QuarkTonal Composition System

Album Title QuarkTonal Composition System Composer's Note The pieces in this collection are built on a technical system developed across three earlier publications. This note summarizes the musical foundations established in that work. The philosophical arguments — involving Kant, Badiou, Rancière, Said, and Freud — are not repeated here. What follows concerns only the musical tools those arguments were written to justify. The Pitch System The basic unit of measurement in the QuarkTonal system is the quark: one quark equals 2 cents (1Q = 2¢). Each octave contains 600 quarks, and each chromatic semitone equals 100 cents or 50 quarks. Pitches are notated as CQ+X for ascending and CQ−X for descending deviations, where X is a whole number from 1 to 49. Each of the seventeen chromatic degrees in the standard base scale — C, C#, Db, D, D#, Eb, E, F, F#, Gb, G, G#, Ab, A, A#, Bb, B — has its own QuarkTonal Set of fifty distinct pitch classes, covering the full distance to the next semitone in 2-cent steps. The choice of 2 cents as the base unit follows from the factorization 600 = 2³ × 3 × 5². This ensures that all common equal divisions of the octave — 12-tone, 24-tone, 20-tone, 30-tone, 40-tone, and others — produce whole-number quark values, keeping every calculation exact. Twenty-two QuarkTonal scales are derived from this system, organized by step size. Scale 1 contains 600 pitches at a step of 2 cents (1Q); Scale 16 corresponds to standard 12-tone equal temperament at 100 cents (50Q); Scale 13 corresponds to 24-tone quarter-tone tuning at 50 cents (25Q); Scale 22 contains 3 pitches at a step of 400 cents (200Q). The first publication includes forty-four audio tracks in ascending and descending formats, along with complete frequency tables for the pitch A from A1 through A7, referenced to A4 = 440 Hz. The name QuarkTonal, rather than microtonal, reflects a specific technical point. The term microtonal provides no unit of measurement: it indicates only that certain intervals are smaller than those of standard practice, without specifying by how much. Without a fixed unit, notation cannot be converted to frequency, analysis cannot be reproduced, and composition cannot be communicated with precision. QuarkTonal replaces a vague, relative description with an exact numerical one. The answer to "finer than what?" is: finer by exactly X quarks. The Temporal System The rhythmic side of the system was introduced in Q Time Machine: Polychronic Time. Here, the quark also serves as the minimal unit of time, fixed at 0.1 seconds — giving a rate of 10 quarks per second (QPS = 10) and 600 quarks per minute (QPM = 600). Each musical line proceeds as a sequence of two event types — Hit (H) or Silence (S) — at its own independently set rate, measured against a shared time reference called the chronoscope, which corresponds to ordinary clock time in seconds and minutes. The key distinction in that volume is between polyrhythm and polychronic time. In polyrhythm, all voices — however complex their individual patterns — share a common pulse and resolve into a single metrical grid. In polychronic time, that shared foundation is removed. Each voice runs at its own speed and follows its own internal logic. When coordination between voices occurs, it happens only at explicitly defined structural points. Two voices in polychronic time do not synchronize: they proceed in parallel without ever merging. The system was demonstrated across fifteen exercises, released in both digital audio and instrumental performance formats, with a fifty-three-page booklet containing full notation. The Contrapuntal System The combination of the QuarkTonal pitch system and polychronic time in two-voice composition was developed in aesthetics of post-orientalism, Vol. II: Subject, Structure, Counterpoint. That work operates within a 24-pitch subset of the full 600-quark spectrum, using a fixed step of 50 cents (25Q). This is not a permanent limitation of the system but a deliberate research choice: to study the conditions for two independent voices in a pitch field simple enough to remain clear to the ear. Four pitch-class operations are used throughout: prime (P), retrograde (R), inversion (I), and retrograde-inversion (RI), all defined within the twelve-tone cyclic system at modular reference 12. The inversion of interval x is defined as 12 − x — not merely as an arithmetic operation, but as an auditory symmetry in which an ascending interval corresponds to its descending counterpart. The smallest pitch-class set capable of supporting genuine contrapuntal