unit-proportion, UP

An invariant used by Ervin Wilson to design sets of chords with gradually increasing interval widths for harmonizing tetrachords.

The unit-proportion of a chord is the set of differences between the harmonic or subharmonic numbers defining the elements.

For example, the UP of 4:5:7:9 is 1+2+2 and that of the corresponding subharmonic chord 1/4:1/5:1/7:1/9 is -1-2-2.

[from John Chalmers, Divisions of the Tetrachord]

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