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Encyclopedia of Microtonal Music Theory

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[John Chalmers, Divisions of the Tetrachord]

A measure of the dissonance due to the size of the prime factors of musical intervals (Barlow, 1987).

The indigestibility, x(P), of the prime number P is defined as 2*(P-1)2/P. Examples are x(3) = 2.667, x(5) = 6.400, and x(7) = 10.286.

The indigestibility of a composite number is the sum of the indigestibilities of its prime factors. For example x(15) = x(3) + x(5) or 2.667 + 6.400 = 9.067.

Indigestibilities are combined to generate the harmonicity and specific harmonicity functions

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[Manuel Op de Coul, private communication with Joe Monzo, Thursday 2003.10.02 5:58 AM]

Hi Joe,

You probably missed my remark that indigestibility isn't meant as a measure of dissonance by Barlow.

So I think you should change this page. Rather, it serves as a measure of divisibility for the harmonicity function, which is a measure of harmonic cohesion.

So harmonicity isn't a measure of dissonance either, but your page doesn't say that.



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