My Piano Collection as Seeds of Polytempic Polymicrotonal Music: part XX, (blog 24)

 

An Arc of Development:

The Piano Collection, Pieces I–XXIII

Peter Thoegersen

I. Origins: The System Before It Knew Itself (Pieces I–VIII)

The Piano Collection does not begin as a collection. The early pieces, written before the polytempic polymicrotonal system had been fully theorized, are a composer discovering the system in the act of writing — reaching toward a language that does not yet have a name. Looking back at Pieces I through VIII from the vantage point of the complete cycle, one sees the essential gestures of the mature work in germinal form: the extreme tuplet vocabulary (3:2 through 15:8), the interest in tempo as a structural rather than merely expressive parameter, the casual address to the performer that coexists with rigorous notational specificity.

Piece III (2007) is representative of this early period and offers the clearest window into where the collection begins. It opens with a tempo instruction that reads, "As fast or as slow as you want to play it :)" — the smiley face is not ironic. At this stage, the composer's relationship to performer freedom is genuinely exploratory, not yet the deliberate philosophical act it becomes in the late collection. Yet the piece is also exacting: the same score that opens with a :) closes 380 measures later with the instruction "as though your life depended on it" and a precise duration marking of 7 minutes and 39 seconds. The contradiction is not resolved. It is the subject.

The tuplet ratios in the early pieces are sequential rather than simultaneous — each ratio returns to the main pulse before the next begins. This is the crucial distinction between a composer using extreme rhythmic notation and a composer who has developed a polytempic system. The early pieces use the materials of polytempic writing without yet unlocking their essential property: the coexistence of incompatible tempi in the same notational moment. That breakthrough comes later, and its emergence across the middle of the collection is the collection's central developmental event.

The early pieces also establish what might be called the collection's emotional grammar: a movement between fragmentation and saturation, between sparse textures that test individual gestures in isolation and dense textures where those gestures collide. This architecture of tension and release, of exploration and declaration, will persist across all twenty-three pieces. What changes is the scale at which it operates and the theoretical clarity with which it is deployed.

II. The Triptychs: System Encounters World (Pieces IX–XVII)

The middle third of the Piano Collection is organized into three triptychs, each exploring a different domain through the fully realized polytempic polymicrotonal system. By Piece IX, the system is no longer discovering itself. It has been theorized, named, and applied across multiple genres and instrumental forces. The question the triptychs ask is not what the system is, but what it can encounter — and what those encounters reveal.

Triptych I (IX–XI): TIME

The first triptych trains the system on time itself — not meter or duration as notational conventions, but time as a philosophical problem. The three pieces that constitute Triptych I approach this problem from different angles: tempo as the boundary of the humanly possible, meter as constructed versus experienced, and the relationship between notated time and performed time. The polymicrotonal dimension is present throughout, but it operates in the background. The foreground is occupied by what the system does to clock time when it is allowed to run at multiple simultaneous rates. The answer, these pieces suggest, is that it reveals the arbitrariness of the single-tempo assumption — the idea that a musical moment belongs to one speed.

Triptych II (XII–XIV): THE INSTRUMENT

The second triptych turns the system toward the specific problem of the piano: an equal-tempered, fixed-pitch instrument confronted with a compositional language predicated on microtonal pitch relationships that the piano, in its standard form, cannot produce. The three pieces navigate this contradiction in different ways — through synthesis and alternative tuning software, through the microtonalism latent in extreme register and resonance, through the compositional decision to write microtonality into the score regardless of whether the standard instrument can produce it. This is not a problem the triptych solves. It is a tension the triptych inhabits, making the instrument's limitations as structurally significant as its capacities.

Triptych III (XV–XVII): THE SELF

The third and most intimate triptych redirects the system inward. These three pieces are not about what the polytempic polymicrotonal system can do with time, or with the piano's physical affordances. They are about what it reveals when it is used to make music about experience — about the self that is doing the composing. Piece XV introduces the six-section spiritual architecture that gives the triptych its structural spine. Piece XVI, the collection's most pianistic moment, deploys pedal indication for the only time in the late collection ("use pedal where you like"), its resonance a form of permission. Piece XVII extends and complicates what XV proposed, bringing the triptych to a close not with resolution but with earned complexity.

Across all three triptychs, a compositional principle is being refined. The polytempic polymicrotonal system is not presented as a technique in search of applications. It is presented as a perceptual frame — a way of experiencing time, pitch, and structure simultaneously at multiple rates — that has natural affinities with different subjects. Time, because polytempic writing is an investigation of time. The instrument, because the equal-tempered piano is the philosophical adversary of a microtonal system. The self, because the multiplication of simultaneous parameters mirrors the multiplication of simultaneous inner states. Each triptych finds its subject, and the system finds itself through the encounter.

