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Encyclopedia of Microtonal Music Theory

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katapyknosis ( καταπυκνοσισ )

(Greek: "densification")

[John Chalmers, Divisions of the Tetrachord]

The division of a musical interval by multiplication of the defining integers and the insertion of arithmetic or harmonic means.

For example, from 16/15, one obtains 32/31 and 31/30 [because 16/15 = 32/30].

. . . . . . . . .
[Joe Monzo]

Below is a diagram illustrating how the ancient Greeks would find the above example on a string; the numbers refer to parts of a string-length:

    |
15 -+- 30
    |
    |
   -+- 31
    |
    |
16 -+- 32
    |
		
. . . . . . . . .

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