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].
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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