ABACABA JI scales: Difference between revisions

(One intermediate revision by one other user not shown)

Line 1:

ABACABA is the ternary [[Fraenkel word]] and the singular [[Rank-3 scale#Pairwise well-formed scales|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, T/A), or equivalently as SNS (P, T, A) etc., 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 ternary [[Fraenkel word]], or the rank-3 power SNS, i.e., the (4, 2, 1) [[SN scale|SNS]] pattern, and the singular [[Rank-3 scale#Pairwise well-formed scales|pairwise well-formed]] generalized step 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, T/A), or equivalently as SNS (P, T, A) etc., 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.

Line 1,879:

|}

[[Category: Just intonation scales]]

[[Category: Step-nested scales]]

[[Category:Wakalixes]]

[[Category:Lists of scales]]

@@ Line 1: / Line 1: @@
-ABACABA is the ternary [[Fraenkel word]] and the singular [[Rank-3 scale#Pairwise well-formed scales|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, T/A), or equivalently as SNS (P, T, A) etc., 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 ternary [[Fraenkel word]], or the rank-3 power SNS, i.e., the (4, 2, 1) [[SN scale|SNS]] pattern, and the singular [[Rank-3 scale#Pairwise well-formed scales|pairwise well-formed]] generalized step 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, T/A), or equivalently as SNS (P, T, A) etc., 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.
@@ Line 1,879: / Line 1,879: @@
 |}
+{{Navbox scale gallery}}
 [[Category: Just intonation scales]]
 [[Category: Step-nested scales]]
 [[Category:Wakalixes]]
 [[Category:Lists of scales]]