Major Scales Bases

I'm glad to hear that Johnny R. entertained the heck out of you (PAULE), and
that you found Mayumi to be a fine microtonalist. Neither fact surprises me in
the slightest.

> Gary: I believe you are right in pointing to the tetrachord as the basis of
> the diatonic scale.

And of course, the similar upper and lower tetrachords are similar but not
identical in the traditional Ptolemaic JI, but are in Pythagorean.

That brings to mind a curious question: How many underlying bases (as in
plural of basis), structurally speaking, are there for the major scale,
historical or not? I can think of three right off the top of my head:
1. Identical upper and lower tetrachords
2. Circle of fifths (one down and five up)
3. Primary triads


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