Case Study 12.2: Harry Partch's 43-Tone Scale — Designing a Tuning System from Scratch

The Most Radical Act in 20th-Century Music Theory

In 1923, a twenty-two-year-old American musician burned his musical manuscripts in a fireplace and started over from scratch. His name was Harry Partch (1901-1974), and the manuscripts he burned represented his previous musical life: compositions in the European tradition, written in standard notation for standard instruments in standard equal temperament. What he built in the following fifty years was entirely his own invention: a new tuning system, new instruments, a new notation, a new theatrical aesthetic, and a body of music that remains like nothing else in the Western or any other tradition.

Partch's central conviction was simple and radical: equal temperament is a lie. Not a convenient simplification, not a practical compromise, but a fundamental betrayal of acoustic reality — an agreement by European musicians to pretend that mistuned intervals were correctly tuned, perpetuated for centuries through institutional inertia, pedagogical convenience, and the dominance of the keyboard. Partch had perfect pitch, and the equal-tempered major third — 14 cents sharp from the pure harmonic ratio 5:4 — was not something he could tune out. He could hear it. And he refused to live with it.

The Philosophy of "Corporeal Music"

Before examining the 43-tone scale itself, it's essential to understand the philosophy that generated it. Partch called his aesthetic "corporeal music" — a term he contrasted with "abstract music." Corporeal music, for Partch, was music rooted in the human body, in speech, in the natural inflections of voice. The ancient Greeks, he argued, had understood this: their music was inseparable from poetry and drama; the pitch inflections of speech were continuous with the pitch inflections of song.

Equal temperament was abstract — it imposed a mathematical grid on the naturally continuous pitch space of the human voice. Just intonation was corporeal — it followed the natural resonances of vibrating strings and human vocal cords. When a voice naturally settles on a pitch, it settles not on 12-TET's compromised approximations but on the actual harmonics of the vocal tract's resonant frequencies, which correspond closely to just intonation ratios.

This philosophical position led directly to the 43-tone scale. If you want to capture the full richness of vocal pitch inflection — including the tiny microtonal variations that distinguish an ascending step from a descending one, the difference between a neutral third and a just major or minor third, the specific frequencies of harmonics that the voice naturally produces — you need far more than 12 notes per octave.

The Mathematics of the 43-Tone Scale

Partch's scale is based on "11-limit just intonation" — a subset of the infinitely large just intonation pitch space, restricted to ratios involving only the prime numbers 1, 2, 3, 5, 7, and 11. (The "limit" refers to the largest prime involved.) Each prime extends the range of available consonances:

3-limit (Pythagorean): Ratios using only 2 and 3 → octaves and fifths
5-limit: Adds ratios using 5 → major and minor thirds (the richness of Renaissance harmony)
7-limit: Adds ratios using 7 → the harmonic seventh (7:4) and related intervals (darker, "bluer" quality)
11-limit: Adds ratios using 11 → the neutral eleventh harmonic (11:8), overtone fifth (11:6), and related intervals (exotic, "Eastern" quality)

From the complete 11-limit pitch lattice — a multi-dimensional grid of frequency ratios — Partch selected 43 specific pitches per octave. The selection was not arbitrary; he chose pitches that would serve his harmonic language, including both "otonal" intervals (based on the harmonic series above a fundamental) and "utonal" intervals (based on the sub-harmonic series, producing minor-quality chords).

The resulting scale has steps ranging from about 14 cents (between 35:32 and 11:10) to about 53 cents (between various adjacent pitches). The smallest steps are genuinely microtonal — far smaller than any conventional chromatic scale could represent. The variety of step sizes gives the scale a fluid, organic quality unlike the uniform grid of equal temperament.

The Instruments

Partch's most remarkable achievement — perhaps even more remarkable than the scale itself — was the construction of a complete ensemble of custom instruments capable of playing it. Since no existing instrument was designed for 43-tone just intonation, Partch spent decades building his own:

The Adapted Guitar: A standard guitar with a different fretting system, allowing it to play pitches in Partch's scale. Later, Partch also adapted viola and kithara (a large plucked string instrument with 72 strings, named after the ancient Greek instrument).

The Chromelodeon: A modified reed organ (harmonium), tuned to Partch's 43-tone scale. The keyboard was relabeled, and the keys were color-coded to indicate different categories of pitches within the just intonation system. Partch's most important early works were written for this instrument.

The Spoils of War: A large percussion instrument consisting of hubcaps, artillery shell casings, whang guns, and other found objects mounted on stands. Tuned to specific pitches in Partch's scale.

The Quadrangularis Reversum: A large percussion instrument shaped like a diamond, with wooden bars that correspond to pitches in Partch's scale — a visual and sonic counterpart to his "Quadrangularis" (a more conventional-shaped version).

The Cloud Chamber Bowls: Made from Pyrex carboys (large glass laboratory containers) salvaged from the Lawrence Berkeley radiation laboratory — the "cloud chambers" used in particle physics experiments. Each bowl was tuned by filling it to a specific volume level. When struck, they produce an ethereal, shimmering tone unlike any conventional instrument.

