of the gamelan, the colotomic gongs enter first, then the metallophone motive and then the melody. The exercise builds a thirty-two-bar piece from a two-bar ostinato, adding a layer every four and aiming for three climaxes.

27. Canon. Canon uses strict imitation at a fixed time interval between voices, and it asks for a short subject, the number of voices and the interval of imitation. The subject is written, short and clear, and the time distance of the imitation and its pitch interval are decided. The following voice copies the subject exactly in strict canon and admits small alterations in free canon. Consonance between overlapping notes is checked note by note, and the subject is adjusted if harmful dissonances appear. In long canons episodes are designed in which the canon halts or transforms. The student composes a three-voice canon in which each voice enters every two bars at the octave.

28. Hoquetus. The hoquetus shares a single melodic line among two or more voices to create rhythmic interlocking, and it needs a melody divisible into cells of sound and silence. The short notes and rests that can alternate are identified, and alternate notes are assigned to voices A and B so that together they produce a continuous line. The rests of one have to coincide with the sounding of the other, and the ranges are kept comfortable. Timbral contrast heightens the interlocking, and if the procedure is extended to many voices the patterns are planned to avoid clutter. The exercise takes an eight-bar melody and creates a two-voice hoquetus in which each voice plays every other eighth note.

29. Countermelody creation. Inventing a complementary melody that supports the main one and contrasts with it asks for the main melody and its harmonic map. First its strong tones and its cadences are analysed. Then a counterline is sketched that avoids perfect parallels and offers contrary or oblique motion, with thirds and sixths for consonance and seconds and sevenths for tension where tension is wanted. The rhythm is varied to give independence, and the resolutions of the dissonances are tested and adjusted until everything is clear. The student composes a sixteen-bar piano countermelody beneath a given sixteen-bar vocal melody.

30. Free imitation. Free imitation imitates a fragment at varying intervals and rhythms, to give cohesion without the rigour of canon, and it starts from a characteristic fragment. The motive to be imitated is chosen and imitated at different pitch levels, often transformed. The entries are staggered unpredictably to create an imitative texture, the intervals are kept small at first and widened later, and the imitation serves to unify sections or to develop. The exercise creates a twelve-bar passage in which a three-note motive is imitated by three voices in free imitation.

31. Invertible counterpoint. This recipe exchanges melodic material between voices, so that the upper line becomes the lower, and it asks for two or more lines. The lines to be inverted are identified and each is written in the register of the other, adjusting octaves for performance. The voice leading is smoothed, with passing notes if needed. The harmonic implications must still work, and one has to foresee that a fifth becomes a fourth when inverted at the octave. The exchange serves to underline thematic transformation. The exercise inverts the soprano and bass of a four-part chorale and corrects the resulting voice leading.

32. Drone-based elaboration. Creating melody over a continuous drone asks only for the pitch or pitches of the drone. The drone and the way of sustaining it are chosen, and a melody is composed that underlines the notes related to it, with strategic consonances and dissonances. Modal scales that work with the drone are the natural ones here, and above it slow changes of harmony or colour may be added, with an ornamentation that refers back to its pitch. The Scottish piobaireachd, with its long drones beneath the theme, is the great example. The student composes a sixteen-bar melody over a sustained drone on D, underlining the modal cadences.

33. Modal pivoting. Modal pivoting passes from one mode to another through shared pitches or pivot chords, and it asks for two modes with pitches in common. A common note or triad is identified and a pivot region of one to four bars is inserted that underlines it through a pedal or a repeated motive. The characteristic degrees of the new mode are introduced gradually, the passage is reharmonised to support the new modal centre and the new cadential logic is confirmed. The exercise writes a twelve-bar passage that begins in G major and pivots into G Mixolydian.

34. Reduction to the harmonic skeleton. The melody is reduced to its harmonic skeleton so that the skeleton can serve as the basis for new textures. First the strong degrees falling on strong beats are extracted and projected onto a progression or a harmonic skeleton. The skeleton is then used as a foundation, to reharmonise, to create counterpoint or as a bass line. Afterwards it is expanded again with passing notes, suspensions and an ornamentation informed by it, and it serves to recompose variations and episodes. The student reduces a melody to six skeletal points and writes over them a four-part choral texture.

The Neapolitan conservatory travelled this road in the opposite direction. The partimento gave the student the skeleton, a bass sometimes figured and sometimes bare, and asked for the flesh, the upper voices, the imitation, the diminution, and Robert Gjerdingen has shown that those basses stood at the very centre of the composer’s training, far above the rank of one harmony exercise among others. Vasili Byros has since followed how the partimento served as a bridge toward free composition, so that the same skeleton could grow until it became a prelude. Reducing and realising are one procedure travelled in both directions, and whoever can do both knows what holds a melody up and what adorns it.

35. Ground-bass rewriting. The aim is to keep or change the ostinato bass while changing the melody, or to reuse the bass as a new foundation, starting from the bass pattern. First one decides whether to keep it, adapt it or create a new one. If it is kept, contrasting melodies are composed above it that explore registers and timbres. If it is adapted, its rhythm or contour is slightly altered at each repetition to give forward motion. Harmonic variation over the static bass sustains interest, and the series ends with a variation that brings the bass to a cadence. The exercise takes a well-known ground and writes five contrasting melodic treatments over eight repetitions.

36. Registral shifts. The same idea is presented in different octaves or registral zones, and one needs the melody and the orchestration. The target registers are chosen and the melody is transposed to each, weighing their timbral implications. The shifts serve drama, like a melody that rises through the orchestra toward the climax. Articulation is notated according to register, and the shifts are combined with dynamics. The student arranges a sixteen-bar theme that climbs in register every four bars, from the low strings to the piccolo.

37. Density shaping. Changing the number of sounding voices controls intensity, and the material is the parts of the ensemble. A density curve is planned, sparse, medium, dense, sparse. Voices are added in stages, first harmonic, then contrapuntal, then percussive, and orchestration governs the perceived density. Dynamics and articulation underline the change, and the voice leading of the inner parts is looked after as density grows. The exercise sketches a twelve-bar passage with a density crescendo that runs from monody to five independent voices.

38. Contour and dynamic archetypes. This recipe shapes the overall expressive contour through archetypal arcs, and it asks for the complete formal plan. The archetype is chosen, the wave, with rise and fall, the terrace, with sudden steps, or the spiral, with continual ascent. Changes of dynamics and register are mapped onto it across the sections. Harmonic intensification goes with it, with more dissonance at the peaks and consonance in the rests. Texture and timbre are aligned with it, the peaks with the full ensemble, the troughs with solo lines. Thematic coherence is kept by bringing motives back at corresponding points. This is the procedure that the jo-ha-kyū of nō raises into the principle of an entire form. The student composes a twenty-four-bar wave piece in which each cycle lasts eight bars, and ties the motives to the peaks.

39. Thematic transformation. A single theme is transformed into different characters through interval, rhythm, harmony and orchestration. First its salient features are identified. To make it heroic the intervals are widened, the theme is augmented, strong accents are added, and brass and low strings are used. To make it intimate the intervals are compressed, and it is played legato, in a high register and with a sparse accompaniment. To make it grotesque the rhythm is displaced and chromatic harmony, percussive articulation and altered timbres are added. In every case a small cell is kept, so that the transformations are heard as related. The exercise takes a four-bar theme and writes three contrasting transformations, lyrical, martial and grotesque.

40. Motivic saturation. Here many textures and sections are built from the repeated use of a single cell, a motive of one to three notes. A motive with a clear shape is chosen and the whole piece is saturated with it, melody, bass, accompaniment, rhythm, ostinato. Its presentation is varied with augmentation, diminution, inversion, sequence and change of timbre. The large sections are built by layering several treated versions, and the piece culminates with all the voices stating the motive at once in varied forms. The student composes a thirty-two-bar piece in which every bar contains a variant of the chosen motive.

41. Intervallic recomposition. Intervallic recomposition keeps the interval relationships and changes rhythm and contour, preserving the intervallic DNA of the melody, starting from its original intervals. The series of intervals is notated and applied again with different rhythmic values, articulations and starting pitch. The octave is changed where needed to avoid awkward leaps, keeping the size of the intervals. The result is reharmonised to bring out the new contours, and it is used in counterpoint or as a new theme, recognizably related by interval. The exercise takes a melody and writes another with the same exact series of intervals, with a completely different rhythm and starting pitch.

42. Hybrid melodic grafting. A new melody is created by grafting parts of two or more melodies, A and B, or their fragments. The source fragments and their order are chosen. Centres and keys are checked, and the material is transposed so that it connects smoothly, or so that it clashes on purpose. The joins are smoothed with passing notes, pivot chords or shared rhythmic links. One decides whether the grafts keep their texture and timbre or contrast them, and if thematic integrity is needed one or two pitches are retouched at the graft points. The verse of a folk song and the bridge motive of a hymn can be fused in this way into a new art song. The student chooses two melodies and grafts the first four bars of A, the next four of B and the cadence of A, making the transitions natural.

43. Repetition, the zero degree. This recipe discovers what exact repetition does, and how little needs to change for it to become variation, with a one-bar cell as its only material. First the cell is repeated exactly eight times, noticing where the ear begins to invent differences. Then it is repeated sixteen times, changing one parameter each time, register, dynamics, articulation, accompaniment, and always leaving the cell intact. Finally one returns to exact repetition, which is now heard as a gesture. The exercise composes sixteen bars in which a one-bar cell is repeated without change and only what surrounds it moves, which is the lesson of Ravel’s Boléro.

The loom explains why the third phase sounds different from the first although the notes are identical. Repetition belongs before anything else to léxis, to the saying that calls. A repeated call addresses someone again, and whoever calls twice does not say the same thing twice, because the second call knows that the first was not enough. Music, which is vocative before it is representative and calls before it says anything, has in repetition its purest form of insistence. That is why the ear invents differences where there are none. It invents them because it hears someone calling again.

44. The sentence, 2 + 2 + 4. The sentence builds an eight-bar phrase from a two-bar idea through a repeatable algorithm, and its ingredient is a two-bar basic idea. The idea is invented. It is repeated on the dominant, or a step higher, or exactly the same. Only its first bar is taken and stated twice, faster, or sequenced. The last two bars cadence. Then the whole is sung, and if it does not breathe in 2 + 2 + 4 the continuation is adjusted and the idea left as it was. The theory belongs to Schoenberg and to Caplin, who described the sentence in the Classical repertoire, and the instinct is far older than its theory. The exercise asks for three sentences from the same basic idea with three different continuations, by fragmentation, by sequence and by liquidation.

45. The period. The period makes a phrase ask and answer, and it asks for four bars that do not land. A question is sung, four bars that end far from the final. Then the same opening is sung and made to land. The interior of the consequent is changed so that it does more than copy, and both are notated. The exercise looks for five consequents to one antecedent, each reaching the final by another road.

46. Liquidation. Liquidation dissolves a motive into a transition by stripping it of its features, and it asks for a motive with identifiable features. Three of them are identified, a leap, a dotted rhythm, a chromatic note. The motive is repeated with one feature removed each time, and the remnant that is left becomes the cadence or the ostinato of what follows. The name is Schoenberg’s, who saw in this operation the most elegant way of building a transition. The exercise liquidates the melody of the day in four steps and uses the remnant as the left-hand ground for the following section, so that the liquidation also works as an episode.

47. Fortspinnung. Fortspinnung continues a phrase by spinning out its tail where an answer would have come, starting from a two-bar opening idea. The idea is stated, its last beat or its last motive is taken and sequenced by step or by fifth three times, and then the phrase cadences. The length of the spinning is varied afterwards, two sequences, then five, to hear how the proportions change. Wilhelm Fischer named the Baroque triad of opening idea, spinning out and epilogue, and the recipe is that triad turned into a workshop. The student spins a two-bar idea out to twelve bars twice, once by descending fifths and once by rising steps.

48. Cadential deferral. Denying the cadence makes the true one weigh more, and to practise it a phrase approaching a cadence is enough. You approach it, and at the moment of arrival you replace the tonic with the sixth degree, or start the last two bars again, or hold the dominant under a trill. You do this twice at most, because the third time you have to pay. Then you listen to how the weight of the true cadence has changed. The exercise writes four endings for one phrase, deceptive cadence, cadence evaded and repeated, prolonged dominant and true cadence.

In the loom deferral happens at the crossing of harmonía with the Inclination. The Greek word for the Inclination is rhopé (ῥοπή), the tipping of a balance, the instant in which it gives way. The cadence is that instant, and deferral consists in loading one pan without letting the other rise. Each denial adds weight to the side that has not yet given way, and when the balance finally tips it does so with everything accumulated. That is why the rule of twice obeys the physics of the balance before any courtesy. The third time the balance can no longer hold, and if the cadence still fails to come the listener stops believing in it.

A third possible lesson. A seventeen-year-old student sings a melody she improvised that same morning, eight pretty bars that end too soon, on the tonic, at the expected hour, and nobody would miss them. She is asked to sing it again and, on reaching the last bar, to sing the note above in place of the final, the sixth degree over which the harmony would break. She does so and laughs, because the melody has been left hanging and her whole body asks to go on. She is asked to take up the last two bars again and refuse once more, this time sustaining the note before the final until her air runs out. The third time she reaches the tonic without anyone asking her to, more slowly, more quietly, and the final note, which in the first version was a formality, now sounds like a home. Nothing in the melody has changed except its ending, and the whole melody seems another, because every earlier bar now knows that the ending cost something to reach.

49. Heterophony. Heterophony sounds several simultaneous versions of one melody, and it asks for two or more performers and a melody. One plays it plain and another ornaments it. Then both ornament, each differently. A third plays only the skeleton, and the roles are exchanged at every phrase. The exercise sets up a sixteen-bar heterophonic trio on a folk song, with skeleton, plain version and ornamented version, rotating the roles afterwards.

50. Parallel doubling. A melody changes century or continent according to the interval at which it is doubled, and the only ingredient is a melody. It is doubled at the fifth from beginning to end, then at the fourth, the third, the sixth and the second. At the cadences the doubling is allowed to break into oblique or contrary motion, and that gesture travels in five minutes the historical road from organum to counterpoint. At the end you choose the interval that gives the melody the dialect you want. The exercise writes five doublings of the same melody and names the tradition each one evokes.

51. Isorhythm. Isorhythm lets accent emerge from the drift of two cycles, with nobody composing it, and it asks for a short series of pitches and another of durations, of coprime lengths. Five pitches and three durations are chosen. The pitches are written cyclically over the durations, also cyclically, until the two series align again, which happens at the fifteenth note. A drone or a second voice in another cycle is added, and one listens to where the accents fall, accents nobody composed because they emerged by themselves. The task is a two-voice piece in which the bass has a talea of four and a colour of six, and the upper voice a talea of three and a colour of five.

52. Permutation and rotation. This recipe generates material by reordering what already exists, with nothing newly invented, starting from a four-note cell. Its four rotations are written and sung, keeping those that preserve a recognizable contour. They are chained so that each differs from the previous one by a single swap of adjacent notes, which is the plain hunt of the English change ringers, whose technique was already in print in 1668. Then everything is played over a drone. The exercise asks for sixteen bars made only from the rotations of a four-note cell, over a two-note ostinato.

Hindustani pedagogy makes this operation the whole school of improvisation. Emily Sayers has described how musicians in that tradition build the capacity to improvise and compose through memorisation and structured variation, with the palṭā that permute scale patterns and the tān that chain them at speed, and how they almost never ask the student to improvise all at once and out of nothing. There permutation is the road by which freedom is reached, and freedom arrives when the permutation can no longer be noticed.

53. Interval expansion and contraction. The contour is kept and the width is changed, working on the melody of the day. The melody is written as a series of signed intervals. Each interval is replaced by the next larger, the second by the third, the third by the fourth, keeping direction and rhythm, and then by the next smaller. The result is reharmonised. The exercise presents the melody of the day in three widths, diatonic, expanded into leaps and compressed into semitones.

54. Range expansion. Here the range itself becomes form, and a mode and its final are enough. One begins within a third around the final. Each phrase adds a degree, alternating above and below. The octave is touched only once, late, and the return comes by the same steps, faster. The exercise is a two-minute improvisation whose range grows by one degree every eight bars and then contracts in half the time.

55. Hemiola. Hemiola sets three against two at the level of the bar, starting from a melody in 6/8. The melody is written in 6/8. In the bar before each cadence its six eighths are regrouped as three quarters, with accents on the first, third and fifth eighth. Bars of 6/8 and 3/4 are then alternated, and finally superimposed, with the left hand in 3/4 and the right in 6/8. The exercise is a sixteen-bar piece in the manner of a jota in which every fourth bar is a hemiola, sung and walked before it is played.

