katapyknosis

(Greek: "densification")

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].

[from John Chalmers, Divisions of the Tetrachord]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

see also pyknon, and my Tutorial on ancient Greek tetrachord-theory

[from Joe Monzo, JustMusic: A New Harmony]

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updated:

2002.9.12
1999.12.19

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(to download a zip file of the entire Dictionary, click here)

For many more diagrams and explanations of historical tunings, see my book. If you don't understand my theory or the terms I've used, start here

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