ABACABADABACABA JI scales: Difference between revisions
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Created page with "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..." |
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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 | 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/ | 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 == | == 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c == | ||
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|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 | |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 | |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 | |||
|} | |} | ||
Revision as of 00:02, 2 April 2023
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, 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
Heptachord to 4/3 -> D = 9/8 (~203.91c)
| A | B | C | Scale | odd-limit of scale intervals |
|---|---|---|---|---|
| 22/21 (~80.54c) | 126/121 (~70.10c) | 49/48 (~35.70c) | 1/1 22/21 12/11 8/7 7/6 11/9 14/11 4/3 3/2 11/7 18/11 12/7 7/4 11/6 21/11 2/1 | 441 |
| 24/23 (~73.68c) | 529/504 (~83.81c) | 49/48 (~35.70c) | 1/1 24/23 23/21 8/7 7/6 28/23 23/18 4/3 3/2 36/23 23/14 12/7 7/4 42/23 23/12 2/1 | 529 |
| 25/24 (~70.67c) | 128/125 (~41.06c) | 27/25 (~133.24c) | 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)
| 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 |