III. The Capstone: Freedom and Everything (Pieces XVIII–XIX)

After the three triptychs have established the system's range of encounter, the collection requires a gesture of declaration. Piece XVIII provides it. Where the triptychs investigated specific domains, XVIII asserts a general principle — freedom as a compositional and existential stance, not a technique but a posture. The word that belongs to this piece is not a formal designation; it is a claim the music makes about its own right to exist outside institutional permission.

Piece XIX, "Quod Libet," is the collection's longest and most overwhelming movement: 585 measures, a tempo range that runs from quarter-note equals 1 to eighth-note equals 300, a performance instruction that truncates a profanity into something that reads as notation. The piece is a quodlibet in the traditional sense — a work that assembles disparate materials — but the materials it assembles are the entire lexicon of the collection's concerns: Bulgarian folk rhythm, waltz meter, bird song, polytempic counterpoint at maximum density, enharmonic mirroring across microtonal systems. Where XVIII declared freedom, XIX enacts it. There is nothing left in reserve after measure 585. The collection has said everything.

XIX is the collection's formal center of gravity — the piece that everything before it has been building toward and everything after it must somehow follow. The pairing of XVIII and XIX is active: declaration followed by enactment, the word followed by the act. This pairing sets the template for the two couplets that complete the collection.

IV. The Resolution: Surrender and Return (Pieces XX–XXI)

The question the collection faces after the quodlibet is not compositional but philosophical: what do you write when you have already written the piece that contains all the pieces? Piece XX answers by giving everything away. "Your Interpretation" strips the score of staff lines, dynamics, articulations, and specified tuning. The composer who has spent twenty-three years developing one of the most elaborately specified notational systems in contemporary piano writing hands the entire system to the performer with a single word of casual address: "bro."

The Scala reference in Piece XX is not incidental. The composer does not simply say "play it however you want." He points toward 5,000-plus mathematically deposited microtonal tuning systems — the entire universe of microtonal possibility that the polytempic polymicrotonal system represents only one corner of. The pitch world that has been under compositional control since Piece I is not merely released; it is opened onto a larger world that the system has always been in conversation with. And buried in the score of this maximally open piece, there is one instruction that the composer cannot relinquish: "sing this. try to sing this." In the piece where the performer decides everything, the composer's only genuine demand is that you stop being a pianist.

Piece XXI, "Renewal," answers the surrender with return. Allegro at quarter-note equals 120: a decisive tempo after XX's total openness. "Secco molto" and "sempre senza sostenuto pedal" — completely dry, no sustain, no resonance. The piece whispers at piano dynamic for 150 measures, deploying the full tuplet vocabulary (3 through 15) not as demonstration but as natural speech — the way you use a language you have been speaking for decades. You are not proving anything. You are not celebrating. You are simply thinking.

The "morendo" that ends Piece XXI — dying away — is the collection's most quietly radical gesture to this point. A piece called Renewal ends by dying. This is not contradiction; it is the cycle itself made explicit. Renewal is what happens through dying, not instead of it. The XVIII–XIX pairing was active (declaration, enactment). The XX–XXI pairing is the consequence: giving it away and finding, in the return, that something remains. The return is not triumphant. It is quiet. It is the sound of someone who has given everything away and discovered they still have something left.

V. The Terminus: Maximum, Twice (Pieces XXII–XXIII)

The collection's final gesture is a pair of pieces that share a name: "Maximus" and "Maximus Part Deux." The decision to end a twenty-three piece collection not with a single culminating statement but with two pieces that are ostensibly the same thing is the collection's most compressed and most profound formal argument.

Piece XXII, "Maximus," is the collection's longest and most formally complex movement after the quodlibet. At twelve minutes and 196 measures, it organizes itself across six tempo regions — Moderato (quarter-note equals 108), Andante (quarter-note equals 80), L'istesso tempo, Allegro (quarter-note equals 120), Dolce, Meno mosso — compressing the entire expressive vocabulary of Western tempo designation into a single arc. The tuplet ratios reach their apex: 15, 14, 13, 12, 11, 10, 9, 7, deployed as structural elements rather than local colorings. "Sempra Secco Staccato" at the opening establishes a dry, unpadded surface across which these extraordinary ratios move without cover. And then, deep in the score, a single "legato" — the piece that begins with maximum dryness allows itself, eventually, to sing.

Piece XXIII, "Maximus Part Deux," has no tempo. No dynamics. No articulations. Any tuning. The score opens with a single parenthetical instruction: "Any tempo. Any dynamic you like." The piece was conceived in 7-limit Fokker tuning — a specific, historically situated, mathematically precise microtonal system — and then released to any tuning the performer chooses. A una corda marking appears partway through the otherwise unspecified score, the single fingerprint the composer could not entirely resist leaving.

