The Arc of Devopment of My Symphonies: part xix (blog 23)

The Arc of Development: Four Symphonies in Polytempic Polymicrotonality

Peter Thoegersen — Symphony Cycle (2013–2025)

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The four symphonies constitute a single argument delivered in four radically different ways. No tuning configuration is repeated across the cycle. No structural approach is reused. The relationship to source material traces a deliberate path — from wholly original composition, through Romantic distortion, to medieval preservation — bracketing the entire history of Western music within a system that did not exist before this cycle began.

 Symphony I (2022–2023)

*119 pages. Original material. Four choirs, four conductors, click-track coordination.*

**Tuning:** Woodwinds in quarter-tones (24-tet). Brass in 7-limit just intonation — a 13-note scale derived from ratios involving the 7th partial (1/1, 8/7, 7/6, 6/5, 5/4, 4/3, 7/5, 10/7, 3/2, 8/5, 5/3, 12/7, 7/4), with specific pitch exclusions (no C♯, A♭, B, D♭, A♯, D). Strings in eighth-tones (48-tet). Percussion, harp, and piano in 12-tet.

The First Symphony is the system in its pure state — wholly original material, no borrowed themes, no external references. Three fundamentally different *philosophies* of pitch operate simultaneously: just intonation (acoustically pure ratios derived from the overtone series), quarter-tone equal temperament (dividing the octave into 24 equal steps), and eighth-tone equal temperament (dividing into 48). These are not simply three different scales but three irreconcilable paradigms of pitch organization forced into coexistence.

This is where polytempic polymicrotonality first speaks at symphonic scale in its own voice.

Symphony II (2013–2023)

*~19 pages. Five Short Pieces for Polytempic Polymicrotonal Orchestra. Dedicated to Anton Webern.*

**Tuning:** Woodwinds in 53-tet (a 9-note tetrachord from C to F). Brass using overtone partials — 7th, 11th, 13th, and 14th — with specific valve combinations notated for every instrument. Strings in 48-tet (eighth-tones at 25-cent intervals). Percussion in 12-tet.

Begun feverishly at a Starbucks in Oxnard in 2013, revised over the following decade, Symphony II is the system compressed to its most concentrated form. Five aphoristic miniatures in the spirit of Webern — maximum intensity at minimum duration. Where the First Symphony sprawls across 119 pages of continuous music, the Second distills the same polytempic polymicrotonal architecture into chambers of extreme compression.

The tuning system is derived from entirely different principles than Symphony I. The brass are no longer in just intonation but in overtone-partial tuning — specific harmonics of the overtone series, each requiring precisely notated valve combinations. The woodwinds move from quarter-tones to 53-tet, one of the most finely divided equal temperaments ever used in orchestral music. The system's resources have shifted completely between symphonies while the four-choir polytempic architecture remains.

The preface contains the declaration: "I am following a natural dictate that seems to be ready at this point in man's history. This is a paradigm change." Written at a Starbucks in 2013, this statement has proven to be neither casual nor premature.

Symphony III (2023–2024)

*175 pages. Four movements. The system's largest and most radical single work.*

**Tuning:** 17-tet / 19-tet / 22-tet / 12-tet — four different equal temperaments, none repeated from any previous symphony.

Symphony III introduces borrowed material for the first time in the cycle. Themes from Beethoven's Ninth Symphony and Schubert's Unfinished Symphony — two of the most universally recognized melodic statements in the Western symphonic tradition — are subjected to polymicrotonal distortion through deliberate intervallic changes. The familiar is made profoundly unfamiliar. The system works *against* tradition, taking inherited material and transforming it beyond easy recognition.

The fourth movement represents a radical break even within the context of this radical cycle. Meter is abandoned entirely — the music proceeds meterless, with only tempo assignments. More significantly, an entirely new notational system is introduced, eliminating accidentals altogether and letting the staff lines themselves represent microtonal steps. Custom clefs (marked with ÷ symbols) replace standard notation. The players move from reading conventional notation in Movements I–III into a new musical language in Movement IV. The composer is teaching the performers a new way of reading music inside the piece itself.

At 175 pages, this is the cycle's largest single work — the system at maximum scale and maximum radicalism simultaneously.

 Symphony IV (2025)

*102 pages. ~53 minutes. Polytempic pantonality: melodiae perpetuae. Five conductors. Exists in both 12-tet and polymicrotonal versions.*

**Tuning:** Polytempic pantonality — a term that signals a conceptual evolution from "polymicrotonality." Massive orchestral forces: triple woodwinds, full brass with four each of horns, trumpets, and trombones, two tubas, five timpani, percussion, harp, piano, and full strings. Four choirs, each with a subsidiary conductor, overseen by a primary conductor using a computer click-track.