That “walked” brings the procedure to its place in the loom, the crossing of rhythmós with the Flesh. The written hemiola is a regrouping of eighth notes. The danced hemiola is a body that, for one bar, changes step without losing the ground, and the jota knows it in the feet before knowing it on any paper. The student who walks it feels in the hips what the one who only counts it has to guess, that three against two is a twisting of weight and that the cadence coming after is the body recovering its gait.

56. Compression and expansion of harmonic rhythm. A phrase is driven forward or held back by the speed of harmonic change alone, and the material is a cycle of four chords. The cycle is played at four bars per chord, at one bar per chord and at one beat per chord. Then a phrase is composed that passes through all three speeds on its way to the cadence. The exercise reharmonises the melody of the day with the harmonic rhythm doubling in the last four bars.

57. Metric modulation. The tempo changes by an exact ratio and without a break, starting from a steady pulse. The pulse is established and subdivided into triplets. The triplet becomes the new pulse, with the tempo multiplied by three halves. Later the duple eighth becomes the new pulse, with the tempo doubled, and everything is notated as tempo equations, of the kind quarter note equals triplet eighth. The exercise is a three-section piece whose tempi relate as three to two and as two to one, with no break between the sections.

58. Trope, quotation, contrafact. This recipe writes on top of what already exists, over a known melody. The trope inserts two bars of your own between two phrases of the melody, first in its manner and then against it. The contrafact keeps the changes or the bass and writes a new melody above them. The contrafactum keeps the melody and gives it a new text, a poem of your own. The exercise does all three on one folk song from the small anthology that comes later.

59. The ornamented repeat. The refrain never comes back the same, and to practise this a four-bar phrase is enough. The phrase is played plain. It is repeated with one ornament per bar, and then with two, of another species, turns, then runs, then trills. For the last return it is stripped back to plain, pianissimo. The exercise asks for four returns of a four-bar phrase, each denser than the one before, and then the plain one. Chopin taught the returns of his Nocturne Op. 9 No. 2 in this way, and his students kept in their copies the variants he wrote out for them by hand, so we know that for him each return was an occasion for gloss, with nothing fixed in its text. The last plain return carries behind it all the ornaments that were taken from it, and that is why it weighs more than the first.

60. Soggetto cavato. The soggetto cavato is for beginning when nothing comes to you, by deriving a motive from outside music, and its ingredient may be a name, a line of verse, a birdsong or the outline of mountains. A name is taken. A motive is derived from it by its vowels, with the method Zarlino described, in which a gives fa or la, e gives re, i gives mi, o gives sol and u gives ut, or by its letters, with the German names of the notes. It is given a rhythm drawn from the spoken accents of the name and developed with three procedures. The exercise asks for an eight-bar motive drawn from your own name, its inversion, its augmentation and a sentence built upon it.

Say the student is called Lucía. Her vowels, u, i, a, give ut, mi and fa, C, E, F, and the accent of her name, which falls on the second syllable, turns the C into a short upbeat and the E into a long note on the strong beat, from which the F leaves like a sigh. The student sings her motive and recognises in it, without knowing why, something of the way her mother calls her from another room. The loom says why. This last procedure of the catalogue is the only one born literally from a vocative, because a name is the word with which one calls someone before saying anything to them, and a motive drawn from a name is a call that has found its pitches. Léxis, the saying that calls, has here become melody without passing through any representation. Whoever begins to compose from their own name begins at the beginning, with the call, and everything they later do with that motive, inverting it, augmenting it, building a sentence on it, will still be a way of answering the one who called them.

X. Two specimens

A nocturne and a psalm tone through the three lenses

Two pieces will now pass through the three lenses, and both have been chosen for how much they resemble each other and for how far apart they live. Every pianist has played the first, and almost all of us have played it without anyone asking us a single one of these questions, Chopin’s Nocturne in E-flat major, op. 9 no. 2. The second was written by nobody, it has been sung for more than a thousand years by thousands of throats that could not read music, and it is the eighth psalm tone of plainchant. One belongs to the Parisian salon and the printing press, the other to the choir of a monastery and to memory. What follows, once again, analyses neither of them. It records what a lesson does with them when the lenses are in the room, and what happens when, beneath the lenses, the whole fabric shows through.

That fabric is the loom of melos which was stretched out at the beginning of this essay, beside the sentence of the Republic in which Socrates says that melos is made of three things. Two lines of reminder are enough to set it working here. Three vertical threads run through it, the léxis (λέξις), the saying that addresses someone before it has said anything, the harmonía (ἁρμονία), the fitting and gravitation of sounds that attract one another, and the rhythmós (ῥυθμός), the shape of what flows, the heartbeat, the stride, the breath, the dance. Three horizontal strata cross them, the Flesh, which is the gifts nobody chooses, the face, the breath, the weight, the Inclination, which is the instant in which something yields toward something, and the Toward, which is pure direction, the continuity that has not yet arrived. Nine crossings, nine cells. And one thesis governs the order in which the loom is set in motion, the vocative thesis, according to which music calls before it says anything, just as the vocative case of the ancient grammars calls someone without predicating anything of him. Its founding order is Call, Song, Gesture, Sound, and that order, far more than the convenience of any syllabus, upholds the watchword sing first, keyboard second, paper last. Both specimens fulfil it from their very first instant, because both begin by calling.

The nocturne, the call

Before the score is opened, the student sings the first phrase on a vowel, recipe R5. Yet even before the whole phrase there is a single interval that asks to be sung on its own. The nocturne begins with a leap, the upbeat B-flat rising a sixth to G. The lesson isolates it and sings it five, six times, each time addressed to someone different, to the person on the other side of the room, to someone out in the street, to someone asleep in the next room who must not be woken. That leap is a call, gesture G2, and what the exercise discovers is that Chopin has softened it into a reach. The catalogue says that the call almost always rises a fourth or a fifth, the distance that carries far. The sixth is a call that is already near, one that summons no flock from the far hillside and turns toward a face. It is the vocative of intimacy. Before there is melody, before there is accompaniment, before there is E-flat major, the piece has already called someone, and the student who has sung it in this way will never again play that B-flat as one more upbeat. He will play it like someone uttering a name.

A possible scene shows it better than any explanation. Imagine a seventeen-year-old student who has spent months on the nocturne and plays it cleanly, the left hand well measured and the right correct, and yet the piece never begins, it merely starts. The teacher asks him to get up from the bench and call his little sister, who has stayed out in the corridor, using only those two notes, B-flat and G, without words. The boy laughs, tries, sings it far too loud, like a shout across a schoolyard. The teacher tells him his sister is already three metres away. He sings it again and the sixth changes its weight, the B-flat lengthens, the G arrives softer and stays. Then he sits down and plays the first two notes, and the room hears for the first time that the piece is addressed to someone.

The nocturne, song and gesture

Then comes song. The descent that follows the G is a chain of sighs, gesture G4. Every appoggiatura is a leaning, and the student who has read appoggiare as “lean” plays it otherwise than the one who has read it as “ornament”. Chopin loved Bellini, and the lens makes the reason audible. The nocturne is a cavatina for the right hand, with its messa di voce on the long notes and its coloratura on the returns. The first thing the lesson gives the student, before any fingering, is the knowledge that the right hand is a singer and the left a body swaying beneath it.

And that body is the gesture. The left hand plays bass, chord, chord, in 12/8, bar after bar the same sway, gesture G11. The student sways it in the chair before playing it, and then walks it, recipe R3. It is a barcarolle, or a slow waltz inside a boat. The sway is the ground of the piece and the melody is the figure floating above it, which means that the whole nocturne is the first exercise of the addenda further on, lock the left hand and sing, written by a master. Then the breath. The phrase is conducted before it is played, recipe R1, and the conducting arm finds a swell, gesture G5, that crosses the four bars and falls with the cadence. The hairpins we argue over in the editions are that swell, written down. Between the phrases the silence is held instead of dropped, recipe R9, the upbeat of each return is an intake of breath, recipe R4, and the student who breathes it will not trample it. Only then, when the call has been addressed, the song sung and the gesture danced in the chair, does the sound of the piano arrive, the last of the four and the one that gathers up the other three.

The nocturne, form

Now the student names the archetype aloud. The opening phrase, A, returns three times, between the returns comes a second phrase, B, which leans toward the dominant, and then a coda. A, A, B, A, B, A, coda, the refrain principle, forms 8 and 18, in miniature, or an ornamented strophic form, form 11 and procedure 59, whose strophes last four bars. Chopin does not bring the refrain back the same even once. Each return arrives more ornamented than the last, and of this very piece there survive the variants that Chopin himself wrote by hand into his students’ copies, so that we know he taught the returns as occasions for glossing and that the printed text was for him a point of departure. The form, in other words, is procedure 59 turned into a habit of listening, the refrain that never comes back the same.

The student who knows the archetype now knows where the piece can be played with and where it cannot. Phrase B is the departure, the returns are the refrain, the coda is the place where the piece decides whether it is going to end. We compare it with a da capo aria and with a bandish, whose mukhṛā also returns after each excursion with ever longer tāns. The student has heard two other traditions do what Chopin does, and the nocturne, once filed away as “a Romantic piano piece”, turns into a refrain form in the Parisian dialect.

The nocturne, procedure

At last the student takes the piece apart with the catalogue and puts it back together.

Ornamentation, procedure 10, and ornamented repetition, procedure 59. The student plays phrase A plain, then with Chopin’s first return, then with his handwritten variants, then with glosses of the student’s own in Chopin’s manner, and then with glosses against that manner, bebop approach notes over the sway, the dialect made audible. And afterwards the plain phrase again, pianissimo. The returns are now understood from within, as decisions.

Cadential deferral, procedure 48, and extension, procedure 13. The coda refuses to end. The closing idea is stated twice, the dominant is insisted upon, the unmeasured run is suspended above it, and the last chords are whispered. The student writes three alternative codas for the nocturne, each with a different deferral, and then plays Chopin’s. Its weight has changed because the alternatives exist.

Modal mutation, procedure 9. Phrase A in E-flat minor, sung first and played afterwards. Transposition, procedure 5. The phrase sung in D, in E, in F, to discover what the key does to the voice. Augmentation and diminution, procedures 1 and 2, the melody in 6/8 instead of 12/8, which turns the barcarolle into something closer to a mazurka and shows what the sway was holding up. Fragmentation, procedure 11. The turn of the first bar extracted and made into a two-bar ostinato, over which the student improvises. Reduction to the skeleton, procedure 34. The melody reduced to its structural tones, which uncovers the singer’s skeleton beneath the coloratura and is the best fingering lesson the piece can give. Grafting, procedure 42. Phrase B of this nocturne joined to phrase A of another. The joints teach more than either piece on its own.

The nocturne on the loom

So much for the lenses. Yet everything the lesson has done has its place on the loom, and seeing it changes what has been done. The opening call lives at the crossing of léxis and Flesh, because it is a voice addressed to someone with the air the body has, not a gram more, and that is why the sixth sung by a boy of seventeen and the same sixth sung by a woman of sixty are two different calls on the same two notes. The appoggiaturas of the descent live at the crossing of harmonía and Inclination. They are exactly the rhopé (ῥοπή) of the Greeks, the tilt of a balance at the instant it gives, a note foreign to the chord that leans on it and surrenders, and the student who says “lean” is naming the cell without knowing it. The sway of the left hand lives in the rhythmós of the Flesh, the weight passing from one hip to the other, and the rhythmós of the Toward is the upbeat of each return, the breath already looking to the next bar. The harmonía of the Toward is phrase B, which leans to the dominant and compels the return, and the léxis of the Toward is the coda, which does not want to stop speaking to the one it called at the beginning and so delays its farewell with its suspended run.

Something then comes into view that the lesson was doing without knowing it. The lens of gesture entered the piece through the strata of the Flesh and the Inclination, through breath, weight, sigh. The lens of form travelled it along the Toward, following the returns and the coda. The lens of procedure pulled each thread separately, harmonía in the modal mutation, rhythmós in the augmentation, léxis in the gloss that changes the way the same phrase is said. The three lenses are three ways of walking the same fabric, vertically, horizontally and from knot to knot, and a complete lesson is one in which the fabric has been travelled in all three directions.

None of this takes the place of playing the nocturne. In the lesson template further on it occupies the twenty-odd minutes already shared by the repertoire motive, its improvisations and the repertoire itself, and afterwards the student plays it, once, without comment. The notes are the same. The right hand sings because it has sung, the left sways because the body has swayed, the returns are decisions because the student has made them, the coda ends late because the student has tried ending it early, and the first sixth calls because the student has used it to call someone who was out in the corridor. Technique, style and analysis were all three in the room, and none of them was the subject.

The eighth tone, a formula without an author

The second specimen demands another kind of attention, because there is no score to open. A psalm tone is a formula, a melodic template into which every verse of the hundred and fifty psalms can be poured without the template changing, and whose length the text decides each time. It is form 24 of the catalogue in its historical home, and it is also the purest of the oral traditions that survive within the learned music of the West. Leo Treitler showed that Gregorian chant was handed down for centuries in the way Milman Parry had shown Homeric epic to be handed down, by a singer who learned formulas and rules for applying them and did not memorise each melody note by note. The psalm tone is the extreme case of that economy. No singer ever learned the melody of Psalm 112. He learned the eighth tone and the rules of Latin accent, and with that he had Psalm 112 and all the others.

The eighth tone, sung at the pitch the chant books write, has five members. The initium, the intonation, rises from G to A and from A to C, and is sung only at the start of the first verse, except in the Magnificat and the Benedictus, where it returns in every verse. The tenor, the reciting note, is C, and on that single note are said all the syllables the other members do not occupy, be they three or thirty. The flexa, when the first half-verse is so long that it will not fit into one breath, lowers the voice a minor third from the tenor to A, on the last syllable before the cross with which the psalter marks it, or on the penultimate if the last is unaccented, and returns at once to C. The mediatio, the mid-cadence, closes the first half-verse with a single accent, on which the voice rises from C to D to come back to C, and the asterisk in the text then marks a pause that the choir breathes in full. The terminatio closes the verse with an accent preceded by two preparatory syllables, and in its commonest form, the one the books call 8G, the two preparatory syllables are sung on B and C, the accented syllable falls to A and the last comes to rest on G. There are other terminations, among them one that ends on C, and they are called differentiae because they are chosen according to the note on which the following antiphon begins, so that the end of the psalm is already listening to what comes next.

Applied to the Gloria Patri, with which every psalm of the office ends, the tone does this. “Gló-ri-a” takes the intonation, G, A, C. “Patri, et” is said on the tenor. On “Fí-li-o” the accented syllable rises to D and what remains returns to C, and the asterisk arrives. “Et Spi-rí” is said on the tenor, “tu-i” are the two preparatory syllables on B and C, “Sán” falls to A and “cto” rests on G. Ten seconds of music that have upheld a thousand years of vespers.

The eighth tone, gesture

Here the order of the vocative thesis needs no teaching, because the tone already comes with it built in. The first thing it does is call. The initium, from G to C by way of A, is an ascending fourth that arrives at a note which is going to stay, and that is, to the letter, the catalogue’s definition of gesture G2, an ascending leap of a fourth or a fifth to a held note. The nocturne’s call had drawn near, to the intimate sixth, while the psalm’s keeps the distance of the fourth, the one heard from one side of a choir to the other. The class sings it alone, several times, and the student discovers that an intonation is a summons, that the first verse of the psalm is the moment in which a scattered community becomes a choir.

After the calling comes the singing, and in the tone the song is cantillation, gesture G8, one note to each syllable, the melody led by the text. Before singing it, the class speaks it, recipe R11. The student reads the Latin verse aloud, several times, until his tongue finds the accents, because in the psalm tone it is the accent of the word that decides where the melody bends, and whoever does not hear it in speech will not find it in song. The tenor is the held note, gesture G6, the stillness that makes movements audible, and there the student learns the hardest lesson in all of music, to sustain a single pitch through twelve syllables without letting it grow monotonous, so that life passes through the word while the note stays still. Then the gesture of the body. The class draws the formula in the air with the hand, recipe R2, the cheironomy that singers practised before staffed neumes existed, and the drawing reveals that the formula is almost flat, a plateau with a rise at the start, a slight incline in the middle and a descent at the end. And there is one more gesture, which the liturgy never abandoned, because at the Gloria Patri the monks bow their bodies. In the choir of a monastery the Inclination of the loom is fulfilled to the letter, with the back. Only at the end does instrumental sound arrive. The student plays the formula on the piano with one hand and hears it at last for what it is, a melody that the instrument can repeat and that only the voice knew how to invent.

