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) [[SN scale|SNS]] pattern. Such scales can be thought of as mirror-symmetric ([[Chirality|achiral]]) tetrachordal scales. As [[step-nested scales]], all ABACABA scales can be described as SNS (P, P/T, A), or equivalently as SNS (P, T, A), where P is the period, and T = ABA, the outer interval of the tetrachord. When they span a 2/1 period (P=2), scales with this step pattern are known as Cantor-2 scales

ABACABA is the singular [[Rank-3 scales#https://en.xen.wiki/w/Rank-3%20scale#Pairwise%20well-formed%20scales|pairwise well-formed]] generalized step pattern, and the (4, 2, 1) [[SN scale|SNS]] pattern. Such scales can be thought of as mirror-symmetric ([[Chirality|achiral]]) tetrachordal scales. As [[step-nested scales]], all ABACABA scales can be described as SNS (P, P/T, A), or equivalently as SNS (P, T, A), where P is the period, and T = ABA, the outer interval of the tetrachord. When they span a 2/1 period (P=2), scales with this step pattern are known as Cantor-2 scales

== 225-limit ABACABA scales with period 2/1, with steps > 20c ==

225 is chosen as the [[odd-limit]] so that the list includes all ABACABA scales with complexity up to that of the [[5-limit]] double harmonic major scale — [[SNS (2/1, 3/2, 5/4)-7|16/15 5/4 4/3 3/2 8/5 15/8 2/1]] — and a lower limit of 20c for step sizes is chosen so that there are no steps smaller than [[81/80]]. For ABACABA scales, 225-odd-limit implies 13-limit.

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-ABACABA is the singular pairwise well-formed generalised step pattern, and the (4, 2, 1) [[SN scale|SNS]] pattern. Such scales can be thought of as mirror-symmetric ([[Chirality|achiral]]) tetrachordal scales. As [[step-nested scales]], all ABACABA scales can be described as SNS (P, P/T, A), or equivalently as SNS (P, T, A), where P is the period, and T = ABA, the outer interval of the tetrachord. When they span a 2/1 period (P=2), scales with this step pattern are known as Cantor-2 scales
+ABACABA is the singular [[Rank-3 scales#https://en.xen.wiki/w/Rank-3%20scale#Pairwise%20well-formed%20scales|pairwise well-formed]] generalized step pattern, and the (4, 2, 1) [[SN scale|SNS]] pattern. Such scales can be thought of as mirror-symmetric ([[Chirality|achiral]]) tetrachordal scales. As [[step-nested scales]], all ABACABA scales can be described as SNS (P, P/T, A), or equivalently as SNS (P, T, A), where P is the period, and T = ABA, the outer interval of the tetrachord. When they span a 2/1 period (P=2), scales with this step pattern are known as Cantor-2 scales
 == 225-limit ABACABA scales with period 2/1, with steps > 20c ==
 is chosen as the [[odd-limit]] so that the list includes all ABACABA scales with complexity up to that of the [[5-limit]] double harmonic major scale — [[SNS (2/1, 3/2, 5/4)-7|16/15 5/4 4/3 3/2 8/5 15/8 2/1]] — and a lower limit of 20c for step sizes is chosen so that there are no steps smaller than [[81/80]]. For ABACABA scales, 225-odd-limit implies 13-limit.