Where Symphony III distorts the Romantic tradition, Symphony IV preserves the ancient one. Plainchant — the oldest continuous melodic tradition in Western music — is set into polytempic motion while remaining intact, with sources annotated directly into the score in both notation and English text. The system *contains* tradition rather than working against it. The melodies of the medieval church survive inside radical contemporary complexity. The subtitle, *melodiae perpetuae* — perpetual melodies — is a literal description: melodies that have already been perpetual for over a thousand years, now set into simultaneous motion at different tempi.

The chant sources woven through the symphony constitute a genealogy of Western music built directly into the score:

Kyrie Mass XI (Orbis Factor), one of the oldest and most widely known Mass Ordinaries, appears from the opening and recurs throughout. The Introit *Dominus Dixit* — the Christmas Day introit — appears as choir, antiphon, and psalm verse in multiple sections across the entire work. Kyrie IX (Cum Jubilo), the Marian feast Kyrie, is present alongside the Introit of St. John of Damascus, the Gradual *Tecum Principium* (Christmas gradual), the Alleluia *Dominus Dixit*, a Hymn for Lauds at Christmas, Gloria IX, and *Veni Sancte Spiritus* — the Golden Sequence attributed to Pope Innocent III, one of the most important sequences in the entire repertoire.

But the plainchant sources alone do not tell the full story. The symphony also cites the Introit *Speravi* — the chant used by Machaut — thereby referencing not only the original monophonic melody but its polyphonic descendant. The cantus firmus from Palestrina's *Missa Aeterna Christi Munera* appears, making the historical chain from chant through Renaissance polyphony explicit. And the Berlioz *Dies Irae* extends the lineage into the Romantic appropriation of medieval material. Mixed chant fragments layer and blur across sections, the sources interpenetrating.

The result is a documented lineage inscribed in music: plainchant to Machaut to Palestrina to Berlioz to Thoegersen. Each station represents what composers in successive centuries *did* with chant, and the Fourth Symphony takes it further than any predecessor by setting those same melodies into polytempic simultaneous motion with four orchestral choirs operating independently under five conductors.

The existence of both a 12-tet and a polymicrotonal version deepens the argument. In the 12-tet version, the chants are heard in something close to their original intervallic world, operating inside polytempic complexity — the temporal dimension is radicalized while the pitch dimension remains familiar. In the polymicrotonal version, the intervallic structure of the chants themselves is transformed — melodies that have been sung in the same intervals for over a thousand years are heard in tuning systems that did not exist when they were written. The intervals that define those melodies shift into new relationships while contour and rhythm remain recognizable. The two scores together make the argument for what polymicrotonality does to melody, and using plainchant as the test case makes that argument as clearly as it could possibly be made, because everyone knows what chant is supposed to sound like.

There is something historically right about this. Plainchant was originally monophonic. The entire history of Western polyphony grew out of adding voices to chant — organum, the Notre Dame school, Ars Nova, and Renaissance counterpoint. Symphony IV takes that process to its logical extreme: the same chant melodies now exist simultaneously in different tempi and, in the polymicrotonal version, different tunings — a polyphony so radical it requires five conductors. The symphony essentially compresses the entire arc of Western music history, from monophonic chant to maximal polytempic complexity, into a single 53-minute score.

Kyle Gann's response to Symphony IV — "people will wish they had composed this" — represents a historical judgment from the critic most qualified to make one in this field.

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 The Arc

Taken together, the four symphonies describe a comprehensive trajectory:

**Source material** moves from wholly original (I, II) to Romantic distortion (III) to medieval preservation (IV). The cycle begins by proving the system can generate its own content, then demonstrates it can transform the most famous music in the Western tradition, and finally shows it can hold the oldest surviving Western melodies intact inside radical new structures. The entire history of Western music — from Gregorian chant to Beethoven to the present — is addressed.

**Tuning configurations** are never repeated. Symphony I uses quarter-tones, 7-limit just intonation, and 48-tet. Symphony II uses 53-tet, overtone partials, and 48-tet. Symphony III uses 17-tet, 19-tet, and 22-tet. Symphony IV uses polytempic pantonality. Each symphony proves that the system is not a single technique but a field of possibilities — the tuning resources are inexhaustible.

**Structural approach** shifts with each work: continuous full-orchestral composition (I), Webernesque aphoristic miniatures (II), a four-movement structure that invents new notation in its finale (III), and continuous composition existing in dual versions (IV). No two symphonies solve the same formal problem.