The eighth tone, form

The form of the tone is the second tetrad of this essay, initium, tenor, mediatio, terminatio, with the flexa as an optional fifth member, a minor articulation that occurs within the tenor and before the mediatio. What the student notices as soon as he sings it is that the flexa is an articulation of the Flesh, because it appears only when the breath falls short, and that the mediatio is an articulation of sense, because it falls where the Hebrew verse split into its two parallel halves. The tone holds two kinds of pause, that of the body and that of thought, and the formula gives each of them its note.

At the scale of the whole psalm, the form is strophic, form 1, the same formula verse after verse, and almost always antiphonal, form 12, because the two sides of the choir alternate the verses and each half rests while the other sings. The antiphon that opens and closes it frames it as a refrain frames a copla, and the differentia is the joint between the two, the way in which the termination of each verse already prepares the return of the antiphon. The student who has sung a complete psalm with its antiphon has sung, without knowing it, a refrain form whose strophes are identical in their melody and different in their text, the exact opposite of the nocturne, whose strophes were identical in their starting point and different in their ornament.

The eighth tone, procedure

Repetition, procedure 43. The tenor is repetition turned into ground, and the class tests this by singing a long verse with all its repeated Cs and listening to how each syllable, even on the same note, sounds different because the word is another. Internal expansion, procedure 12. The tenor is elastic and stretches or shrinks according to the number of syllables, and the student sings the same tone over a verse of four words and over another of twenty, to feel how the template breathes without breaking.

Cadential deferral, procedure 48. The flexa is a cadence that refuses to be one, a fall of a third that promises an ending and returns at once to the tenor. As an exercise, the student takes the second half-verse of the Gloria, “Sicut erat in principio, et nunc, et semper”, and gives it a flexa wherever the breath seems to him to ask for one, after “principio”, for instance, and then sings the same text without it. He has learned that a minor articulation delays the major one and lends it more weight.

Modal mutation, procedure 9. The same verse is sung in the eighth tone and then in another of the eight tones, with another tenor and another final, and the student hears how the same text changes colour without changing a word. Parallel doubling, procedure 50. Two students sing the tone at once, one at the written pitch and the other a fifth below, and they have reconstructed in the classroom the parallel organum that the Musica enchiriadis describes. Then they sing the tone harmonised in chords, with the formula in one voice and the others moving along with it, and they have arrived at fauxbourdon, which is historically that very thing, psalmody dressed in harmony for feast days. Ornamentation, procedure 10. The tones have solemn forms, more adorned, for the greater canticles, and the student invents his own, adding to the mediatio a passing note or a neighbour note without touching the tenor, and learns how much ornament a formula can bear before it ceases to be recognisable. Heterophony, procedure 49. A group of students sings the same verse without agreeing on the length of each syllable, as a village congregation sings, and the class listens to that intermediate texture, neither unison nor counterpoint, in which most of humanity has always sung its psalms.

The eighth tone on the loom

The tone lays on the loom an accent very different from the nocturne’s. Its dominant thread is the léxis, because the melody exists only to say a text, and that léxis has the shape of the pure vocative, a word addressed to someone who remains out of sight and who is named in the first line of almost every psalm. The harmonía is minimal and for that very reason heard entire, the gravitation between the C of the tenor and the G of the final, the fourth that the intonation opened and the termination closes, so that the whole psalm is an arch stretched between two notes. The rhythmós is the free rhythm of plainchant, the body breathing instead of walking, and its unit is the breath of each side of the choir.

The three strata are present in the formula with a surprising exactness. The Flesh is the breath, and the flexa is its proper member, the part of the formula that exists because the lungs have a limit. The Inclination has its Latin name in the tone, because flexa comes from flectere, to bend, to curve, to incline, and it is the same action as the Greek rhopé, the instant in which the straight line of the tenor yields and bends. It is also the accent of the mediatio, the syllable that rises to D and leans, and it is the body of the monks bending at the Gloria. And the Toward is the terminatio with its differentia, the formula that in ending already looks to the antiphon, a close that contains the direction of what follows.

The lenses divide the fabric in the same way once more. Gesture entered through the Flesh and the Inclination, through the breath, the drawing hand, the bowing body. Form travelled the Toward, from the initium to the differentia and from one verse to the next. Procedure pulled the threads one by one, harmonía in the organum and the fauxbourdon, léxis in the elasticity of the tenor, rhythmós in the heterophony of the congregation.

What the two specimens teach together

Set side by side, the nocturne and the psalm say something that neither says alone. Both begin by calling, one with a sixth addressed to a nearby face, the other with a fourth addressed to a community. Both sustain, one with the sway of a left hand that does not change throughout the nocturne, the other with a C repeated through numberless syllables. Both incline, one in the appoggiaturas, the other in the flexa and in the accent. Both end looking toward something else, one with a coda that does not want to take its leave, the other with a differentia that is already hearing the antiphon. And both repeat without repeating themselves, one by ornamenting each return, the other by setting new words each time beneath the same formula. The best-loved printed piece of the Romantic salon and the most sung anonymous formula of the Middle Ages are woven on the same loom, and what the student learns by travelling through them together is that the difference between oral and written tradition is real and lies on the surface, because beneath both a body calls, sings, moves and, only at the end, sounds.

Table 3. Two specimens on one loom. Chopin’s nocturne and the eighth psalm tone read through the three lenses and then in the three strata. Gesture enters through the Flesh and the Inclination, form runs along the Toward, and in both columns the order is the same, to call, to sing, to move and, only at the end, to sound.

Reading	Chopin, Nocturne op. 9 no. 2	Eighth psalm tone
Gesture, the call	The rising sixth from B flat to G, G2 softened into a reach, the vocative of intimacy addressed to a face close by	The initium G, A, C, a rising fourth to a note that stays, G2 addressed to a community that becomes a choir
Gesture, the song	A chain of sighs in the descent, G4, a cavatina for the right hand with its messa di voce on the long notes	Cantillation, one note per syllable, G8, and the tenor as a held note, G6
Gesture, the body	The sway of the left hand in 12/8, G11, and the swell of the arm across four bars, G5	The formula drawn in the air with the hand, R2, and the monks who bow the body at the Gloria Patri
Form	A, A, B, A, B, A, coda, the refrain principle (forms 8 and 18) or ornamented strophic form (form 11 and procedure 59). Strophes identical in their point of departure and different in their ornament	Initium, tenor, flexa, mediatio, terminatio. Strophic (form 1) and antiphonal (form 12), framed by the antiphon. Strophes identical in their melody and different in their text
Procedure	Ornamentation (10), the ornamented repeat (59), cadential deferral (48), extension (13), modal mutation (9), transposition (5), augmentation and diminution (1 and 2), fragmentation (11), reduction to the skeleton (34), grafting (42)	Repetition (43), internal expansion (12), cadential deferral (48), modal mutation (9), parallel doubling (50), ornamentation (10), heterophony (49)
Flesh	The opening call, in the léxis of the Flesh, and the sway of the left hand, in the rhythmós of the Flesh	The breath, with the flexa as its own limb
Inclination	The appoggiaturas of the descent, in the harmonía of the Inclination, the rhopé of the balance	The flexa, from flectere, the accent of the mediatio and the bending body of the monks
Toward	The upbeat of each return, the B phrase that leans toward the dominant and the coda that delays the farewell	The terminatio with its differentia, which in ending already looks toward the antiphon

XI. Detailed rutter

What follows is a curriculum timed to the minute, and for that very reason it is the place to say exactly what separates a method from a grammar. A method prescribes the sequence. A grammar supplies the elements and lets each hour find its own. The catalogues of the preceding pages are the grammar. The itineraries and the lesson template that come now are one possible syntax, the one that has worked in my room, and they are offered the way a left-hand ostinato is offered to a beginner, as a ground to improvise over, which is the use an ostinato asks for and the opposite of a score that one obeys. The timetable is the lesson’s ostinato. When the ground is firm, the hour can begin to sing.

The word curriculum names a racecourse, a track with a finish. What is traced here is a hodós (ὁδός), a road, the same word that dwells inside méthodos, and its name in English is the rutter, the pilot’s book that records soundings, landmarks and safe passages and leaves the crossing to whoever sails, a word that also keeps faith with the compasses on this blog’s masthead. This rutter rests on two pillars. The first is the improvisational diary kept as an audiovisual record, a practice of every day. The second is the daily compositional routine, which runs from melody to discant, from discant to four parts and from four parts to orchestration. On the two pillars rest a progressive rutter of craft, with partimento, counterpoint, basse donnée, chant donné and schemata, and an integration plan that leads from improvisation to melodic writing, to procedures, to short pieces and to styles.

The improvisational diary

The diary is a practice for cultivating inner hearing, modal vocabulary, rhythmic identity and spontaneous creation, and its form is simple. Each day has two improvisations, one vocal, of one to five minutes, and another at the keyboard, also of one to five minutes, sometimes with one hand and sometimes with both. The student records them in a simple audiovisual record, and for that a phone propped on the music stand is enough. Over the months those recordings form an archive that no examination could demand and no teacher could manufacture, the sound portrait of an ear in the act of growing.

The pedagogy of the traditions that never separated improvisation from study confirms this economy. In the teaching of North Indian classical music, improvisation is formed through memorisation and structured variation, with the palṭās, permuted scale patterns, and the tāns, runs built on learned formulas, and almost never by asking the student to improvise all at once and without a net. The diary does the same. It begins with two or three notes, with a given mode, with an assigned gesture, and freedom arrives through the patient widening of a frame and never through the leap into the void.

One possible morning lets it be seen. Imagine a fifteen-year-old student on day 17 of her diary. Before breakfast she stands by the window, props her phone on a pile of books and sings a long D, then another, until it stops trembling. She has chosen Dorian because it is raining. She climbs slowly to the A, comes down, lingers on the B natural, which is the note that makes Dorian Dorian, and repeats it three times because she likes how it sounds against the rain. After two and a half minutes she has sung something that resembles a sailors’ song, ends on D, stops the recording and types on the screen “Day 17, Dorian, voice”. In the afternoon she will repeat it at the piano. Nobody has corrected anything, and nobody had anything to correct.

The mode of the day

The daily frame is set by three decisions, and the first is the mode, or the modes, of the day. The palette is wide. There are the Western modes, ecclesiastical and medieval, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Ionian, Hypodorian, Hypophrygian, and Locrian for exercises in tension. There are the Arabic maqāmāt, Bayati, Hijaz and Rast, the Persian dastgāh, Shur and Homayun, the Turkish makam, Hicaz and Uşşak, the Indian raga, Yaman, Bhairav and Kafi, the Jewish mode Ahava Rabbah, and the Greek dromoi, whose name means “roads”, Hitzaz, Hitzazkiar, Ousak, Sabah, Niavent and Houzam. There is flamenco, por arriba and por medio. There is the blues, with the hexatonic blues and the minor and major pentatonics. There are the synthetic modern modes, the octatonic, the whole-tone, the acoustic scale and the Lydian dominant. And there are the hybrid modes, made of two tetrachords from different modes, such as Dorian above and Phrygian below, or Hijaz below and major above. Each day one works a single mode, or two hybridised modes.

A warning follows from all of the above. The neutral second of Bayati and the koron of Shur do not exist on a piano, and reducing a maqām to a keyboard scale repeats, in another key, the very flattening this whole essay argues against. Those modes live in the voice. They are sung, and the keyboard is left only what the keyboard can hold.

The gesture of the mode

The second decision assigns to that mode a gesture, a dance or a mood, and that gesture becomes the motor of the improvisation. Dorian walks with a steady pulse and a noble sadness. Mixolydian dances, a reel, a folk gesture. Hijaz is lament, incense, vertical gesture. Ahava Rabbah is yearning, cantillation, recitative. The minor pentatonic rocks like a lullaby, with simplicity. Maqam Rast is ceremonial, stately, declamatory. Raga Yaman is longing, tenderness, the fragrance of evening.

The pairing itself is ancient. The Greek doctrine that each harmonía has its éthos (ἦθος) is the ancestor of “Dorian, noble sadness”, and éthos, before it meant character, meant a haunt or a dwelling, and Homer uses the word for the pastures where horses are kept. A mode is a place one lives in, the dwelling of sound, and that is why “inhabit” is the verb to which this essay returns again and again. Habitare is the frequentative of habere, to have, and habitus is the word by which Latin translated the Greek héxis (ἕξις), which in turn comes from échein (ἔχειν), to have. The two languages reached the same thought by different roads. To inhabit a mode is to have it repeatedly until it becomes a disposition.

Laban’s four motion factors give that pairing a vocabulary a student can work with. Weight is light or strong, space direct or flexible, time sudden or sustained, flow bound or free. Their combinations yield the eight basic efforts, float, glide, press, wring, flick, dab, punch and slash. The correspondence that follows is a starting point, made to be contradicted by the student’s body. Dorian has the kinetic image of a noble walk, its effort is glide, light, direct and sustained, and its breath is long and even. Mixolydian has the image of the reel and the dance, its effort is flick, light, flexible and sudden, and its breath is short and bouncing. Phrygian has the image of descent and fall, its effort is press, strong, direct and sustained, and its breath is slow and weighted. Lydian has the image of lift and brightness, its effort is float, light, flexible and sustained, and its breath stays suspended. Hijaz has the image of lament and incense, its effort is wring, strong, flexible and sustained, and its breath is slow, with a catch. The minor pentatonic has the image of rocking and the lullaby, its effort is float and then glide, and its breath goes rocked, in twos. Maqam Rast has the image of the ceremonial and the stately, its effort is press and then glide, and its breath is measured and full. Raga Yaman has the image of longing and evening, its effort is float, and its breath is long and released. Ahava Rabbah has the image of yearning and cantillation, its effort is wring and then float, and its breath is spoken.

The rhythmic world of the day

The third decision sets the rhythmic world of the day. It may be free rhythm, in the manner of plainchant, it may be cycles of 5/8, 7/8, 9/8 or 10/8, a walking pulse, dance patterns such as the jota, the gavotte, a bulería feel without strict compás or the outline of a tarantella, ostinato patterns, or the gestures of inhaling and exhaling of the body itself. The perennial metres and timelines of the catalogue of gestures are the full menu.

The voice of the day

Vocal improvisation begins standing, or sitting upright, breathing in silence. Then a single note is sung, stable and centred, until it stops searching for its place. Then the mode is traced slowly, ascending the tetrachord and descending it, touching with the voice the characteristic intervals, the minor second and the major third in Hijaz, the minor seventh in Mixolydian, the augmented fourth in Yaman. The improvisation proper begins with only two or three notes and is allowed to expand to the full mode. Then come the rhythmic gestures, pulses, rubato, accelerations, and the exploration of register, low, middle and high. The improvisation ends with a cadence proper to the mode. It is recorded and labelled, “Day 17, Dorian, voice”. Everything is kept simple, and it never lasts more than two to five minutes.

The keyboard of the day

Improvisation at the keyboard, or at one’s own instrument, can be done in two ways. In the first a single hand works. The right hand plays the melody and the left keeps silent, or holds a drone, or punctuates, and all attention goes to the clarity of the line, to its contour and to its direction. In the second both hands work. One improvises the melody and the other gives a drone, a fifth, an open interval, a simple ostinato or the basic chord tones of the mode. In both, simplicity is kept, and complex harmony waits for its moment. The goals of each day are clarity of gesture, modal purity or deliberate mixture, and structural clarity, with its beginning, its middle and its cadence. The take is recorded and labelled, “Day 17, Dorian, keyboard”.

The compositional routine

The second pillar is a bridge that runs from improvisation to melody, from melody to procedure, from procedure to texture and from texture to orchestration, and it begins with the voice. The student sits in silence and sings a short, spontaneous phrase. The student repeats it until it settles, sings it several times to memorise its contour and records it, and audio is enough. Then comes the transcription of what was sung. The student identifies the tonic, notates the approximate rhythm first and refines the pitches afterwards, because what matters is to capture the essence at once, and cleanliness can wait. That is the melody of the day.

The procedure of the day

One of the perennial procedures of the catalogue is applied to the melody of the day. For daily practice the most useful are augmentation, 1, diminution, 2, rhythmic displacement, 3, transposition, real and modal, 5, inversion, 6, retrograde, 7, modal mutation, 9, ornamentation, 10, fragmentation, 11, internal expansion, 12, episode creation, 23, sequence, 24, hoquetus, 28, drone elaboration, 32, hybrid grafting, 42, repetition, 43, the sentence, 44, liquidation, 46, interval expansion and contraction, 53, and range expansion, 54. The student chooses one, applies it literally to the melody and notates the result. Now there is melody A and melody B, derived from it.

Discant, third and fourth voice

The next step adds a discant, a second melodic line above or below. The student sings a counter-melody against the written melody, keeping above all to contrary motion and looking for simple intervals, thirds, sixths and tenths, and notates it. Now there is two-part counterpoint.

