ABACABADABACABA JI scales: Difference between revisions

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ABACABADABACABA is the (8,4,2,1) [[SNS]] pattern (the rank-4 power SNS). When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two ABACABA scales separ

ated by an interval D, akin to how ABACABA scales can be conceived of as two ABA tetrachords separated by an interval C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call a heptachord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, H/P, T/H, A), or equivalently as SNS (P, H, T, A), where P is the period, H is the interval subtended by ABACABA, the heptachord, and T is the interval subtended by ABA, the tetrachord

ated by an interval D, akin to how ABACABA scales can be conceived of as two ABA tetrachords separated by an interval C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call a heptachord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/H, H/T, A), or equivalently as SNS (P, H, T, A) etc. where P is the period, H is the interval subtended by ABACABA, the heptachord, and T is the interval subtended by ABA, the tetrachord.

== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==

Line 31:

|1/1 25/24 16/15 10/9 6/5 5/4 32/25 4/3 3/2 25/16 8/5 5/3 9/5 15/8 48/25 2/1

|625

|}

=== Heptachord to 7/5 -> D = 50/49 (~34.98c) ===

{| class="wikitable"

|+

!A

!B

!C

!Scale

!odd-limit of scale intervals

|-

|21/20 (~84.47c)

|64/63 (~27.26c)

|125/112 (~190.12c)

|1/1 21/20 16/15 28/25 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 25/14 15/8 40/21 2/1

|441

|}

@@ Line 1: / Line 1: @@
 ABACABADABACABA is the (8,4,2,1) [[SNS]] pattern (the rank-4 power SNS). When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two ABACABA scales separ
-ated by an interval D, akin to how ABACABA scales can be conceived of as two ABA tetrachords separated by an interval C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call a heptachord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, H/P, T/H, A), or equivalently as SNS (P, H, T, A), where P is the period, H is the interval subtended by ABACABA, the heptachord, and T is the interval subtended by ABA, the tetrachord
+ated by an interval D, akin to how ABACABA scales can be conceived of as two ABA tetrachords separated by an interval C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call a heptachord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/H, H/T, A), or equivalently as SNS (P, H, T, A) etc. where P is the period, H is the interval subtended by ABACABA, the heptachord, and T is the interval subtended by ABA, the tetrachord.
 == 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==
@@ Line 31: / Line 31: @@
 |1/1 25/24 16/15 10/9 6/5 5/4 32/25 4/3 3/2 25/16 8/5 5/3 9/5 15/8 48/25 2/1
 |625
+|}
+=== Heptachord to 7/5 -> D = 50/49 (~34.98c) ===
+{| class="wikitable"
+|+
+!A
+!B
+!C
+!Scale
+!odd-limit of scale intervals
+|-
+|21/20 (~84.47c)
+|64/63 (~27.26c)
+|125/112 (~190.12c)
+|1/1 21/20 16/15 28/25 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 25/14 15/8 40/21 2/1
+|441
 |}