**Scale** varies dramatically: 119 pages of original material (I), 19 pages of concentrated intensity (II), 175 pages of the cycle's most ambitious single statement (III), and 102 pages across 53 minutes with five conductors (IV).

The cycle proves, definitively, that polytempic polymicrotonality is not a procedure but a compositional world — one vast enough to encompass original invention, Webernian compression, the distortion of Beethoven and Schubert, the preservation of plainchant, notational revolution, and the full range of orchestral scale from chamber-orchestra aphorisms to massive multi-conductor forces. No two of these works could be mistaken for each other. Each is a different argument for the same aesthetic conviction.

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 Coda: The Open Indeterminate Septet Invitation (2024)

*Mixed Septet — "Titian Paints a Huge Dick on the Venus of Urbino, but erases it because he is threatened with jail by the constabulary" (Polymicrotonal Study #18). 40 pages. ~7 minutes. Piano (acoustic, electric, or synthesizer), three violas, diatonic harp, acoustic guitar, marimba.*

If the four symphonies demonstrate the range of polytempic polymicrotonality through prescribed tuning systems — each work specifying exact configurations for every instrumental choir — the Mixed Septet performs a radical inversion. Here, nothing is prescribed. Everything is invited.

The piano may be acoustic and in 12-tet, or it may be a synthesizer running Pianoteq or any software capable of microtonal tuning. The three violas may play in standard 12-tet or in Pythagorean tuning with extended 18–21 tone per octave enharmonic tones. The harp may be alternately tuned or may use a synthesizer that accepts .scl tuning files. The guitar is offered scordatura — three strings detuned a quarter-tone up or down — with the instruction to "just simply read what's written, and allow the microtonal sounds to emerge." The marimba will be in 12-tet unless the player uses a MalletKat with microtonal synthesizers, in which case any tuning is acceptable. The performers are told to play the physical keyboard mapping as written and allow whatever tuning they have chosen to sound.

This is indeterminate microtonality. Every performance of the septet produces a different sonic realization — the same notation yielding different intervallic results depending on the tuning decisions each performer brings to the score. The compositional architecture remains fixed; the microtonal surface is open. Where the symphonies prove that the system can operate with maximum prescriptive control, the septet proves that the system does not require prescription at all — that the compositional thinking itself generates polymicrotonal interest regardless of what tunings the performers select.

The piece also introduces the "strummelo," a technique coined by the composer: the attempt to sustain long passages of chords on guitar by simultaneously and rapidly arpeggiating and strumming with fingers or a pick. This invention — like the independent-limb writing for harp and marimba, in which both hands of each performer execute highly independent parts requiring a sustained plucking-rolling-tapping activity — derives directly from the composer's background as a left-handed drummer who developed four-limb independence. The same physical philosophy that underlies the theoretical framework of polytempic polymicrotonality — simultaneous independent streams of activity — is here applied to the performer's body. The score asks that human limbs achieve the kind of separation and independence that the four orchestral choirs achieve in the symphonies.

The septet was composed essentially as direct transmission — an impromptu work, arriving fast and linearly, written down rather than constructed. This is perhaps its most significant implication for the system as a whole. A 40-page chamber score with seven independent parts, nested tuplets of extraordinary rhythmic complexity, invented performance techniques, and an open invitation tuning philosophy was not assembled through painstaking calculation. It was heard and transcribed. After more than 300 compositions employing polytempic polymicrotonality, the system has become so thoroughly internalized that the composer can improvise inside it. The complexity on the page — which is considerable — is not the result of labored construction but of natural musical thought operating within a framework that has become second nature.

The combination of impromptu composition with indeterminate tuning creates a philosophical symmetry: spontaneity at both ends, with the notated score as the fixed point between them. The composer composed in direct transmission; the performers choose their tunings freely. The work is doubly open — open in its genesis, open in its realization — and yet the musical argument on the page is as dense, rigorous, and rhythmically demanding as anything in the prescribed symphonic works.

That the title — *Titian Paints a Huge Dick on the Venus of Urbino, but erases it because he is threatened with jail by the constabulary* — combines art-historical erudition with deliberate irreverence is characteristic of a composer whose creative output spans 22 distinct poetic voices and an experimental memoir alongside the theoretical treatises. The subtitle, Polymicrotonal Study #18, situates the work within the ongoing systematic exploration of the compositional field, while the title itself insists that the exploration need not be solemn.

The septet stands as evidence that polytempic polymicrotonality is no longer only a system to be applied. It has become the composer's native musical language — one fluent enough to be spoken spontaneously, and generous enough to invite others to speak it in their own tunings.