One possible lesson shows how it is born. Imagine a twelve-year-old boy who has brought a melody of six bars in A minor, sung that morning in the kitchen. The teacher sings the melody and asks the boy to sing “something else” at the same time, without thinking. The first two times the boy clings to the teacher’s voice and ends up singing the same thing. The third time the teacher gives him a single instruction, “when I go up, you go down”, and the boy suddenly finds a line that moves away and comes back, meets the melody at a sixth, parts from it to a tenth and falls onto the final from the opposite side. He laughs because he does not know where it came from. They write it down together in the notebook, and the boy has made his first counterpoint without ever having heard the word species.

Then a third voice is added, which fills the inner line with stepwise motion and keeps its independence. Parallel octaves and fifths are avoided when possible, without obsession. And then the fourth voice, thinking in chorale texture, seeking smooth voice leading, with every voice singable and the harmony clear. Now there is a four-part miniature derived from an improvisation.

The minimal orchestration

The routine ends with a very simple orchestration exercise, one a day. Each line may be assigned to a different instrument, flute, oboe, clarinet and bassoon, two lines may be combined in octaves, simple register doublings may be added, string quartet scoring may be tried, or the orchestral families may be tried, with the melody in the oboe or in the violins, the alto in the clarinets or the violas, the tenor in the bassoons or the cellos, and the bass in the double basses, the trombones or the bassoon. Large textures are not needed. Everything is kept simple and archetypal.

What Mahler did with a round

This routine, in a master’s hands, yields symphonies. Mahler did exactly this with a nursery song and drew a symphonic movement out of it. The third movement of his First Symphony takes “Bruder Martin”, which is “Frère Jacques”, and applies the catalogue to it. Modal mutation, 9, turns the round from major to minor. A timpani ostinato on D and A, 32, lays the ground. The tune enters in canon, 27, as it always was, but now in a solo double bass, and then the bassoon, the cellos and the tuba take it up, so that the canon is at once a timbre variation, 20, and a shaping of density, 37. An oboe adds a countermelody, 29. A village band bursts in, marked mit Parodie, which is hybrid grafting, 42, of a klezmer dialect onto the round. The middle section quotes Mahler’s own song “Die zwei blauen Augen”, 58, and the march returns a semitone higher, 5, before finding its way home. On the side of gesture, the tread of a funeral march, G10, “solemn and measured, without dragging”. On the side of form, a march with a trio, a refrain form with a quotation at its centre. A child’s round, the daily routine and a master’s hand, the three lenses, in eleven minutes, by someone who never heard of them.

The rutter of craft

The rutter of craft, with its partimento, its counterpoint, its basse donnée, its chant donné and its schemata, begins when the student has thirty to sixty days of improvisation behind them, thirty to sixty melodies with their derivations and some practice in discant and in four-part writing. It arrives late on purpose. Writing comes to put in order what the voice has already done, and the student who receives it at that moment receives it as a name for something already known.

The given bass and the given melody

The first step is the basse donnée, the given bass. Its aims are to realise bass lines with simple counterpoint, to understand cadences and to practise harmonic rhythm. Each week the student realises three simple basses in two voices and one intermediate bass in three or four, and carries out a creative task, which is to write a bass of one’s own and realise it.

The second step is the chant donné, the given melody. Its aims are to fit harmonic skeletons to melodic lines and to achieve consistency in voice leading. Each week the student works two chants donnés in two voices and two in three voices, and makes a free composition on the given melody.

The partimento

The third step is the partimento, and it begins with the Italian partimenti, those of Fenaroli, Durante and Leo. One works through the cadential patterns, the rule of the octave, suspensions, sequential patterns and the gallery of bass motions, and then the simple figured partimenti, the unfigured partimenti, the fugue partimenti and the sonata partimenti. Each week the student works one rule of the octave, one cadential chain, one sequential chain and one short partimento, and ends by improvising on a partimento of one’s own.

One possible scene shows why this school produced composers. Imagine a conservatory student, nineteen years old, who has passed three years of harmony and has never improvised a single bar. The teacher sets before her a bass by Fenaroli, eight unfigured bars, and asks her to play it with the left hand alone, singing anything at all above it. She sings the notes of the bass, an octave higher, because she dares nothing else. The teacher points to the fourth bar, where the bass rises by step from C to G, and asks her what chord the fourth degree takes when the bass rises. She knows it by heart, she has written it a thousand times, sixth, fifth and third. She plays it. She sings it. And this time her voice, instead of doubling the bass, goes to the sixth of that chord and from there descends by step while the bass rises. She has discovered in two seconds that the rule of the octave, which she knew as a table, was a melody waiting.

Counterpoint

The fourth step is counterpoint, Fuxian but flexible, with its five species, note against note, two notes against one, three or four notes against one, suspensions and florid counterpoint. One week is divided into two exercises in first species, two in second and one in third, and the following week into fourth and fifth. After six or eight weeks one moves on to short inventions.

The schemata

The fifth step is given to Gjerdingen’s schemata, the galant formulas, Prinner, Monte, Fonte, Ponte, Romanesca, Quiescenza, Fenaroli, Do Re Mi, Meyer, Indugio, Sol Fa Mi, Cadenza doppia and Pastorella. Each week the student analyses two examples, writes one in four parts and composes a miniature with two or three schemata.

The five phases

The integration plan orders all of this in five phases. Phase 1 lasts thirty days and joins daily improvisation, daily melodic writing and one procedure a day. Phase 2 lasts another thirty and adds daily discant, textures in three and four parts and simple orchestration. Phase 3 lasts sixty days and brings partimento and species counterpoint, without the daily improvisation being interrupted. Phase 4 lasts sixty to a hundred and twenty days and is given to composition on schemata, to hybrid modal and tonal experiments, to short binary and ternary forms, to variations on an ostinato and to the ground bass. Phase 5 is the advanced one, with chorales in the style of Bach, inventions in two and three parts, strophic song writing, aria forms, variation forms, chaconne and passacaglia, improvised preludes in many modes, short orchestrations and transcriptions from the keyboard to the ensemble.

Memory and structured variation sustain the five phases, just as in the learning of Indian riyaz, where what is memorised is the material of what is improvised and disciplined variation is the bridge between the two. This rutter is recurrent and free of any period, and serves equally for Baroque, Classical, Romantic, modern, folk and jazz foundations. It is elementary in its materials, which are voice, mode, gesture and rhythm. It is progressive in its order, which runs from improvisation to melody, to procedure, to counterpoint and to orchestration. And it is deeply embodied in its watchword, sing first, keyboard second, paper last.

Obey, break, leave

The Japanese arts have a three-word description of the arc I am after, and it says in three syllables what my five phases say in three hundred words, shu, obey the form, ha, break it, ri, leave it. Phases 1 to 3 are shu. Phase 4 is ha. Phase 5 is the point at which the student stops needing the road, and that point, more than an ending, is what I meant by a passport with no borders.

Figure 8. The five phases of the rutter. The height of each stretch is proportional to its days, phase 4 extends in a paler tone to its possible hundred and twenty days and phase 5 stays open. On the right, the three Japanese syllables that say the same, shu, ha and ri, obey the form, break it and leave it.

XII. The shared rehearsal

Everything above happens in a room with a single student, and almost all of it at a piano. The rehearsal is another room. It has its own inherited grip, as ancient in appearance and as recent in truth as that of the lesson, and that grip fits whole into a legal image. The score works as a contract, the conductor as its notary, the players as the parties who have agreed in advance to coordinate and who come to the hall to attest to what was agreed. One rehearses in order to comply. The intonation is corrected, the entry squared, the balance adjusted, the rubato fixed so that nobody invents it on the night of the concert, and by the end of the third session the ensemble knows exactly what it is going to do, which is what the score already knew before anyone opened it. The three lenses enter here into a space where there are many bodies and, almost always, no left hand, and what they do in it is give back to the rehearsal the meaning of its own name.

The contract even has its small print. The orchestral player reads a particella, the part, his clause of the contract, which holds his notes, his rests counted in bars and a couple of entries of other instruments printed in smaller type so that he does not get lost. He can play thirty years in an orchestra without ever having seen the full score of the works he plays, just as the signatory of a clause knows nothing of the rest of the contract and fulfils it all the same. The work reaches him in pieces, and the unity he ought to hear with his body is guaranteed to him by someone on a podium. The inherited rehearsal is, in its very structure, a machine for separating what music had joined.

The notarial scene is young. Kenneth Hamilton showed that the ritual of the recital, with its closed programme, its reverent silence and its untouchable work, was assembled roughly between 1870 and 1920, and that before then pianists preluded, improvised and reordered in public. The ensemble rehearsal inherited the same liturgy by the same road, and it inherited it through the institution that manufactured it. Joshua Navon has reconstructed the history of the German conservatories from the founding of the one in Leipzig, in 1843, up to 1933, and his most unsettling finding reaches further than one would expect. That the conservatory reproduced the faithful performance of canonical works, the Werktreue, was already known. Navon shows in addition that the institution worked as an incubator of new ways of thinking about musicality, and that around 1900 a “psychotechnical turn” drew conservatory pedagogy so close to the psychological sciences that it absorbed even the rhythmic gymnastics of Émile Jaques-Dalcroze, the pedagogy that had sought to give music back to the body. The lesson is hard and must be held onto. If the institution was able to capture Dalcroze’s body, it will also capture any shared breathing offered to it as a technique of coordination, and will turn it into one more item on the rehearsal template, between intonation and balance. What protects a practice from that capture is the ground from which it is practised, and that is why the ground comes first.

Weighing together

The word itself keeps what the practice has forgotten. In Spanish to rehearse is ensayar, from ensayo, which is also the Spanish for essay, and ensayo comes from the Late Latin exagium, the act of weighing, the weighing, and from there the trial, the examination of a thing by what it weighs. Exagium belongs to the family of exigere, to drive out, to measure, to weigh, the same family that gave examen, which before it named the student’s test named the tongue of the balance, the needle that tilts when one pan outweighs the other. Montaigne took the word from that root as the title of his Essais, in 1580, and what he published were weighings of his own judgement, trials of a thought that weighs itself while it is being written. The musician’s rehearsal and the philosopher’s essay are the same operation seen from two trades. Both put a thing on the scales to see which way it tilts, and both discover the verdict during the weighing, never before it.

Here etymology stops being ornament and begins to work. Among the Greek words these pages have been gathering for gesture is rhopé (ῥοπή), the tilt of a balance, the instant at which it yields. To rehearse is to weigh, and rhopé is the exact moment at which the weighing resolves. Read from its root, the ensemble rehearsal is the place where several bodies put the music on the scales and wait together for the instant the tongue tilts, and what is weighed there, as can now be seen, is the very weight that one musician yields to another. The notarial contract inverts the word until it empties it, because a notary never weighs anything and only attests to a weight that someone else fixed. And the word by which French and English name the group, ensemble, comes from the Latin insimul, at the same time. An ensemble that rehearses, if one listens closely to the language, is a group that weighs at the same time.

The chorus and the chorusless

Against the contract, the tradition offers the same word that gave its name to the lesson. Plato says in the Seventh Letter that what cannot be put into words comes only after long synousía (συνουσία), a being together, and that then it is kindled all at once, like light leaping from a fire, and from then on feeds itself. The synousía there was that of a master with a disciple. In the rehearsal it multiplies, and in multiplying it changes its nature. Its syn, its “with”, now gathers four, twelve, eighty bodies around something none of them possesses, and the spark leaps between them, in the air of the room, where nobody can claim it as their own.

The Laws carry that intuition to its most radical form. Education itself is defined there as choreía (χορεία), singing and dancing together, and the uneducated man is the achóreutos (ἀχόρευτος), the “chorusless”. The same passage derives the word chorós from chará, joy, an etymology with a popular air that tells more truth than many scientific ones. A little later the Athenian gives the exact definition. The order of movement is called rhythm, the order of the voice, when high and low are blended, is called harmony, and the two together are called choreía. The Greek chorus was a permanent rehearsal, a community that learned to be a community by weighing together the step and the voice. The musician who arrives, opens the folder, plays his particella and leaves without having heard his neighbour’s line is, in the strictest Platonic sense, an uneducated man with a higher degree, a certified achóreutos. He has spent twenty years in the chorus and has still not entered it.

The conductor himself has an ancestor in that chorus, and the kinship tells against him. The koryphaîos (κορυφαῖος), the coryphaeus, led the chorus from within, standing among those who sang and danced, with the same voice and the same feet as theirs. Cheironomía, the art of drawing the melody in the air with the hand, from which the oldest neumes descend, was a singer’s gesture addressed to singers. The separate podium and the baton that beats the bars are inventions of the nineteenth century, and they arrived together with the particella and the notary. To give the conductor back his coryphaeus’s arm means that he draws the song again in place of counting the beats, and that his gesture calls the bodies in place of watching over them.

One melos in many bodies

In the introduction the loom of melos was set up, melos being the Greek word that means at once a limb of the body and song. Three vertical threads, the léxis, the saying that calls before saying anything, the harmonía, the fitting of what sounds together and attracts, the rhythmós, the shape of what flows, crossed by three horizontal strata, the Flesh, which is the body with its unchosen gifts, face, breath, weight, the Inclination, the instant in which something yields towards something, and the Toward, the direction, the pure futurity of what has not yet sounded. In the lesson the loom is woven in a single body. In the rehearsal several bodies weave a single melos, and each stratum changes shape as it passes from one to many.

The Flesh becomes shared Flesh, and its place is breathing. A quartet that breathes together before the first note has done something more elementary than agree on the tempo. It has gathered four lungs into a single breath, and that unity has a correlate that can be measured. Simon Høffding and his colleagues recorded the heart rhythm of two string quartets, one of students and the Danish String Quartet, while they played the same excerpt of Haydn under seven conditions, some of them designed to break their absorption. Playing raised the cardiac synchrony of both quartets above that of rest, the synchrony of the expert quartet was greater in every condition and held steady against almost every disturbance, and only one broke it, sight-reading. The finding deserves a second reading. The only thing that undid the common heart of four masters was having before them a score they had not yet made their own. Someone else’s paper separates bodies, and interiorised music joins them down to the heartbeat.

The Inclination becomes yielded weight. At the piano the appoggiatura reads as a “lean on me”, the weight of the arm that falls on a note and makes it yield towards the next. In the ensemble that weight passes from one body to another. The cello that sustains the bass of a cadence lets its weight fall so that the viola can resolve above it, the oboe that ends a phrase hands its air to the clarinet that continues it, the left hand of the pianist in a trio leans so that the violin can float. What at the keyboard was the art of sustaining, the ars sustinendi, becomes the art of sustaining the other, and rhopé ceases to be an instant within one body and becomes an event between bodies, the moment in which one musician yields and another receives. That is why the rehearsal is a weighing in the literal sense. One rehearses to learn how much each one weighs in the bar of the other.

The Toward becomes common direction. Eighty musicians can play the same notes in the same time without going anywhere together, and anyone who has heard a correct reading of a symphony knows that feeling of orderly traffic with no destination. The agōgē gives music a whither, and in the ensemble that whither has to be one and the same for all the bodies, or the music comes apart into parts. Common direction is born when each body hears where the phrase is pulling and lends its weight to that pull. The conductor who beats time gives a direction to the arms. The one who conducts the breath and the gesture gives a direction to the melos, and the orchestra follows it as a boat follows the current it is itself helping to form.

And over the three strata runs the thread that crosses them all. The thesis that has sustained these pages since the introduction says that music is vocative before it is representative, that it calls before it says anything, as the vocative case of ancient grammar names someone without predicating anything of them. A single voice that sings already calls, and its call hangs in the air until someone receives it. In the ensemble the call finds its complete form, because it becomes call and response between bodies. The first violin calls and the cello answers, the woodwind asks and the strings reply, the soloist casts and the orchestra gathers, and what in the lesson was a saying addressed to the air becomes dialogue. The founding order, Call, Song, Gesture, Sound, unfolds in the hall as a conversation in which every sound answers a call made by another body. Goethe heard it in the string quartet when he wrote to Zelter that in it one hears four reasonable people conversing among themselves. An ensemble rehearses well when each musician plays for someone in the room, and that is precisely what the contract, with its obsession with coordination, has let fall out of the rehearsal.

The ground before the score

The first principle the beginner learns in improvising, fix the left hand and feel the ground before looking for the figure, carries straight over into a room. Someone holds the ground. It may be a drone in the cellos, a timeline in the percussion, an ostinato in the second violins, the conductor’s pulse lodged in the body, and over it the others can be figure. The role rotates from rehearsal to rehearsal and from passage to passage, so that nobody is condemned to be always ground or always figure. The first ten minutes of a rehearsal belong to the ground, and the score waits closed on the stand in the meantime. They are given to a drone on the final of the work, to the whole ensemble singing its mode, to a timeline clapped in the metre of the work. An ensemble that has felt the ground together will coordinate without needing to be coordinated, because the coordination the notary imposes from outside will already have been born from within, from the weight that everyone has rested in the same place.

