ABACABA JI scales: Difference between revisions

One scale under such constraints is a degenderate case, wherein A = C: the Pythagorean diatonic scale, where A = C = 9/8, and B = 256/243, with a rank-2 form ABABABA. This scale is well-formed, and (5, 2) SNS. Specifically it is SNS (2/1, 3/2)[7]. The most complex interval in this scale is the Pythagorean augmented fourth — 729/512 — and it's inversion, the Pythagorean diminished fifth — 1024/729. Accordingly, the scale is 729-limit. 729 is chosen as the limit so that the list includes all ABACABA scales with complexity up to that of the Pythagorean diatonic scale (with steps > 20c). All other ABACABA scales can be described as SNS (2/1, 2/T, A), or equivalently as SNS (2/1, T, A), where T = ABA, the outer interval of the tetrachord.