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Encyclopedia of Microtonal Music Theory

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[Harry Partch 1974, Genesis of a Music, 2nd ed., p. 75]

A psychological phenomenon having as its chief characteristic a tonal polarity around a 1 Identity; the sounding of various of the identities -- either Odentities or Udentities -- with a Numerary Nexus will create this polarity, and the smaller the >odd-number identities played the stronger the polarity.

Acoustically, the identities of a tonality represent the maximal consonance of any given number of stipulated identities because of the Numerary Nexus:

the tones of the triad 8/7 - 10/7 - 12/7 -- with the Numerary Nexus 7 -- are in the relation 8:10:12, or 4:5:6 (Identities 1-5-3), and create a polarity around 8/7, the 1 Odentitiy. This is the maximal consonance that three different tonal identities in music can attain.

Were the triad 10/7 - 12/7 - 7/7 (= 1/1) chosen, with the relation between the tones of 5:6:7 (Identities 5-3-7), the polarity around 8/7 would still be created, though it would not be as strong.

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[Joe Monzo]

Essentially, Partch is saying that any collection of musical pitches whose frequencies can be expressed as proportional relationships which form a subset of an arithmetic series, will exhibit tonality.

He is assuming octave-equivalence, thus, only the odd factors really matter. The lower the odd numbers are, the stronger the perceived sensation of tonality.

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