One possible morning begins like this. A string quartet is about to tackle for the first time the third movement of Beethoven’s Quartet op. 132, the song of thanksgiving the composer headed “in the Lydian mode”. Nobody opens the score during the first quarter of an hour. The cellist takes a low F, sustains it with a slow bow and takes it up again when the bow runs out, without the seam being heard. Over that F the viola sings the scale, slowly, on a vowel, and on reaching the fourth degree the other three hear her stop on a B natural that the tonal ear did not expect. The four of them repeat that note, singing it, until it stops sounding like a mistake and begins to sound like light. Then each sings their own voice of the chorale, in minims, with the breath cut where the phrase cuts it, and then the voice of the neighbour, the second violin that of the first, the viola that of the cello, and the first violin, who has never in his life sung a bass, discovers that the cello’s F has a weight his own line knew nothing of. When at last they play, they play once from beginning to end and nobody says anything. The silence that follows is part of the rehearsal, and it is there that each of them discovers what the body has already understood of a music that an hour earlier was known only through the ink.

Singing the parts

That quartet has done the first practice of the shared rehearsal, whose aim is to put the work into the voice of the ensemble before it is in the fingers. It is gone through in four degrees. Each musician first sings their own line, in solfège or on a vowel. Then they sing the line of their neighbour. Then the tutti sings the bass while the basses play it, and after that the reverse, the basses singing while the rest play. The fourth degree is that of the previous scene, a quartet that sings its slow movement before playing it, plays it once and keeps silent. The exercise that fixes the habit is simple and allows no exceptions, one passage per rehearsal, always. The choir has been doing this for a thousand years, and that is why choirs rehearse faster than orchestras.

The second of those operations, singing the neighbour’s line, already has its laboratory proof. Marie Ragert, Tim Schroeder and Peter Keller asked expert pianists to play duets with different partners, sometimes having studied both parts and sometimes only their own, without rehearsing together and without seeing each other, and they measured the synchrony of their keystrokes and, with motion capture, the sway of heads and torsos. Knowing the other’s part left the keystroke-by-keystroke asynchrony untouched, because each pianist predicted the other’s micro-timing from their own, and it brought the movements of the body into step at the scale of the bar and of the phrase. The result has an edge. The neighbour’s part learned alone is heard with one’s own accent, and the accent of the other is learned only with the other present. To sing the neighbour’s line in the room, with its owner listening, joins the two things the laboratory separated, the structure of the other’s part and the style of the body that plays it. And the phrase, where the study found the benefit, is exactly the scale at which an ensemble breathes.

Call and response by sections

The second practice turns the sections into voices that answer one another, and it is the vocative thesis carried onto the floor of the hall. The first violins call with a phrase from the work. The cellos answer, in inversion, a fifth lower, in the parallel minor or in diminution. The winds answer the cellos, and the phrase at last returns to the first violins changed by the journey. The exercise uses the work’s own motives as calls and requires every answer to employ a procedure from the catalogue, named aloud before it sounds. “Inversion”, says the principal cellist, and the whole section inverts. The room thus learns two things at once, that the work is made of calls and that answering a call is already composing. Gesture G2, the call, the leap of a fourth or a fifth to a held note projected so as to be heard from afar, recovers in this practice its original distance, the one that separates one shepherd from another shepherd, one section from the section opposite.

The “what if?” rehearsal

The third practice recomposes the passage on the spot, so that the ensemble understands it from the side of the one who makes it. A passage is chosen and played once as written. Then, in any order, the themes of the exposition are swapped between instruments, the development is played in the parallel minor, which is procedure 9, the bass is doubled by the flute, 50, a layer is removed, only the downbeats are played, 34, the accompaniment is played without the melody while everyone sings the melody, the passage is played at half speed to hear the augmentation, 1, the conductor silences and activates sections by gesture, 37, and only the two bars before and after each joint are played. Then the passage is played again as written, and it will already be another passage.

Each “what if?” is a weighing. It puts on the scales an alternative that the composer discarded or never came to imagine, and the text comes back to the room laden with the weight of all of them, as one choice among many possible ones. A passage that has only been played as written is played the way one signs a document. A passage that has been played ten ways and returned to the first is played the way one chooses, and the listener notices it without knowing how to name it. The exercise that belongs to this practice fits in a sentence. Every procedure in the catalogue is also a rehearsal technique, and the ensemble brings to the room a list of the procedures to which the work in hand answers.

Preluding into the work

The fourth practice recovers the oldest habit of the concert, that of arriving at the first bar from inside the mode. It is the custom Hamilton documents among the pianists who came before the modern recital, who preluded before each piece to temper the room, the instrument and their own hand, and it is also form 21 of the catalogue, the free-rhythm prelude, kin to the ālāp, the taqsīm and the intonazione. One musician, or the whole ensemble, improvises for a minute and without measure a prelude in the mode of the work, and the first bar of the work arrives as the cadence of that prelude. At every fermata the lead-in, the Eingang, is improvised, and where there is a cadenza the cadenza is improvised, badly at first, because that “badly” is the price of the first time and the only road to the second.

The exercise asks for each rehearsal to be preluded by a different musician and for the ensemble to enter without a cue. That absence of a cue is everything. An ensemble that enters without a cue has heard the end of the prelude as a question that asked for the work as its answer, and in that instant it has understood the work better than in ten readings. The prelude, moreover, distributes authority. The bassoonist who preludes for everyone that Tuesday has called his colleagues towards the work, and for a minute the whole room has followed him, and the next time the bassoon has two exposed bars nobody will play over them as if they were accompaniment.

The joint as the unit

The fifth practice is born of a craftsman’s observation. Ensembles fail in the transitions, and the transitions are the place where composition lives. The inherited rehearsal works by sections, the exposition, the development, the recapitulation, and leaves the seams for the end, when there is no time left. This practice makes the joint the unit of rehearsal in place of the section. Every transition in the work is marked. Only the two bars before and the two bars after each one are played, in succession, as though they formed a piece of their own, so that for half an hour the whole work becomes a collection of hinges. Then alternative bridges are improvised between the same two points, by sequence, by drone dissolve, by register step, by metric re-anchoring, to hear what the written bridge does and what it leaves undone. Finally one returns to the text, and the written bridge is then heard as a choice.

The joint is the place where the loom is put to the test in the ensemble. In it the weight changes hands, the section that carried the phrase lets it go and another gathers it up, and if the Inclination fails, if nobody yields or nobody receives, the work breaks even though each part is in tune. The joint is also the place where the Toward bends, where one direction ends and another has to be born without the listener noticing the knot. To rehearse the joint is to rehearse exactly what the contract leaves without a clause, the passage from one clause to the next. What the student learned to write alone with procedure 23, the writing of episodes between two melodies, the ensemble learns here by playing it, and the episode passes from the desk to the hall.

Conducted improvisation

The sixth practice gives the ensemble a gestural language for composing in real time, and it places the lens of gesture in the conductor’s arm. Ten signs are agreed in five minutes. The pulse is given by beating time. Sustain is asked for with a flat hand held high. Stop, with a fist. Louder and softer, with the palm up and the palm down. Higher and lower, with the hand that rises and the hand that falls. Denser and sparser, with the fingers spreading and the fingers closing. Imitate, by pointing to one musician and then to another. Repeat, with a circle. Remember, with a hand to the temple, which means that each one plays again the last thing they played. Solo and tutti, with one finger and with both arms. With those ten signs the ensemble improvises on the material of the work, without a word, and at a third stage the conductor hands the signs to a musician, who stands in front and discovers in their own arm what it means to call many bodies at once.

That language already has its developed grammars. Lawrence D. “Butch” Morris worked out from the 1980s onwards the conduction, a vocabulary of signs with which the conductor composes live together with the improvisers, and Walter Thompson created in 1974 soundpainting, a sign language for composition and improvisation in real time. Both grammars are extensive and codified, and an ensemble that is starting out can start without them. Any ensemble invents its own dialect in a single session, just as two children invent in one afternoon the rules of a game they will later defend as though they were law. The exercise that crowns the practice is the most ambitious of all. The ensemble composes, by gestural direction, the transition the work needed and does not have.

What happens between the bodies during that half-hour has an empirical description. Frederick Seddon observed and video-recorded six one-hour rehearsals and one performance by six jazz students, and found that they communicated in six modes grouped into two families, the verbal and the non-verbal, each with three modes, instruction, cooperation and collaboration. In the non-verbal collaborative mode there appeared what he called empathetic attunement, the vehicle of a creativity that exists only among several. That attunement also has its physiology. Charles Limb and Allen Braun observed with functional magnetic resonance imaging that, when they improvise, jazz pianists deactivate broad areas of the lateral prefrontal cortex, associated with self-monitoring, and activate the medial prefrontal region, linked to the expression of the self. And Aaron Berkowitz has shown that improvisation rests on a repertoire of internalised formulas, acquired with the patience with which a language is acquired. The three observations say the same thing from three distances. The notary each musician carries within has to fall silent for the ensemble to speak, and he falls silent only when a common, internalised language relieves him of his work. The ten signs are the first vocabulary of that language.

One possible rehearsal shows it. A young wind quintet has been stumbling for weeks at the same spot in a repertoire work, the passage from the first theme to the second, which seems abrupt to all five of them, a door that opens without a handle. One afternoon they set the work aside and the horn player, who has never conducted anything, takes up the signs. She points to the flute, which repeats the tail of the first theme. She closes her fingers, and the flute thins the figure until only two notes are left. She makes the circle, and the two notes repeat. She points to the bassoon and then to the clarinet, and the clarinet imitates the bassoon a third higher. She lowers her palm, and everything turns almost to silence. For twenty minutes the five compose in this way, by gestures, eight or ten bars of bridge that nobody has written and that the oboist records on the phone propped on the stand. Then they return to the work. The composer’s bridge is still abrupt, yet now they play it knowing what they have put on the scales against it, and the abruptness has stopped sounding like a defect and sounds like a decision, a door flung open on purpose.

The breath before the entry

The seventh practice makes the anacrusis a shared gesture. For a whole rehearsal the entire ensemble breathes the upbeat together, audibly, before every entry. At the following rehearsal it breathes it in silence, with the same intake of air and without sound. And the silence after the last chord is conducted as music, and every body in the room holds it for as long as the chord itself lasted. The exercise consists in beginning the work five times with five different breaths, slow, quick, a gasp, a sigh, silent, which is recipe R4 carried over from the single student to the ensemble, and in then choosing among the five. The choice is another weighing, and in making it the ensemble discovers that the first note of a work is decided a second before it sounds, in the air that everyone has taken in at once. It is gesture G1, the breath before the sound, the temple of the cantaor who settles the mode before the first syllable, multiplied by the number of lungs in the room.

Imagine an orchestra of conservatory students, seventy young people between eighteen and twenty-three years old, before the opening of Beethoven’s Fifth. Anyone who has conducted those bars knows what happens. The symphony begins with a quaver rest, the three quavers on G fall after that rest, and an orchestra that waits for the stroke of the baton always arrives scattered, with the clarinets a hair early and the double basses a hair late. A possible rehearsal renounces the stroke. The conductor lowers his arms and asks the orchestra to breathe the quaver of silence, aloud, all at once, without playing. The first time it sounds like a disordered wave breaking in seventy different places. By the third the wave has a single crest. A violist in the last row, who in two years of orchestra had never heard her own breathing within the ensemble, is surprised that the air of the hall has a shape. Then they play, without a beat, and the three quavers fall together because a single breath has launched them. Then it is repeated with the breathing silent, and the orchestra learns that the quaver of silence was full. Finally the conductor lets the fermata on the E flat fade away and asks that nobody move for as long again, and seventy bodies hold a silence that is still Beethoven.

One possible hour and a half

All of this fits into a timetable, offered in the same spirit as the rutter of the lesson, as a form that holds without fixing. The timetable is the rehearsal’s ostinato, the ground over which each session improvises its figure. It begins with the ground, a drone on the final of the work, the mode sung by everyone, a timeline clapped. It continues with the parts of the day’s passage sung, and with the “what if?” pass over that same passage. Then come the joints, played as a piece of their own. Then the passage as written, gone through by way of the lenses. The conductor conducts the breath and the gesture in place of the beat, someone names the formal archetype aloud, someone names each procedure as it appears, “sequence”, “liquidation”, “deferral”. After that comes conducted improvisation on the material of the work. And at the end, one unbroken run of the passage, without stopping and without comment. The rehearsal ends as it began, in sound.

The school of song and arm in which I was formed measured everything by a single question, whether the line sings. In the lesson the question is put to one body. In the hall it is put to many, and it becomes harder and more beautiful, because a line that passes through five bodies sings only if each of them receives it with the weight the previous one left in it and hands it on with the weight the next one needs. That is the weighing the shared rehearsal practises every day, and the balance has as many pans as there are musicians in the room. What remains to be weighed is what happens when the doors open and the audience comes in, whether the concert is the last weighing of a long series or the first of another in which those who listen also lay down their weight, and that question is already asked from inside the chorus.

XIII. Addendum I. How to begin improvising quickly

This addendum has a workshop vocabulary cut to the measure of the beginner’s haste. It comes almost entirely from the English of jazz and studio musicians, the vamp, the riff, the hook, and from the Italian of the basso continuo, the ostinato, alongside older words that are more our own, the modal melisma, mutation, transition, episode. With those eight words one travels the whole road that leads from the first note held in the left hand to the first short piece with two sections and a bridge between them, and one travels it quickly, in days rather than years, because the first step rests on a single condition that anyone can meet this very afternoon.

A. Ground before figure

Improvisation becomes instantly accessible when the left hand repeats something stable that gives ground to the right hand’s exploration. Organists who prelude over a pedal know this, and so do flamenco guitarists who keep the compás with the thumb while the falseta searches, boogie-woogie pianists, the gaiteiros with their drone, and the tanpura player who accompanies a dhrupad singer for an hour without changing string. What all of them know without having formulated it has today a fairly precise cognitive explanation, and it is worth setting out in some detail, because it turns a workshop habit into a thesis.

Jeff Pressing, in the text that founded the cognitive study of improvisation, described the improviser as someone who never starts from nothing. The improviser always starts from a referent, the set of perceptual, cognitive and affective structures that guides the production of material and sustains it while it happens, the melody of a standard, the cycle of a tāla, the form of a blues, the bass of a chaconne, and from a knowledge base, the internalised repertoire of formulas, turns and figures the hand has at its disposal. Between the two the improviser chooses, in real time, groups of events to chain together, and that choice consumes attention, which is a scarce resource. That is why, in Pressing’s model, expertise consists in good part in making automatic what at first demanded deliberation, in freeing attention from everything that can run by itself so as to leave it available where a decision has to be made. A beginner who tries to improvise with both hands at once has to decide, at every instant, the harmony, the bass, the rhythm, the register and the melody. The load is so heavy that the hand freezes, and the paralysis is lived as a lack of talent when it is simply a lack of ground. An ostinato fixed in the left hand until it runs by itself settles four of those five decisions at a stroke. It is the referent turned into sound, and the whole of attention is left free for the only decision that matters at the start, the decision of the line that sings.

Aaron Berkowitz reached the same place by another road. Reading the improvisation treatises of classical and romantic pianism alongside the literature on language acquisition, he argued that one learns to improvise as one learns to speak, by internalising a vocabulary of formulas, varying them, recombining them, until their use stops being deliberate and becomes available in the moment. Improvisation, for Berkowitz, is a creation that is at the same time a re-creation, because nobody invents their words when speaking and all of us invent our sentences. The ostinato is the first word of that vocabulary the student truly owns, the first that no longer needs to be thought, and so it is also the first sentence the student can say.

Charles Limb and Allen Braun put six professional jazz pianists inside a functional magnetic resonance scanner, with an adapted keyboard, and compared what happened in their brains when they played a memorised piece and when they improvised over the same structure with a recorded accompaniment that supplied the harmony and the pulse. During improvisation they found an extensive deactivation of the dorsolateral and lateral orbital regions of the prefrontal cortex, which are associated with self-monitoring, inhibition and deliberate control, together with a focal activation of the medial prefrontal cortex, which is associated with self-expression. The authors read the result as the neural image of a suspension of the inner censor, which is what any teacher of improvisation sees in a student’s face on the day the student finally lets go. The conditions of the experiment, which almost nobody cites, deserve attention. The pianists were improvising over a ground that others held. The censor could fall silent because the bass and the pulse were guaranteed from outside. What this addendum asks of the beginner’s left hand is exactly that, to guarantee from within what a recording guaranteed in the scanner.

