ABACABA JI scales: Difference between revisions
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ABACABA is the singular pairwise well-formed generalised step pattern, and the (4, 2, 1) SNS pattern. Scales with this step pattern are known as Cantor-2 scales. Such scales can be thought of as symmetrical tetrachordal scales. | ABACABA is the singular pairwise well-formed generalised step pattern, and the (4, 2, 1) SNS pattern. Scales with this step pattern are known as Cantor-2 scales. Such scales can be thought of as symmetrical tetrachordal scales. | ||
== 729-limit | == 729-limit ABACABA scales with steps > 20c == | ||
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. This scale is well-formed, and (5, 2) SNS. Specifically it is SNS (2/1, 3/2)[7]. All other scales can be described as SNS (2/1, 2/T, A), or equivalently as SNS (2/1, T, A), where T=ABA, the size of the tetrachord. | 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. This scale is well-formed, and (5, 2) SNS. Specifically it is SNS (2/1, 3/2)[7]. All other scales can be described as SNS (2/1, 2/T, A), or equivalently as SNS (2/1, T, A), where T=ABA, the size of the tetrachord. | ||