Does the Human Animal's Ears Hold 53tet as the Standard Aural Perceptual Resolution? Part XXXVII

 

53 as Natural Attractor: Three Independent Convergences

Three musical traditions, in geographic and cultural isolation from one another, across a span of roughly two thousand years, arrived independently at the same tuning resolution: the 53-tone division of the octave.


53 as Natural Attractor: Independent Convergences Across Cultures and Millennia

Three lines of origin, in geographic and cultural isolation from one another, across a span of roughly two thousand years, arrived independently at the same tuning resolution: the 53-tone division of the octave. One of those lines traces back further still — to ancient Greece.

The Chinese theorist Jing Fang documented the relationship between 53 stacked pure fifths and 31 octaves in approximately 45 BCE. The observation was mathematical — a near-perfect closure of the Pythagorean spiral — but it arose from a tradition already grounded in the overtone series. The guqin's harmonic positions, marked by dots along the string, reflected natural acoustic ratios from the start. The 53 convergence was not imposed on Chinese music; it was found inside it.

The Ottoman makam tradition arrived at 53-TET through a route with deeper roots. Aristoxenus, writing in the 4th century BCE, broke decisively from the Pythagorean tradition by treating musical intervals not as ratios between string lengths but as linear magnitudes — distances on a line, fully divisible into equal parts. For Aristoxenus, the whole tone could simply be cut into equal segments. This was theoretically irreconcilable with the Pythagorean and later Ptolemaic positions, which held that intervals were superparticular ratios and could not be equally divided. Ptolemy, in particular, was a strict rationalist; equal division of the tone was for him a category error.

Al-Farabi, the 10th-century Islamic theorist, working explicitly from Aristoxenian ideas, divided the whole tone into 9 equal parts. Six tones to the octave yields 54 parts — one step from 53, within the same acoustic neighborhood by any meaningful measure. This division passed into Islamic music theory and from there into Ottoman practice, where it stabilized, through the work of theorists including Urmevî and Merâgî, into the 53-TET framework. The microtonal intervals of the makam system — the komaless, the bakiye, the küçük mücennep — acquired their names and melodic functions within this inherited architecture. By the early 20th century, 53-TET had become the standard theoretical framework for Ottoman classical music, with each step named and specified.

The intellectual genealogy is therefore: Aristoxenus → Al-Farabi → Ottoman makam → 53-TET. The Greek tradition did not arrive at 53 independently; it generated the transmission vector through which the Islamic and Turkish traditions found their way there.

The Norwegian case is the most striking because it was entirely unconscious. Eivind Groven, born in Vest-Telemark in 1901, grew up inside a hardingfele and vocal folk tradition that had never been touched by conservatory instruction or equal temperament. When he began measuring the actual intonation of folk singers and fiddlers — empirically, with acoustic instruments — he found that the pitch relationships they used, without any theoretical awareness, corresponded to a 53-tone just intonation system derived from the overtone series. The farmers were not approximating a theory. They were simply listening accurately, for generations, until the tuning stabilized into something that measurement could identify.

The conventional interpretation of this convergence is that 53-TET is a mathematically elegant system — a near-perfect reconciliation of the pure fifth and the octave — and that sophisticated musical cultures naturally discovered it. This is true as far as it goes.

The stronger interpretation: 53 is not a system that cultures discover but a condition that human hearing tends toward when left undisturbed. The cochlea is a frequency-ratio detector. The overtone series is not a theory; it is a physical property of vibrating bodies and the auditory anatomy that evolved to process them. Equal temperament, by contrast, is a historical compromise — a solution to the practical problem of fixed-pitch instruments needing to function across multiple key areas. It flattens the major third by approximately 14 cents and introduces systematic beating into every interval except the octave. Every ear trained exclusively on equal temperament has been habituated to accept a deviation from acoustic accuracy as the norm.

What Jing Fang calculated, what the Greek-Islamic-Ottoman transmission carried forward, and what Norwegian farmers sang without knowing it may not be independent discoveries of an elegant system. They may be instances of the same thing: human hearing, in acoustic conditions, finding where it naturally rests.

A Compositional Implication

This argument cuts both ways.