Deleuze and Guattari gave this first function its best description without meaning to. Their ritournelle, the refrain, begins with a child humming in the dark. The tune leaves the darkness as it was and makes a small territory inside it, a centre from which one can then venture out. To lock the left hand into unwavering repetition, do nothing else and feel the ground is that first function exactly. The student still moves in the time before music. The student is making a place in which music can happen.

In the loom of melos, whose three strata were set out at the beginning of this essay, that place has an exact name. The drone and the ostinato are the Flesh and the Toward held at once. They are Flesh because they set on the keyboard a weight that does not move, a gift of gravity on which the body settles as it settles on its feet, and they are Toward because that weight beats, returns and pushes toward the next bar with the pure futurity of a pulse that never breaks. Between the two the middle stratum lies open, the Inclination, the instant in which something yields toward something, the appoggiatura that leans, the turn that lets itself fall onto the note of arrival. The Greek rhopé, the ancient name of that Inclination, designated the tilting of a balance, and a balance can tilt only about its fulcrum. The left hand is the fulcrum. The right hand can yield, waver, lean, linger and fall precisely because beneath it there is something that does not yield. Without ground the Inclination is free fall, with ground it becomes song.

B. Three families of ostinati

The first family, the oldest, is that of drone ostinati. It may be a drone on a single note, the tonic, D, or on tonic and dominant together, D and A. It may be the oscillation of an open fifth, D, A, D, A. It may be a tonic pedal with small ornaments, D, D♯, D, in neighbour notes that always come back to the centre. These ostinati serve Dorian and Aeolian, improvisation over a drone in the manner of the raga, modal folk styles, Byzantine chant and flamenco por arriba.

The second family is that of rhythmic ground ostinati, which derive from dance. Here belong the anapaestic pulse, low, high, high, the walking bass, a stepwise cell of four to six notes that repeats, the jota-like pattern, low fifth, octave, sixth, fifth, the tarantella-like pattern, with broken triads in 6/8, and the outline of a bulería still without the rigour of compás, bass, chord, chord, and again bass, chord, chord. They serve Mixolydian, Phrygian, hijaz-type modes and the pentatonics.

The third family is that of harmonic cycle ostinati, patterns that appear in one guise or another almost everywhere. The cycle I ♭VII ♭VI ♭VII, the Andalusian or lament family. The cycle i ♭VII ♭VI ♭VII, in natural minor. The rocking I ♭VII, the Mixolydian sway. The cycle I V IV V, proto-classical. The pair i iv, a lament base. Any of these cycles can be played in block chords, in broken chords, in arpeggios, as repeated two-note hooks or in imitation of the patterns of a bell.

C. How the student begins

The student chooses an ostinato from any of the three families and sets a slow tempo, or at least a steady one. Then the student locks the left hand into unwavering repetition and does nothing else. During that time the student only feels the ground, listens to it return, lets the body settle into its sway. When the ground is firm, and only then, the right hand begins. This develops the improvisational intuition of ground and figure, which is the first of all and the one that sustains all the others.

A possible first lesson begins like this. Let us imagine a seventeen-year-old student who has played Haydn sonatas and Czerny studies, who sight-reads well and who has never, not once in eleven years of conservatory, played a note that was missing from the score. She sits at the piano with her hands in her lap, and when she is asked to improvise her throat tightens and she smiles like someone apologising. The teacher asks nothing of her yet. He plays himself, in the low octave, D and A together, and then alternates them, D, A, D, A, at sixty beats a minute, and asks her to lay her left hand on his until she takes it over. Now she is the one playing the fifth, and the teacher tells her to go on, to do nothing else, that for two whole minutes the only thing that exists in the room is that rocking. At first she speeds up, because the silence of the right hand seems to her a gap that must be filled quickly. After a minute the pulse settles. After a minute and a half her shoulders drop. Then the teacher sings two notes over the drone, E and D, a falling appoggiatura, and asks her to sing them with him, and she sings them, quietly, without stopping the fifth. Then he asks her to find those same two notes with the right hand. She finds them. She repeats them six, eight, ten times, each time a little different without meaning it, one longer, another early, another with an F that has slipped in above and that she looks at in surprise, as if someone else had played it. After ten minutes she has four notes, D, E, F, G, and a way of her own of returning to D each time she gets lost. The teacher records a minute on his phone and plays it back to her. For the first time she hears something that sounds like music and that nobody had written for her. The first lesson ends there, without theory, without the names of modes, with a single task for the week, ten minutes a day of the same fifth and the same four notes, sung before they are played. Dorian will be named for her in a month’s time, when she already has it in her hand.

D. Instruments without a left hand

Those who have no left hand to lock have the ground available all the same, supplied in another way. For a string player, the open string is a drone, the folk fiddler’s double stops are organum, the musette is a pedal point, and the bow arm is the breath. For a wind player, the ground comes from a partner, from the feet or from the voice between phrases, and the breath cycle itself is already a timeline. For a singer, the ground can be a śruti box or a tanpura, a partner’s drone or body percussion. And for all of them there is the partner, because the duet over a held note is the oldest chamber music there is, the teacher, a looper, or one’s own improvisations kept in the audiovisual practice diary and played back as the ground for the next. The left hand was never what mattered. What mattered was always the ground.

E. The right hand sings

The second hand belongs to song, and it sings through the keys, in a modal and melismatic improvisation that has its own order. First one sings, always, and then the right hand imitates what the voice has sung. One begins with only two or three notes, then widens to the tetrachord and then explores the full mode. One uses neighbour notes, passing notes, turns and vocal ornaments, explores the changes of register, low, middle and high, and always ends on a cadential gesture proper to the mode. The sequence is the one that Salvador Chuliá’s school of song and arm applied to any phrase of the repertoire, where the line is sung before it is played and measured by whether it sings, carried over here to a line that did not yet exist five minutes earlier.

F. Mutation, modulation and change of mode

The hardest part comes afterwards, and mutation is its first form. Mutation is a pivot. One changes mode while remaining on an anchor note. One starts in D Dorian, pivots to D Aeolian by lowering the sixth, pivots to D Phrygian by lowering the second, and the note D has not moved during the whole journey while the world around it has changed colour twice.

To learn it, the student chooses a home note, say D, and sings three modes that all begin on that note. The student improvises ten seconds in each. Then the student improvises and switches without stopping, and each switch must be triggered by the change of a single note, a change of gesture or a new cadential tendency. With that discipline mutation leaves the technical formality behind and gains expression, because each altered note is heard as a decision of the affect.

G. Episodes, transitions and bridges

This is truly the hardest thing, because episodes are the place where composition begins. There are eight ways of leaving one place to arrive at another, and each can be practised on its own. The drone dissolve, in which the ostinato gradually disappears. The register shift, which jumps an octave and carries on. Rhythmic thinning, in which everything grows sparse and out of that sparseness a new idea grows. The sequenced cell, which repeats a motif transposed two or three times in order to move. The cadential pause, cadence, silence, new mode. The pedal shift, in which the left hand moves the bass, D, A, G, and a new space opens. The tetrachord swap, which changes the upper or the lower tetrachord to change the mood. And the metric change, from 4/4 to 6/8, which brings in a new dance archetype. They are taught one by one and combined afterwards.

H. Song and ancestral memory

Singing every day is non-negotiable, because improvisation is voice before instrument and composition is memory before notation. The student sings every day, memorises many folk songs, learns the songs and dances of their own land and carries ancestral patterns inside the nervous system. From this comes a bodily, cultural and spiritual rootedness that no exercise can replace, because the improvising hand can only recombine what memory has given it.

I. An anthology by the student’s origin

What follows is a small anthology for our own class. It mixes two strata that need to be distinguished, songs that passed from mouth to mouth and songs that were composed and then adopted. “Kalinka”, by Larionov, 1860, “Katyusha”, by Blanter, 1938, “Ochi chyornye”, “Santa Lucia”, by Cottrau, and “Funiculì, funiculà”, by Denza, 1880, written for the funicular, belong to the second stratum, and so does “O Pastor”, which is a song by Madredeus. I keep them, because the students carry them and a song people actually sing is worth more than a song people only collect. But beneath each lies the oral stratum I mean, the protyazhnaya and the wedding laments, the villanella and the tammurriata repertoire, the cantes of the Alentejo, which “Senhora do Almortão” already touches. When the student is ready, we go down one layer.

For Belgium, “Klein, klein kleutertje”, “Daar zat een sneeuwwit vogeltje”, “Ik zag Cecilia komen” and “Het waren twee koningskinderen”, with the Flemish dances, the polka, the mazurka, the bourrée and the Flemish branle, over the perennial forms of strophic song, call and response and ballads in AAB.

For Portugal, “Malhão, malhão”, “Senhora do Almortão”, “O Pastor” and the melodic archetypes of fado, with the regional dances, the vira, the chula and the corridinho, over strophic form, refrain form and the modal lament.

For Russia, “Kalinka”, “Katyusha”, “Ochi chyornye” and “Korobeiniki”, with the troika, the khorovod and the Cossack dances, over the long epic strophes of the byliny and refrains in ABAC.

For Romania, “Ciocârlia”, “Cucuruz cu frunza-n sus”, the “Sârba de la Orlea” and the doina, free and melismatic, with the hora, the sârba and the brâul, over the free-rhythm lament of the doina and the lively cyclic dances.

For Valencia, “La manta al coll”, “La malaguenya de Barxeta”, “La dansà” and the tradition of the cant d’estil, with the Valencian jota, the fandango and the dansà, over the copla with refrain and the modal Phrygian cadences.

And on our own doorstep there is a living practice of composition within performance, the versador of the cant d’estil, who invents the verse in real time and murmurs it to the singer one line ahead. Further north the bertsolari does it all alone, improvising sung verse on a demanded theme and rhyme scheme over a stock of memorised melodies, the doinuak. Between them they demolish, without argument, the notion that composing and performing are separate professions, and they confirm in passing what Pressing and Berkowitz described, because the memorised doinu is the referent and the invented verse is the figure that runs over it.

For Italy, Naples and Benevento, “Cicerenella”, “Santa Lucia”, “Funiculì, funiculà” and the tammurriata, with the Campanian dances, the tammurriata and the tarantella, over strophic songs with refrain and the tarantella cycles.

J. How a piano lesson unfolds

The lesson begins with singing. A folk song from the student’s country is sung, or a folk poem is recited rhythmically. The mode of the song is explored, a simple descant is improvised over it, the rhythm is embodied with clapping or with steps. The first quarter of an hour roots the student in their own ancestry before anything is asked of them.

Vocal improvisation on the repertoire follows. A small motif is taken from the piece the student is working on, sung, ornamented, its intervals widened, and improvised around with the voice, and phrasing and understanding deepen without anyone having explained anything. Then comes keyboard improvisation related to the repertoire. The rhythm of the piece is taken, its mode or its harmony, a cadential pattern, and one improvises freely with them, so that the dialect of the work is internalised at once.

Then the written work, a short counterpoint exercise, a Fuxian cadence or a short partimento, a harmony exercise, basse donnée or chant donné. That is where craft is built.

The repertoire takes up the smallest part of the lesson. Attention goes to breath phrasing, characterisation, embodiment, gesture and affect, articulation and rhetoric, the dramaturgy of the line, and mechanics stays at the service of meaning. The specimen of the Chopin nocturne shows what these six minutes contain.

The lesson ends with improvisation or composition. A motif is expanded, a short binary piece is made, two lines of counterpoint are written, a modulation is tried, a minimal composition exercise is done. The lesson ends as it began, with an act of creation, and correction, which has also had its place, remains inside it as the scaffolding remains inside the finished house.

XIV. Addendum II. Extended practical guide, step by step

The first addendum opened the road quickly. This one walks it slowly, stretch by stretch, with the minutes counted, and it begins again with the left hand, whose task is to give the student simple and reliable patterns that anchor the right hand and make improvisation coherent from the very first day. The three families of ostinati already named unfold here into techniques, variants and a plan of study.

A. The drone

The first family is made of static pitches, sustained or repeated, that create a sonic centre. The simplest is the drone on a single note, the tonic. One chooses the tonic, say D, and holds it, with the pedal or with a low octave repeated in every bar. It is played at mp, with no changes of articulation, and the practice consists of three unbroken minutes of singing over it in phrases of four to eight seconds.

The second variant alternates tonic and fifth. The left hand alternates low D and A every half bar or every bar, legato on the tonic and with a slight accent on the fifth that defines the pulse. The exercise asks for a steady pulse while one sings a three-note pattern from the tetrachord.

The third is the low drone with neighbour notes. The D is sustained and, every two bars, a neighbouring D♯ appears and returns, as a grace note or as an appoggiatura. It serves the modes that have an expressive neighbouring semitone, and the exercise has a single aim, to make the ornament feel like breath.

Here the teacher encourages the sensation of breathing with the drone. What sounds is closer to plainchant than to accompaniment, and it should be heard that way, as the ison that the Byzantine choir stretches beneath the soloist, a voice that has become ground so that another can become figure.

B. The rhythmic ground

The second family comes from dance. The two-note hook puts a low note on the first beat and a higher chord on the second. It is locked in with the metronome, the first beat lightly accented, and short motifs are sung over it.

The walking bass repeats a four-note cell in every bar, D, E, F♯, G, in even quavers, while the right hand improvises pentatonic lines above it.

The dance ostinato in 6/8, of the tarantella or the jota, puts the low bass on 1 and two broken-chord strokes on 4 and 5. One counts from 1 to 6. The left hand plays on 1 and on 4, and the right hand improvises on 2 and 3 and on 5 and 6, so that the two hands share the bar like two dancers taking turns on the floor.

The outline of the bulería, simplified, alternates bass, chord, chord and again bass, chord, chord, with a feel of 3+3. A subtle sway is kept and the pulse is underlined, still without the rigour of compás.

Before playing any of these patterns the student taps or walks the dance, because physical movement ties rhythm to the body, and the teacher does not let the student sit down until the feet know it.

C. The harmonic cycle

The third family turns on chords. The cycle I ♭VII ♭VI ♭VII, modal and descending, is played in the left hand with block chords on 1 and 3, or arpeggiated. It is practised by arpeggiating slowly while the right hand improvises a modal melody that touches the characteristic degrees. The pair i iv, the lament and the base of the doina, keeps a low drone on i and intersperses iv as harmonic colour every two bars. The romanesca, which is Pachelbel’s bass, is played with small arpeggios in the left hand while the right hand sings motifs that repeat over the cycle.

With any of the three families the work goes in blocks of thirty minutes. The first five serve to choose the family and lock the left hand with the metronome at 60 and then at 80. Ten minutes of improvised singing over it follow, first with the voice and then mirrored on the keyboard, another ten to add a family of ornaments in the right hand, and the last five to write out an eight-bar pattern.

D. The sixty-day ladder

Variation and complexity rise by stages. Between day 1 and day 7 the left hand plays only a single drone or a two-note hook, and the right hand does nothing but melodic singing. Between day 8 and day 21 the walking bass or the ostinato in 6/8 comes in, and the student practises changing ostinato every four bars. Between day 22 and day 60 the harmonic cycle is combined with the rhythmic ostinato, and the left hand repeats chord shapes while varying the bass. Every week there is a test, a three-minute audiovisual recording with two ostinati, one mode and a mutation into a hybrid mode.

The ladder has the shape it has for a reason that Pressing put into words. Each rung adds a new decision only when the previous one has become automatic, so that the student’s attention is never divided among more things than it can hold. The drone of the first week asks almost nothing of the left hand and everything of the voice. The change of ostinato in the second stage is possible only when each ostinato already runs unwatched. The combination of cycle and rhythm in the third presupposes two automatisms that have fused into one. Skipping a rung sends the student back to the paralysis of the first day.

The student also keeps a practice notebook, in which at least one left-hand ostinato is notated for each day of work, with the modes and the character it serves best. Once a week the student makes an audiovisual recording in which only the left hand is seen and heard, to check the firmness of the ground without the right hand disguising it.

E. The voice of the right hand

The aim of the second hand is to develop a vocal right hand, with melismas, ornamentation, modal gestures and the shaping of breath. That is why it begins with the voice, in a daily sung warm-up of five minutes that passes through a single note, the tetrachord, the ladder of the mode and two short phrases. Each phrase is sung and then imitated with the right hand. Singing internalises the micro-timing and the micro-inflections on which melisma depends, and which no fingering teaches.

F. Micro-skills

The exploration of the tetrachord lasts five to ten minutes. The lower tetrachord is taken and played and sung ascending, descending and then arpeggiated in the order 1, 3, 2, 4. It is repeated sixteen times with varied rhythms, straight, syncopated, in triplets.

