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.
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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