If 22.6 cents — the 53-TET comma — is where human hearing naturally rests, then it functions not only as a tuning unit but as a perceptual threshold. Intervals smaller than the comma are not heard as intervals in any meaningful sense; they register as color shift, as near-undetectable inflection, as the acoustic equivalent of tuning variance. The comma is the floor of distinct intervallic perception.

This has a structural consequence for polytempic polymicrotonal composition. If one simultaneous tuning system operates at the 53-TET comma level — at the very edge of human perceptual resolution — then the other independent systems should operate not merely at larger intervals but at unrelated ones. Not multiples of 22.6 cents. Not commensurate with it in any systematic way. Genuinely foreign in their interval sizes.

The result is a layered perceptual architecture: one system at the human floor, maximally intimate, where the ear already lives; the other systems operating at larger, alien intervals with no acoustic kinship to the first. The 53-TET layer becomes the human ground. The other systems define otherness against it. The listener is simultaneously inside and estranged — at home in one dimension, adrift in the others.

This is not a commitment to 53-TET as a governing tuning. It is a commitment to plurality and independence, in which the comma serves as one layer's unit of measure precisely because it marks the threshold of what the human ear can distinguish as an interval at all. The system remains plural. The independence remains absolute.

Peter Thoegersen is the originator of polytempic polymicrotonality, documented in two published academic treatises with Jenny Stanford Publishing (2022, 2024).

Comments

Post a Comment

Popular posts from this blog

Ode to the Gatekeepers of New Music, Part LI

No Master Clock: Peter Thoegersen, Musical Totalitarianism, and the Architecture of Freedom by Peter Thoegersen I've been reading a good deal of Emerson and Whitman recently. What I am rediscovering on these pages is the true voices of democracy; a democracy so unbridled and pure that we, as Americans, ought to feel completely ashamed today. Every goddamned page has a pro-democracy sentiment, philosophy, aphorism, and spiritual invocation. Every page is a damnation of Trump and the notion of gatekeeping in general. Every page abhors what the billionaire oligarchs have done with our country, an outgrowth of the Gilded Age that Teddy Roosevelt swore to break up, but never did, completely. Today, the wealth inequality is consolidated into the fewest hands in our American history and is destroying our country, AND our music via our academic institutions, whether we realize it or not. Today, Viktor Orbán lost in Hungary. Today, Donald Trump flails before Iran with the strategic depth o...
Read more

Checkmate, Adorno. Part XLVIIA

Beating Adorno at His Own Game (Without Trying) There is a particular irony embedded in the reception history of new music. The composers most celebrated for radicalism—those associated with Darmstadt and, later, the New Complexity—grounded their work in a philosophical framework that presents itself as universal while quietly defending a highly specific cultural premise. That framework is the aesthetic theory of Theodor Adorno, and it has shaped the definition of “serious” composition for over seventy years. I did not set out to oppose it. I was not working within it. I was following the internal demands of my own music. What follows is not a critique from within the tradition, but the emergence of a system that renders its central assumption unnecessary. What Adorno Actually Demands Stripped of its dialectical language, Adorno’s demand is clear: a serious work must fully engage the complexity of its historical material. It must resist simplification, refuse reconciliation, and m...
Read more

The Double Theft: Adorno, New Complexity, and the Jazz Musicians Nobody Credited

There is a contradiction at the heart of the New Complexity movement so glaring that it should have ended careers. It hasn't, because the people who benefit from it control the conversation. This essay is an attempt to change that. The New Complexity — Ferneyhough, Barrett, Dench, the UK network that decides who exists and who doesn't — presents itself as the apex of Western musical thought. Rigorous. Uncompromising. Intellectually serious in ways lesser musics cannot be. Its theoretical self-image draws heavily on Theodor Adorno, whose withering dismissal of jazz as a regressive, pseudo-individualist commodity form remains foundational to the European new music worldview. Jazz, for Adorno, was not serious music. It was administered rebellion — the appearance of freedom within a system designed to prevent it. And yet. The extended technique vocabulary that defines New Complexity on the instrumental level — multiphonics, overblowing, singing while playing, microtonal inflection,...
Read more