motion was identified as the three-element set {0, 1.5, 10.5}, derived from a base of C with an opening interval of 1.5 semitones and its modular inversion. From this starting point, and expanding progressively to a ten-element pitch field, the second voice is defined not as a response to or reflection of the first, but as a fully independent line drawing from the same material without any hierarchical relationship. That independence — the refusal of the second voice to be an echo of the first — is the structural condition for counterpoint in this system. For each of three melodic lines — the first using the minimal three-element set, the second expanding to ten elements, the third introducing full rhythmic independence between voices — fourteen contrapuntal configurations were constructed: note-against-note (1:1), two-against-one (2:1), three-against-one (3:1), four-against-one (4:1), mixed counterpoint, and free counterpoint, each applied from both the lower and upper voice. This produces forty-two exercises in total, all generated by a Python script with fully transparent and reproducible logic. The script applies no subjective aesthetic judgments; it executes declared transformation rules and selects from candidate contrapuntal paths using explicit scoring functions. The aesthetic evaluation of the results remains the composer's responsibility. This system does not replace the canonical treatises of Fux, Piston, Kennan, and Carter, which remain essential reading for any serious student of Western compositional practice. It works alongside them — as a parallel investigation for composers who have mastered the inherited tradition. The aim is to rebuild the problem of two voices from the ground up, free from both the modal structures of Eastern music and the tonal hierarchies of Western functional harmony. The QuarkTonal Synthesizer From the outset, my intention was to write this collection for string quartet. I knew, however, that under present circumstances — the high cost of live performance and the practical constraints that accompany it — this would not be a realistic possibility. I therefore turned to the four basic electronic waveforms and accepted them as they are, with all their inherent characteristics, unmodified. I accepted the saw wave with its raw, abrasive edge — just as one accepts the sound of the violin. The square wave with its unmistakable evocation of 8-bit computer music. The sine wave with its acoustic isolation from the other voices — like a solo flute standing against a battalion of brass. And the triangle wave with its remarkable capacity for blending: when doubled with another voice, it absorbs that voice's color entirely, much as woodwinds double with strings in the orchestra. Accepting these four raw waveforms without modification shifted the problem away from the string quartet toward something else entirely: the balance, timbre, and orchestrational possibilities within four voices whose frequency spectra do not overlap. This became the central challenge of the collection — and the force that shaped its harmony and counterpoint. These twelve pieces are among my first compositional works built on the QuarkTonal System. Written with full technical precision, they are intended above all to be heard — with the same vitality and warmth as the string quartets of Haydn and Mozart, but in the language of the QuarkTonal System. Not to set aside modal music. Not to deny the genius of the tonal system in European history. And not to dismiss the finest works of atonality — the twelve-tone and serial music of Schoenberg, Webern, and Berg. My only hope is that the QuarkTonal System may stand alongside that magnificent historical tradition and add something to the world's harmony, form, and counterpoint — not negate it. I hope you enjoy listening to them. Ehsan Saboohi Composer and Theorist Earlier Publications in This Series Saboohi, Ehsan. aesthetics of post-orientalism, Vol. II: Subject, Structure, Counterpoint. Washington, D.C.: Post-Orientalism Label, 2025. Catalog No. PO.0138. https://postorientalism.bandcamp.com/album/aesthetics-of-post-orientalism-vol-ii-subject-structure-counterpoint Saboohi, Ehsan. aesthetics of post-orientalism: Philosophy of Composition. Washington, D.C.: Post-Orientalism Label, 2025. Catalog No. PO.0117. https://ehsansaboohi.bandcamp.com/album/aesthetics-of-post-orientalism-philosophy-of-composition Saboohi, Ehsan. Q Time Machine: Polychronic Time. Washington, D.C.: Post-Orientalism Label, 2025. Catalog No. PO.0111. https://ehsansaboohi.bandcamp.com/album/q-time-machine-polychronic-time