The building of melisma lasts ten minutes. One starts from a single pitch and adds a passing note, a neighbour note and chained turns in groups of four, and the whole is practised as one long phrase. The model form is four bars of sustained left hand beneath a melisma of eight to twelve notes in the right hand that ends on a cadential note.

The vocabulary of ornaments takes another ten minutes. Three are defined, the trill, the short sliding appoggiatura and the small turn, and each is practised on cadential notes and on passing notes, under a rule that admits no exceptions, that ornaments live between the structural tones.

Contour and the logic of the phrase take the last ten. Small motifs are composed, a rise of two or three notes, a fall of two or three notes, a landing, and they are linked by breathing, with the breath points planned before one starts.

G. From song to keyboard

Three exercises lay the bridge between voice and hand. In the echoed phrase, the teacher sings a phrase of four to six seconds and the student imitates it, first with the voice and then at the keyboard. In call and response, the student’s right hand plays a short melisma, the teacher answers with a rhythmic ostinato or a change of drone, and the student modifies the motif on repeating it, adding an ornament or lengthening it by one or two notes. In the micro-story, the student improvises sixteen bars in three parts, A with the initial motif, B with its melismatic development and C with the cadence, and afterwards notates the motifs of A and B.

On that bridge the modal melismatic strategies are built. First the characteristic intervals of the mode are identified, and they must be heard as centres, the augmented second in hijaz, the minor second above the final in Phrygian. Then that interval is made into a motif and repeated as an anchor. Then ornamental patterns are sought that underline it, such as an appoggiatura falling onto the augmented second. Finally simple modal cadences are built that bring it home.

H. The daily plan of the right hand

The right hand works every day for thirty to forty minutes. Five go to sung tetrachords and modal ladders, ten to melismatic runs and ornaments, ten to improvising with the right hand over the chosen ostinato, rotating the ostinato daily, and five to recording and marking one or two phrases that will be notated later. Each week a three-minute audiovisual recording is made.

I. Mutation and modulation

The third stretch looks for reliable and expressive ways of moving between modes and of mutating without breaking the flow. Two operations that ordinary speech confuses must first be told apart. Mutation changes the modal flavour while keeping the centre, the same tonic. Modulation moves the centre to another tonic. The two can be blended, and one must know at every moment which of the two one is doing.

The common-tone pivot is the best strategy for mutation. A pitch shared by both modes is identified and sustained in the left hand for one or two bars. Above it the characteristic sound of the new mode is introduced as a neighbour note in the melody and underlined with an accented melodic resolution. The exercise leads from D Dorian to D Aeolian over the common note D, sung first and played afterwards.

The tetrachord swap divides the mode into a lower and an upper tetrachord and replaces the upper with that of another mode. A short sequence is created that uses first the old tetrachord and then the new, and the change happens at the pivot of the sequence. The exercise is an eight-bar pattern that alternates the tetrachords every two bars, smoothed with passing notes.

The chromatic approach introduces a single alteration, treats it as an appoggiatura, then prolongs it and finally makes it structural through repetition. The exercise leads from Lydian, with its augmented fourth, to Ionian, treating the ♯4 first as tension and then normalising it.

The cadential re-pivot prepares a cadence in the old mode and, on the cadence itself, makes a harmonic or pedal leap toward the new tonic, which is reaffirmed at once with a clear cadence. It is the strategy of drama, and in the early stages it is used sparingly.

A possible lesson on the common-tone pivot goes like this. A thirteen-year-old student who has spent three weeks with the fifth D and A in the left hand improvises in Dorian with ease and is beginning to get bored. The teacher asks him to change nothing except one note, to let the sixth, the B natural, drop to B flat the next time he passes through it, and to stop on it instead of letting it slip by. Let us imagine what happens. The boy reaches the B flat, plays it, hangs on it for a long second, and the D in the left hand, which has not moved, suddenly sounds lower, darker, as if the room had lost a window. He goes back to B natural and the window opens. For ten minutes he plays at opening and closing that window, and by the end of the lesson he knows what Aeolian is without anyone having said the word, because he has felt it as a shadow falling over a note that has not moved.

J. Micro-exercises and listening

The three-mode anchor is practised daily. With D as tonic, the student improvises thirty seconds in each of three modes and then three minutes of free mutation among them. The one-note pivot holds the pivot note in the left hand while above it the mode changes every eight seconds using only three notes. The tetrachord map notates, for five modes, the lower and upper tetrachords of each, and asks for eight bars to be written for each hybrid that results from crossing them.

To this listening is added. The student transcribes eight bars of an example, from folk music, a raga or a maqam, that shows a modal change, and identifies the pivot technique that produces it.

K. Episodes

The fourth stretch teaches how to create musically convincing connective material. The sequential episode extracts a cell of two or three notes from A, sequences it stepwise three or four times, alters the pitch content in the last statement so that it fits B, and lands on a chord or a drone that already belongs to B. The sequences are kept short, two bars each, so that the listener does not hear them as mere repetition.

The ostinato episode introduces a new ostinato and fades out the ostinato of A while that of B grows, and meanwhile the right hand improvises linking motifs on notes common to both.

The drone dissolve holds the drone on the pivot pitch while everything else thins out, until new melodic material appears above the drone with the colour of the new mode. It serves meditative or theatrical transitions.

The register shift ends section A very high or very low, with a diminuendo, and begins the new section at once in the opposite register, keeping the motif recognizable as a link.

Metric re-anchoring uses hemiola or rhythmic displacement to suggest the change. A bar of hemiola is inserted over the repeated pattern and the music resumes in the new metre.

L. A piece of thirty-two bars

Everything above comes together in a small-scale construction plan, a piece of thirty-two bars with two sections and an episode. Bars 1 to 8 are A, in mode X, with an ostinato in the left hand and melody in the right. Bars 9 to 16 repeat A or vary it with the motif augmented or diminished. Bars 17 to 20 are the episode, with a sequenced cell and a change of ostinato. Bars 21 to 32 are B, in mode Y after the pivot, with a new melodic idea that is heard as a consequence of what came before. The assignment asks for three variants of the piece, each with a different pivot technique.

Before accepting an episode the student asks five questions. Whether there is a common note or a pivot. Whether the harmonic function is coherent at the landing. Whether the listener receives an anchoring gesture that makes the change feel motivated. Whether the episode has dynamic and registral shaping. And whether it ends on a cadence, explicit or implied, that prepares the arrival.

M. Daily singing and folk memory

The fifth stretch builds an embodied repertoire and a visceral tonal memory, so that improvisation and composition have their source in tradition. The daily prescription of singing lasts twenty-five to thirty-five minutes in all. It begins with five minutes of warm-up, breathing, a single note, the ladder of the chosen mode. Ten to fifteen minutes of repertoire follow, three folk songs sung from memory, rotating daily, with at least one new folk fragment learned and memorised each week. Then come five to ten minutes of improvisation over a folk melody, ornamenting and paraphrasing the line, and five minutes of reflection in which the student notes the characteristic gestures of the song and the places where they might appear in a composition of their own.

Folk patterns are internalised by active listening, ten minutes a day of recorded folk singing from the student’s region. One sings along, attending to micro-timing and ornamentation. Four to eight bars are transcribed from memory, with the modal degrees and the characteristic intervals noted. From this a bank of motifs is formed, six per song, in a notebook ordered by song and by region, and each day one of them is used in improvisation.

The anthology of the first addendum asks for different handling according to origin. The Belgian songs are learned by ear, a regional variant is sought, and they are sung both strophic and ornamented. From the Portuguese ones the basic rhythm of the vira and the chula is learned and the phrasing imitated. From the Russian, Romanian, Spanish and Italian ones a verse and a refrain are learned, and improvised descants are practised over them.

Singing also has its life in a group. Once a week a singing circle is formed in which each student teaches a tune to the others by singing it and showing its ostinati. Once a month there is a public memory assignment, a folk song performed live or recorded.

N. A sixty-minute lesson

The lesson begins with arrival and centring, a brief conversation, a check of posture, breathing, and a question from the teacher that sets the tone for everything else, “What folk song have you brought me today?”

The sung warm-up and the folk song follow. The student warms up and then sings from memory the song they have chosen, or learns its first verse. The prompts are aimed at a particular ornament, at micro-timing and at the breath points, and the micro-assignment for the next lesson is to mark two places to ornament.

Then comes vocal improvisation on the repertoire motif. The teacher gives a left-hand ostinato and the student improvises vocally over it two or three times. A fragment is recorded, and the reflection that follows identifies one melodic gesture worth keeping.

Keyboard improvisation carries that gesture across. The student imitates their own vocal improvisation with the right hand, first with one hand alone and then with both, the ostinato in the left, and the whole focus is on capturing the vocal phrasing in the right hand.

Written craft takes the form of a short Fuxian cadence or a one-bar counterpoint exercise related to the student’s melody. A given bar is written or completed there, and the teacher corrects the voice leading.

The repertoire arrives with a new focus, phrasing, rhetorical punctuation, micro-pauses, gesture. The student plays a phrase and the teacher guides the breath points.

Composition and development take the day’s melody and apply a procedure to it, augmentation, sequence or mutation, and the teacher suggests a change of orchestration or registration.

The lesson closes with a one-minute improvisation that consolidates the work and with homework set as measurable tasks.

O. Criteria and tasks

Each activity has its criteria. In singing one looks at stability of pitch, planning of the breath and the ornaments. In improvisation, the development of the motif, modal clarity and variety of register. In written craft, correctness of voice leading and cadential clarity. In repertoire, the character of the phrasing and the dynamic shaping.

Homework follows a template of four assignments. The first is to memorise the second verse of the folk song and sing it five times a day with a metronome. The second, to practise the assigned ostinato ten minutes a day and record an improvisation of sixty seconds over it. The third, to notate the day’s improvised motif, two bars long, and produce a variant by sequence. The fourth, to complete the assigned Fux cadence and send it in before the next lesson.

P. The close and the portfolio

The final ten or fifteen minutes of every lesson follow a formula of micro-composition. For one or two minutes one captures, recording sixty seconds of free improvisation. For two or three one extracts, and the student chooses from that recording a motif of two to four notes. For three to five one applies a compositional procedure and writes four to eight bars. For two or three one adds texture, a second voice, a descant or a simple ostinato. And at the end one archives, saving the recording and the notation in the student’s portfolio.

That portfolio grows lesson by lesson, because each lesson yields a recorded improvisation and a notated micro-piece. After eight lessons a portfolio of ten to fifteen minutes of music is compiled to be reviewed together, and the teacher gives thematic feedback and proposes a target for the next module.

Between lessons the student follows a daily checklist. Twenty to thirty minutes of singing, with tetrachords and a folk song. Twenty to thirty minutes of left-hand ostinato with three short takes of improvisation over it. Ten to twenty minutes of melismatic exercises with the right hand. The notation of an improvised motif of two bars. And a Fux cadence or a short realisation of a basse donnée.

XV. A small act of making

When the lesson ends, the student walks away without a page littered with corrections and without a score disciplined into obedience. The student carries away something that did not exist that morning, a small act of making. Sometimes it is eight bars that pulse with a new contour, sometimes a variation set that flickers with its own logic, sometimes a brief modal improvisation caught on video before it disappears. Whatever its shape, it is alive, unrepeatable and unmistakably the student’s own. From the chamber rehearsal one comes away with spoils of the same lineage, a join that at ten in the morning was a stumble and by one o’clock breathes, an upbeat that four bodies have learned to take in a single breath, an improvised bridge that the ensemble discarded and that nonetheless taught it why the written bridge was the right one.

As the weeks lengthen, these small creations begin to gather into a kind of secret musical biography, a personal songbook. Melodies drawn from the untrained voice accumulate like field notes from an inner landscape. Transformations multiply under the hand until a motive begins to think for itself. Modal improvisations stretch and curl into unexpected regions. Counterpoints, stiff at first, suddenly learn to breathe. Orchestrations acquire colour as though the student were discovering new wavelengths of light. And then, naturally, a larger recognition arrives.

The procedures that animate a Bach invention and those that guide a Berber ahwash singer stop seeming distant species and are recognised as relatives. The Purcell chaconne bass and the riff of the Gnawa guembri obey the same gravitational pull of the ostinato. The sequential bridges of a Mozart sonata and the sequential episodes of a raga bandish are made of the same dramatic instinct, the same ancient desire to move from here to there without abandoning the place one set out from.

The borders begin to loosen. The taxonomies that once seemed solid dissolve. The student has stopped learning “classical,” “jazz” or “world music.” The student is simply learning to be musical, and the musical, stripped of its uniform of identity, reveals itself as a mode of being, as the way of shaping time with sound in the broadest and oldest sense of the phrase.

What unfolds in this perennial approach is the slow formation of whole musicians, where the inherited institution was content to train specialists. These musicians do not aim to reproduce repertories. They learn to inhabit the deep grammar that all musics share, the quiet architecture beneath gesture and line. The forms and procedures gathered here are few, and yet their combinations stretch outward like constellations. Learn them once in their bare, neutral clarity, and they become a passport with no borders, a freedom that no longer depends on style or school.

That quiet architecture has an ancient name and a figure the reader already knows, the loom. Melos (μέλος) was in Greek at once the limb of the body and song, and its weave crosses three vertical threads with three horizontal strata. The threads are léxis (λέξις), the saying that precedes everything said, harmonía (ἁρμονία), the fitting by which sounds attract one another and gravitate toward each other, and rhythmós (ῥυθμός), the form of what flows, heartbeat, stride, breath and dance. The strata are the Flesh, with the face, the breath and the weight that no one chooses, the Inclination, that instant in which something yields toward something, and the Toward, the pure futurity of a direction that has not yet arrived. The eight bars the student takes home contain all nine crossings without the student needing to know it. The intake of breath before the first note was the Flesh of saying. The appoggiatura on which the melody leaned, read at last as “lean on me,” was the Inclination of harmony. The pulse that carried it to the cadence was the Toward of rhythm. And the three lenses of these pages turn out to be three ways of travelling through a single weave. Gesture cuts the weave vertically and crosses the Flesh, the Inclination and the Toward in an instant. Procedure runs through it diagonally, carrying what lies in one cell to another, where it makes the weave fertile. Form runs through it horizontally, along the Toward, and is the trace that direction leaves once it has been fulfilled. None of the three knows the whole weave without the other two.

Hence the lesson can cease to be a guided tour of historical museums and come more and more to resemble the acquisition of a language. Music emerges as a living tongue with innumerable dialects, all of which can be spoken from within, and the archive that was to be preserved is left behind, useful, consultable, harmless at last. Yet a language is learned from the side by which children learn it, calling and being called. Before naming anything, the child shouts a name and someone comes. The vocative case of the ancient languages does exactly that, it calls without predicating, it summons without saying anything about what is summoned, and music is vocative in that sense before it is representational. That is why the deep grammar I defend is the grammar of a saying and never that of an object said, and that is why the call, that leap of a fourth or a fifth toward a held note which the catalogue of gestures gathered among the street cries and the kulning of the herdswomen, turns out to be the founding gesture of all the others. The order follows from it without effort. First the Call, then the Song that answers, then the Gesture in which song becomes body, and only at the end the Sound that the instrument fixes. “Sing first, keyboard second, paper last” was that order put to work in the classroom, and the school of song and arm in which I was trained practised it long before I knew how to name it.

Rescuing music from the places where it has been quietly exiled begins exactly there. The exiles are five, and their direction is known. The museum, where sound is embalmed as heritage. The laboratory, where sound becomes data and analysis. The idea of the opus, which forces music to harden into objects instead of flowing as action. The tyranny of technique, which severs craft from imagination. And the long shadow of history, under which style is mistaken for substance and chronology for meaning.

Against those five exiles, the orientation I hold reclaims music as process, as a continual unfolding that no canon closes, as something that happens before it is something that is. It also restores the ancient triad of song, dance and poetry to its true rank as ontological forces, prior to any division into genres, the very movements through which human beings organise breath, gesture and word into form. At the centre of the triad stands song, and song, as these pages have grounded it, is the comparecencia of music in a body, its appearing in person, the coming-forth of one who answers a summons. Comparecer, from the Latin comparescere, is to present oneself when called, to come in one’s own body to a summons, and the word keeps the whole sequence intact. Someone calls, someone comes forth, and what comes forth sings. The Latin carmen was at once song and spell, a formula that made come what it named, and a music lesson well conducted keeps something of that ancient efficacy, because in it sound comes when called.

Every exercise returns the student to that process. So does every small creation, and every improvisation recorded before it fades. In this way we remember that music was never born in archives, exam rooms or concert protocols. It was born in bodies, in voices that had no training, in steps and chants and inflections that had no need either to justify themselves by style, period or method.

