3GMP

Keenan: I've looked at trivalence as a function of the tuning of seven tone harmonic scales (those in which all the notes
are part of at least one generalized major or minor triad) and find them quite sparse. Scales of the diatonic class, those which
have identical triads on roots a constant interval apart (such as the major or minor modes with triads on the tonic,mediant and dominant degrees, etc.) have a fair number of trivalent tunings as do scales related to the Partch incipient tonality diamond (5-limit diamond), but they are very sparse among scales related to the melodic and harmonic minors and the other classes.

--John