The two pieces are the maximum of compositional specification and the maximum of compositional openness, and they share a name because they are, in the collection's deepest argument, the same thing. XXII achieves Maximus by specifying everything down to the finest tuplet ratio across six tempo regions for twelve minutes. XXIII achieves Maximus by writing "any tempo. any dynamic you like." and signing it with the same title. The maximum of a system and the surrender of that system are not opposites. They are the same gesture, approached from different directions, arriving at the same place.

What the quodlibet of Piece XIX could not resolve — what even the surrender of Piece XX and the morendo return of XXI left open — is this: that the outer limit of polytempic polymicrotonal specification and the act of handing the score to a performer with no instructions are not competing values. They are the same value, expressed through opposite means. The collection's last word is Maximus. Twice. The same word, both directions.

VI. The Arc as a Whole

Viewed across its full span, the Piano Collection traces a developmental arc that moves through five distinct phases: Origins, where the system discovers itself in early works whose ambitions exceed their theoretical apparatus; the Triptychs, where the mature system encounters three domains of inquiry — time, instrument, self — and is transformed by each encounter; the Capstone, where two paired pieces declare and then enact the freedom the system has been moving toward; the Resolution, where that freedom is surrendered and recovered in quieter, more durable form; and the Terminus, where specification and openness reveal themselves to be the same gesture.

The tuplet vocabulary develops in parallel with this arc. In the early pieces, ratios through 15:8 appear sequentially, returning to a shared pulse. In the triptychs, they begin to coexist — producing genuine polytempic counterpoint, multiple simultaneous tempi that do not resolve into each other. By the late collection, the ratios (reaching 15, 14, 13 as structural rather than ornamental elements) are the basic grammar of the system, used at piano dynamic without pedal resonance in Piece XXI as naturally as simpler rhythms might be used in other composers' work. The arc of the collection is partly the arc of a rhythmic vocabulary from exploratory to instinctive.

The microtonal dimension follows a complementary arc. The early pieces are written for piano as standard equal-tempered instrument. The triptych dealing with the instrument confronts this directly, raising the equal-tempered piano as a philosophical problem for a microtonal system. The late pieces resolve this problem not by solving it but by embracing it as a productive tension: the score specifies microtonal relationships regardless of whether a standard piano can produce them, and the invitation to use synthesis software, Scala tuning files, or any available instrument reframes the piano as one possible realization among many. By Piece XXIII, the tuning is entirely the performer's choice. The collection ends with its microtonal system released back into the larger world of microtonal possibility from which it came.

The relationship between composer and performer also undergoes a complete development across the twenty-three pieces. The early pieces negotiate this relationship somewhat naively, mixing :) with extreme notational specificity. The triptychs are fully specified, leaving the performer very little freedom. Piece XVIII declares freedom as a value. Piece XIX enacts it with ferocious compositional authority — the freedom of the quodlibet is the composer's freedom, not the performer's. Pieces XX and XXIII give that freedom away. Pieces XXI and XXII reclaim it. The collection's final pair presents both versions of this relationship simultaneously — the two Maximuses — and refuses to choose between them. This is the collection's mature position on the composer-performer relationship: not a resolved hierarchy in either direction, but a productive oscillation between two different kinds of maximum.

The complete architecture of the collection is as follows:

Pieces I–VIII: Origins — the system before it knew itself

Triptych I (IX–XI): TIME

Triptych II (XII–XIV): THE INSTRUMENT

Triptych III (XV–XVII): THE SELF

XVIII–XIX: FREEDOM → EVERYTHING

XX–XXI: SURRENDER → RENEWAL

XXII–XXIII: MAXIMUM (specified) → MAXIMUM (released)

What is remarkable about this arc, viewed whole, is its fidelity to a single animating question: what does it mean to reach the outer limit of a system? The early pieces approach this question through accumulation — more tuplets, greater density, wider dynamic range. The triptychs approach it through encounter — what does the system reveal when it meets time, instrument, self? The capstone approaches it through declaration and enactment. The resolution approaches it through the discovery that you can give the whole system away and find it still there when you return. And the terminus approaches it by demonstrating that maximum specification and maximum openness, traveled far enough, arrive at the same destination.

The Piano Collection is not a pedagogical document, though it teaches. It is not a manifesto, though it declares. It is not a survey of techniques, though it deploys the full vocabulary of polytempic polymicrotonal composition across twenty-three pieces. It is, finally, an account of a system becoming conscious of itself — discovering what it is by discovering what it can do — and then, having reached the maximum, choosing freely to release what it has earned. That release, and the quiet return that follows it, and the two pieces at the end that prove the release and the maximum are the same: this is the arc.