The Zymo-Xyl: A marimba-like instrument that incorporated the bodies of empty Coca-Cola bottles of different sizes, producing a peculiar combination of rich wooden tones and the hollow resonance of the bottle interior.

The visual spectacle of a Partch ensemble — featuring these unusual, large, often visually striking instruments — was central to his theatrical aesthetic. Partch intended his music to be seen as well as heard; the performers' relationship to the instruments, the visible effort of playing them, was part of the "corporeal" experience.

The Music

Partch's compositions are inseparable from his philosophy, his instruments, and his scale. Key works include:

"Barstow: Eight Hitchhiker Inscriptions from a Highway Railing at Barstow, California" (1941, rev. 1968): Settings of actual texts scratched into a guardrail by hitchhikers during the Depression — "I'm hitching to Kansas City Mo. My name is Harold Musson born Nov. 28, 1909." The setting is for voice and adapted guitar, with the melodic lines following the natural speech inflections of the texts. The connection between vocal inflection and microtonal just intonation is explicit.

"U.S. Highball: A Musical Account of a Transcontinental Hobo Trip" (1943): Another piece based on found text — notes from Partch's own journals of riding freight trains across America during the Depression. This is music about the American underclass, set in a tuning system built as an explicit rejection of European high-culture convention.

"Delusion of the Fury: A Ritual of Dream and Delusion" (1966-69): Partch's final large theatrical work. In two acts — one based on a Japanese Noh play, one based on an Ethiopian folk tale — performed by actors, dancers, and an ensemble of all his instruments. The 43-tone scale gives the work an otherworldly sonic quality that standard Western instruments could not achieve; it sounds genuinely ancient and genuinely futuristic simultaneously.

"Oedipus: A Music-Dance-Drama" (1952): A full-length theatrical retelling of the Sophocles play. The 43-tone scale allows for microtonal inflections in the vocal lines that mimic the heightened emotional speech of Greek drama — the connection between Partch's tuning philosophy and his theatrical roots is explicit.

What Partch Reveals About Physics and Creativity

Harry Partch's career raises several important questions about the relationship between physical constraints and creative freedom:

The 43-tone scale is more physically grounded than 12-TET, but it required more creative effort. Just intonation is acoustically purer than equal temperament — its ratios correspond more precisely to the natural harmonics of vibrating strings and human voices. But using just intonation in a complex musical context required Partch to solve problems (instrument construction, notation, ensemble coordination) that equal temperament had already solved for composers working in the standard system. Physical accuracy demanded greater creative investment.

The instrument-building was not peripheral but central. In the standard musical tradition, instrument construction is a craft separate from composition. Partch collapsed this distinction: the instruments were compositions in physical form. The Cloud Chamber Bowls are both instruments and sculptures; the Spoils of War is both a percussion kit and a comment on American militarism and waste. The physics of the instruments (the resonant frequencies of glass containers, the decay times of hubcaps) shaped the music written for them.

Constraint at one level (just intonation) generates creativity at another (instrument invention). This is an instance of the book's recurring theme: constraint as creativity. Partch's commitment to just intonation made standard instruments unavailable to him — so he invented his own. The acoustic constraint propagated upward into instrument construction, theatrical staging, and eventually an entire alternative aesthetic philosophy. A single physical decision (reject equal temperament) generated an entire world.

The music is evidence, not just art. Partch's compositions can be heard as demonstrations that the harmonic world of 11-limit just intonation is coherent, emotionally potent, and aesthetically viable — not just theoretically interesting. Recordings like the Columbia/Odyssey release of "Delusion of the Fury" provide the most direct evidence that a complete musical world can be built on a tuning foundation very different from 12-TET.

Discussion Questions

The sacrifice. Partch burned his early manuscripts — his previous musical identity — to pursue his acoustic convictions. This is an extreme act of commitment. Is this kind of sacrifice compatible with living a sustainable life as a musician? What does it suggest about the relationship between artistic purity and practical compromise?
The audience problem. Partch's music remains largely unknown outside specialist circles, despite being one of the most original bodies of work in 20th-century American music. Is this obscurity a consequence of the 43-tone scale itself (listeners find it difficult to perceive)? Or is it a consequence of the institutional systems that define "classical music" (concert halls, conservatories, recording labels)? Could Partch's music be made accessible to a mass audience without betraying its essence?
The "corporeal" argument. Partch argued that equal temperament is "abstract" and just intonation is "corporeal" — rooted in the body and natural acoustic resonance. Is this argument convincing? Is there a sense in which the blues scale (discussed in Case Study 11.2) is also "corporeal" — grounded in the body's natural pitch production — and that the blues tradition independently arrived at some of the same acoustic territory as Partch?
The instrument question. Partch's instruments are currently housed at the University of Illinois, where they have been maintained, repaired, and used in periodic productions of Partch's works. Is a musical tradition that requires specific custom instruments — which exist in only one set of copies, maintained by one institution — sustainable? What are the risks, and what does this suggest about the relationship between physical instruments and musical traditions?