Polytempic Polymicrotonality and the Da Vinci Vitruvian Man, part XXVIII

 

The Body as System: Vitruvian Man and the Origin of Polytempic Polymicrotonality

Peter Thoegersen

There is a drawing that has haunted Western thought for five hundred years. Leonardo da Vinci's Vitruvian Man — a figure inscribed simultaneously within a circle and a square, arms and legs extended in two positions — is universally understood as a statement about proportion: that the human body contains within itself the mathematical relationships governing architecture, art, and the cosmos. What has not been observed is that this same body, read geometrically, encodes the exact polyrhythmic structure at the foundation of polytempic polymicrotonality.

I arrived at this discovery not in a library but unexpectedly, watching a film late at night, when the Vitruvian Man appeared on screen and something clicked into place. The connection I had been unable to articulate — between my body as a drummer and my compositional system — suddenly had a name and an image. What follows is what I saw.

The Geometry of the Figure

The Vitruvian Man presents two superimposed positions of the same body. In the first, arms are outstretched horizontally and legs together — the T formation, which, with the head, defines the square. In the second, arms and legs are spread to their fullest extension, touching the circumference of the circle. It is from the geometric relationships between the points of this figure that the structure reveals itself.

Draw a line between the two feet in the spread position: a triangle is implied, three points — head, left foot, right foot. The number 3.

Connect the two hands to the head and back to the feet and across: a pentagon emerges from the figure's outstretched limbs. The number 5.

Draw lines from both sets of arms — all four arm positions from both superimposed figures — through the head and down to the legs: a heptagon, seven points distributed around the circle. The number 7.

And of course the square itself, defined by the outstretched arms and the standing height of the figure, gives the number 4.

The Vitruvian Man encodes, in its geometry, the simultaneous relationships 3 against 4 against 5 against 7.

Figure 1. The Vitruvian Man's geometry encodes 3 : 4 : 5 : 7

The Rhythm I Had Already Written

When I was eighteen years old, I was writing music built on the polyrhythmic structure of 3 against 4 against 5 against 7. I did not derive this from a diagram. I derived it from my body — from the four-limb independence I had developed as a left-handed drummer, where each limb moves in its own temporal stream, and the composite rhythm emerges from their simultaneous independence rather than from any single dominating pulse.

I did not know, at eighteen, that I was encoding what da Vinci had drawn. I did not know that the same proportional relationships embedded in the human figure — 3, 4, 5, 7 — were what my four limbs were enacting each time I played. The body was ahead of my understanding of it.

This is what the Vitruvian Man actually says: the body does not merely inhabit mathematical proportion. The body generates it. The relationships are not imposed on us from outside — from architecture or theory or tradition — but are latent in our physical structure, waiting to be read.

From Four Limbs to Four Dimensions

The mature system of polytempic polymicrotonality operates on four simultaneous dimensions: four independent tempi running concurrently, and four independent microtonal tuning systems coexisting within a single work. The number four is not arbitrary. It is the number of limbs the human body has. It is the number of independent temporal streams a drummer develops through years of practice. It is the number of sides of the square in which the Vitruvian Man stands.

The architecture of the system is a somatic architecture. It did not emerge from purely intellectual construction — from reading the right books or following the right theoretical tradition. It emerged from the inside of a body that had trained itself, over years, to sustain genuine independence across four simultaneous streams of motion. Theory followed experience. The system is a formalization of what the body already knew.

This is what I believe distinguishes polytempic polymicrotonality from other complex compositional systems: its proportions are human proportions. The fourfold structure is not an aesthetic preference or a mathematical convenience. It is the number we are. The Vitruvian Man, that ancient image of the body as the measure of all things, turns out to have been a compositional diagram all along.

A Note on Discovery

I have spent decades developing this system, writing two published treatises to document it, composing over three hundred works to realize it. The connection to da Vinci's drawing arrived not at the end of this labor but unexpectedly, in a moment of recognition rather than research. This is, I think, how the deepest structural truths tend to arrive — not through accumulation but through sudden visibility, when something you have been circling for years finally shows its face.

The Vitruvian Man does not explain my system. My system does not explain the Vitruvian Man. What they share is a common source: the human body, four-limbed and proportioned, generating through its own structure the mathematics that music — and perhaps all art — is attempting to embody.