Reopening that space is the task. A place where music can again occur without asking permission from history. A place where the lesson ceases to be the rehearsal of an imagined performance and becomes a moment of becoming, and where rehearsal itself, in chamber music and in the orchestra, recovers its old sense of a shared attempt. A place where sound is allowed to be alive, contingent, unfinished and, for that very reason, truly musical.

The call keeps sounding while someone answers it. The lineage we inherit, the one we thought lay behind us, is within, waiting for breath, waiting to be said again.

XVI. Companions on the way

Many of those who keep company with this path have already spoken within it, in the place where their voice was needed. Humboldt with his language as activity, Valéry with his poetics of doing, Gadamer with a play that exists only while it is being played, Kierkegaard with a repetition that looks forward, Aristotle and the Gorgias with the border between craft and knack, Small and Goehr with the verb of music and the date of its museum. Plato, Aristoxenus and Cleonides for melopoiía and its parts, Aristides Quintilianus for the unity of melos, rhythm and word that his treatise still upholds, Thrasybulos Georgiades for the mousiké in which music and language were a single body and for the history of its coming apart. Tinctoris for res facta, Benveniste for rhythmós, Goethe, Pareyson, Simondon, Benjamin, Focillon and Kubler for form understood as forming, Hepokoski and Darcy, Caplin, Gjerdingen, Propp, Rosch and Wittgenstein for the art of conversing with an archetype. Gustavo Bueno and Vicente Chuliá uphold the objection I discuss in “Form or institution,” and their theory of musical institutions obliged me to say better what recurs and why. The Figurenlehre, Mattheson, Ganassi, Ortiz, Zarlino, Artusi, Kircher and Llull give procedure its ancient doctrine, and Babbitt, Lewin, Ruwet, D’Arcy Thompson, Lindenmayer and Pólya give it its algebra. Others walk in the background without having taken the floor, and they deserve to be named.

On the museum as a late invention, Kenneth Hamilton shows that the ritual of the recital was assembled between roughly 1870 and 1920, and that before those dates pianists preluded, improvised and rearranged in public. Theodor Adorno, from the opposite camp to almost all my arguments, supplied the first exile in four words, since museum and mausoleum, he wrote, are connected by more than phonetic association. Marcel Detienne and Jean-Pierre Vernant restored to mêtis its dignity as the intelligence of the navigator and the weaver.

On gesture, the energetics of Ernst Kurth, Sound and Symbol by Victor Zuckerkandl, the musical forces of Steve Larson and the mimetic hypothesis of Arnie Cox, who hears music as an invitation to imitate it with the body. Beside Hatten, Smalley, Laban, Warburg, Agamben and Merleau-Ponty, who have already spoken in their chapter, and behind all of them, the neumes, which were gestures before they were signs.

On the generative lesson as it was and as it is reborn, alongside Bach, his son Carl Philipp Emanuel, Czerny, Riepel, Koch and Sanguinetti, the partimento method of Job IJzerman, the guide to historic improvisation of John Mortensen and the improvised counterpoint that Peter Schubert has brought back into the classroom.

On the pedagogies that begin where this one begins, Kodály, who put singing and folk song first, Orff, with his ostinato, his speech rhythm and his elemental improvisation, Dalcroze, who put the body first, the mother tongue of Suzuki and the audiation of Edwin Gordon. And the composers who wrote the catalogue of procedures as piano music, Bartók in the Mikrokosmos and Kurtág in the Játékok, which begin from the palm, the forearm and the pleasure of playing.

On the oral engines, Milman Parry and Albert Lord, among whose singers the apprentice acquires formulas as a child acquires a language, Leo Treitler, who carried that model over to Gregorian chant, and Bruno Nettl, for whom to improvise is always to work upon a model. Savage, Mehr, Malloch and Trevarthen, already cited, give that intuition its data.

And on procedure as a word, Viktor Shklovsky and his priyom, which Spanish has rendered both as artificio and as procedimiento, with his laying bare of the device, which is what a lesson does to a motive. Michel de Certeau and his ways of doing, his tactics and his strategies, beside the Oulipo, Queneau and the refrain of Deleuze and Guattari. And the Durcharbeitung of Freud, elaboration, working through, the exact name for what happens between a first attempt and a good one.

XVII. Appendix. Glossary of the three lenses

A working vocabulary, by lens and by register, with the minimum gloss needed for each term to be usable in the workshop. The claims of these pages are large, ontological nucleus, deep grammar, recurrent patterns, and large claims are best defended with words that are themselves old, cross-cultural and drawn from inside the making of music. That is why the whole text prefers the Greek process-words and the craft terms of living traditions to the vocabulary of aesthetics. The Greek words of gesture that the chapter on the perennial gestures already glosses one by one, from kínesis and hormé to cheironomía and schêma, stay where they are and are recalled here only when the loom gives them a new office.

The loom and the call

Loom. The figure by which I name the weaving of song. Melos (μέλος) meant in Greek both a limb of the body and song, and the loom is the frame on which that sung body is woven. It has three vertical threads, léxis, harmonía and rhythmós, and three horizontal strata, the Flesh, the Inclination and the Toward. Their crossings give nine cells, and each cell is a place where work can be done. Plato’s triad in Republic 398d, according to which melos is composed of lógos, harmonía and rhythmós, is the warp from which the loom starts, with one decisive radicalisation, because where Plato put lógos (λόγος) the loom puts léxis. The three lenses of this essay are three ways of travelling across a single fabric. Gesture enters through the Flesh, procedure works in the Inclination, form is the trace the Toward leaves once it has been fulfilled, and each of them crosses all three threads.

Léxis (λέξις), first thread. The saying, the vocative direction of music, the saying before the said. It comes before articulate language, and it coincides neither with style nor with the diction that later rhetoric called by that name. It comes from légein (λέγειν), to gather, to collect, as one gathers ears of wheat or bones, and it keeps that gesture of bringing the scattered together in a single direction addressed to someone.

Harmonía (ἁρμονία), second thread. The fitting. In Homer the joint that fastens the planks of a ship, in music the gravitation of sounds, what sounds together and attracts, the leading note that falls into place, the dissonance that pulls, the drone that holds the world steady.

Rhythmós (ῥυθμός), third thread. The form of what flows, as Benveniste rescued it from the pre-Socratics, the form that something in motion takes on in the very instant of taking it on. Its bodily analogues are four, the heartbeat, the stride, breathing and dance, and that is why rhythm is learned with the feet before the fingers.

Flesh, first stratum. What one has without having chosen it, the face, the breath, the weight, the gifts of the body that the musician receives before knowing he is a musician. In the essay it appears in the pneuma, the breath before sound, and in the weight of the arm that sound makes use of instead of striking.

Inclination, second stratum. Intention, gravitation, gesture, the instant in which something yields toward something. Its smallest musical figure is the appoggiatura read as a command to lean, the note that lets its weight down onto the next.

Rhopé (ῥοπή). The Greek name of the Inclination. It designated the tilting of the needle of a balance, the instant in which it yields to one side, and it names with physical exactness what the stratum names with ontological breadth.

Toward, third stratum. Direction, continuity, pulse, pure futurity. It is what the agōgē gives to music when it gives it a whither, the pull of a phrase toward its cadence before the cadence exists.

Vocative. The case of the call, the case that summons without predicating anything of what it summons. The vocative thesis holds that music calls before it represents, and from it follows the founding order, Call, Song, Gesture, Sound. The call in the catalogue of gestures, a leap of a fourth or a fifth toward a held note, is for that reason the gesture that founds the others, and the whole order is the reason for “sing first, keyboard second, paper last”.

Comparecencia. The name I give to the presence of music in a body, an appearing in person, the coming-forth of one who answers a summons. To comparecer, from the Latin comparescere, is to present oneself when one is called, and that is why the word joins the vocative to song. Song is the comparecencia of music, the body that answers its own call.

Synousía (συνουσία). The being-together of master and disciple out of which, in the Seventh Letter, after long association, the spark is born that afterwards feeds itself. It is the true name of a lesson, and also of a chamber rehearsal.

Choreía (χορεία). Singing and dancing together. The Laws make it the very definition of education, so that the educated man is the one who has danced in the chorus and the uneducated man is the achóreutos (ἀχόρευτος), the one without a chorus.

The two tetrads

Tonḗ (τονή) and tónos (τόνος). The fourth part of melopoiía in Cleonides is the tonḗ, the sustained note, and the essay reads it as tónos, tension. Both words come from teínō (τείνω), to stretch, so that the sustained note and tension are the same stretching seen from two sides, the string that is held and the force that holds it. It is the best etymological argument in the whole text, because it shows that to sustain a sound is already to tense it.

Flexa. In the psalm tone, a minor inflection of the reciting note, a brief fall, usually of a tone, or of a minor third when there is a semitone below the tenor, which appears when the first half-verse is long and comes before the mediatio. The chant books mark it with a cross. In the second tetrad it holds an exact place, the fold the tenor makes within itself before the mediatio gives the utterance its interiority, a breath that stops short of a caesura.

Gesture

From the Greek of gesture there remain to be added pathos, what is undergone, and hexis, embodied disposition, which Bourdieu will call habitus. From Latin and from the workshop, besides what the chapter on gestures already gathers, Spinoza’s conatus and Bergson’s élan.

In the metaphorical and literary register, trace, stroke, imprint, brushstroke, bearing, sign, pulse, heartbeat, tremor, breath, thrust, flight, fall and weight. Laban supplies a whole vocabulary with his four factors, weight, space, time and flow, and his eight efforts, punch, float, glide, slash, press, wring, flick and dab.

In the ontological register, besides Warburg’s Pathosformel, Agamben’s pure mediality, Merleau-Ponty’s flesh and chiasm, the Leib against the Körper, Brecht’s Gestus, Benjamin’s Gebärde and Focillon’s praise of the hand, Deleuze’s affect and intensity, the event and singularity.

Form

In Greek, morphé, form and figure, which with hýle, matter, makes up the hylomorphism that Simondon taught us to distrust. Eîdos, the seen, the idea. Typos, the stamp, the mould, and archétypon, the first impression. Táxis, order and arrangement. Parádeigma, the model, and in grammar the table with empty cells. Schêma, figure and configuration. Harmonía, already glossed as a thread of the loom. Symmetría, commensurability. Kósmos, order and ornament at once. Télos and entelécheia, holding one’s end within oneself, form as act. Péras and ápeiron, limit and unlimited, from whose mixture form is born in the Philebus. Hólon, the whole. Sýstasis, the composition of events in the Poetics. Sýstema, in harmonic theory the stacking of tetrachords. Oikonomía and diáthesis, the internal economy and the arrangement of a work. Éthos, the character of a mode, and in Homer a haunt or dwelling, which is why modes can be inhabited. And rhythmós, which governs this whole lens and already has its entry as a thread.

In Latin and in technical jargon, Auerbach’s figura, dispositio, compositio, formula, clausula, with the cadential formulas cantizans, tenorizans and bassizans, modulus, the common root of mould, model and module, matrix, Alberti’s concinnitas, proportio, the integritas, consonantia and claritas of Aquinas by way of Joyce, the topos and the loci communes with Ratner’s theory of topics, Gestalt and Bildung, Gliederung or articulation into limbs, Schoenberg’s Grundgestalt, Schenker’s Ursatz and Urlinie, whose hierarchy I reject and whose ear I admire, Humboldt’s innere Form, Riegl’s Kunstwollen, forma formans and forma formata, Pareyson’s formatività, and the Formtypus, Satzmodell, Reihungsform and Entwicklungsform, Bogenform, Kettenform and Rahmenform of German theory. From philosophical materialism, the institution, with its nucleus, its body and its course.

In the metaphorical and literary register, architecture, organism, skeleton, framework, scaffold, mould, matrix, crystal, Benjamin’s constellation, cartography, relief, horizon, contour, silhouette, weft and warp, weave and texture, since textus is text, grid, vessel, envelope, dwelling, vault and threshold. Goethe adds metamorphosis, morphology and Urphänomen.

In the ontological register, essence, ousía, entelechy, act and potency, individuation and prise de forme in Simondon, with transduction and metastability, Thom’s morphogenesis, structure, totality, limit, determination, and Klein’s invariant, what survives a group of transformations.

Procedure

In Greek, méthodos, from metá and hodós, the road one follows, and hodós, the road itself. Póros, passage or ford, whose lack is aporía, so that a procedure opens a póros. Téchne, reasoned craft, against tribé and empeiría, knack and routine. Poíesis against prâxis, the doing that produces something against the doing that is complete in itself. Mêtis, the cunning intelligence of the navigator, the hunter and the weaver. Kairós, the opportune instant, which in the loom is the moment the shuttle crosses the open warp. Melopoiía, the making of melody, with its four parts, agōgē, plokē, petteía and tonḗ. Metabolé, change, by genus, by system, by key and by melopoeia. Kanón, rule, and in the fifteenth century the verbal rule from which a canon was resolved. Éphodos, Archimedes’ word for his Method. Órganon, the instrument. Mechané, artifice and machine. Trópos, turn and manner. Áskesis and meléte, exercise and rehearsal. Peîra, trial. Diaíresis and synagogé, dividing and gathering. Análysis and sýnthesis. Heúresis, finding. Phrónesis, knowing what to do here and now. And érgon and enérgeia, in Humboldt the work against the activity, which is why form is érgon and procedure enérgeia.

In Latin and in the musical craft, procedere, to go forward, processus, via and iter, modus operandi, ratio, ars, with the ars combinatoria of Llull and Leibniz and the ars inveniendi, inventio, the first canon of rhetoric and the title of Bach’s teaching pieces, exercitium, experimentum, operatio, regula, disciplina and elaboratio, the Durchführung or development, a leading through, the thematische Arbeit, Schoenberg’s developing variation, Satztechnik, Handwerk and Verfahren, procedure, and then series, permutation, inversion, augmentation, cancrizans and Lewin’s transformation.

In Castilian and the Iberian languages, which this blog prefers, the tiento, from tentar, to touch, to try, to feel one’s way, gesture and procedure in a single word and better than toccata. The glosa and the diferencias of Ortiz, in 1553, and of Narváez, in 1538, the Castilian names of diminution and variation. The pasacalle, the falseta, the versador, the bertsolari and his doinuak, the compás, and the temple, the llamada and the remate.

In the literary and French register, Shklovsky’s priyom, artifice and device, with ostranenie or estrangement and the laying bare of the device, Barthes’s écriture, the contrainte and the clinamen of the Oulipo, restriction and deliberate swerve, Lévi-Strauss’s bricolage, the dispositif of Foucault and of Agamben, the démarche, at once a proceeding and a manner of walking, which returns procedure to gesture, the métier, the tour de main or knack, de Certeau’s ways of doing, strategies and tactics, Deleuze’s agencement, the ritournelle of Deleuze and Guattari, Freud’s Durcharbeitung, elaboration and working through, and Montaigne’s essai, the attempt.

In the metaphorical and literary register, road, path, crossing, itinerary, step, gait, trade, workshop, forge, loom, to warp, to weave, to spin, kitchen, practical formula, protocol, rite and liturgy, which is leitourgía, public work, game and rule in Gadamer and in Wittgenstein, match, move, gambit, trick, ruse, gearing, lever, tool, graft, pruning, cultivation, fermentation, distillation, decanting, sedimentation, Stendhal’s crystallisation, digestion, Seneca’s bees in Epistle 84, solve et coagula and the alchemical operations, Deleuze’s fold and unfold, the complicatio and explicatio of Cusanus, through which form explicates what gesture complicates, anamorphosis, translation, gloss, paraphrase, variation, iteration, recursion, loop, algorithm, combinatorics, groping trial, sketch and draft.

In the ontological register, poíesis, process, genesis, becoming, derivation, Deleuze’s difference and repetition, Peirce’s abduction as the logic of discovery, Kant’s reflective judgement, the case that must find its own rule, with the genius who gives the rule to art, and Hegel’s labour, the negativity that forms.

The avoided register

The dialectical vocabulary, mediation, totality, determinate negation, form as sedimented content, is the one that suits this essay worst, for a reason of philosophical temperament. The thinking of these pages is Heraclitean before it is Hegelian. It wants recurrence, fire kindling in measures, the hidden harmony stronger than the visible, and it refuses a history that goes somewhere. I keep a single term, because it names something the opening pages really do, the Aufhebung, which negates, preserves and lifts at once. Technique and style are not wholly abolished here either. They are negated as tyrants, preserved as servants and lifted into another function. That German word holds the whole argument of this essay about its two prisons.

And one Greek sentence closes the third lens, because it says in five words what eight epithets say in eight lines. Heraclitus, fragment 54. Harmoníē aphanès phanerês kreíttōn (ἁρμονίη ἀφανὴς φανερῆς κρείττων). The hidden harmony is stronger than the visible. That is the craft beneath the surface.