ABACABA JI scales: Difference between revisions
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== 729-limit ABACABA scales with period 3/2, with steps > 20c == | == 729-limit (675-limit) ABACABA scales with period 3/2, with steps > 20c == | ||
Given the scales repeat at 3/2, factors of 3 in the odd-limit vary with transposition by a period. Accordingly the odd-limit listed is the odd-limit for intervals in a single period of the scale. | Given the scales repeat at 3/2, factors of 3 in the odd-limit vary with transposition by a period. Accordingly the odd-limit listed is the odd-limit for intervals in a single period of the scale. There are no 729-limit ABACABA scales with period 3/2, with steps > 20c. The list has an effective odd-limit of 675. | ||
=== Tetrachord to 6/5 -> C = 25/24 (~70.67c) === | === Tetrachord to 6/5 -> C = 25/24 (~70.67c) === | ||
| Line 1,794: | Line 1,794: | ||
|1/1 25/24 12/11 25/22 33/25 11/8 36/25 3/2 | |1/1 25/24 12/11 25/22 33/25 11/8 36/25 3/2 | ||
|625 | |625 | ||
|} | |||
== 729-limit (675-limit) ABACABA scales with period 4/3, with steps > 20c == | |||
2/1 period scales with two periods of these ABACABA scales and a remaining interval of 9/8 may be built, akin to octave species scales built of two copies of a tetrachord (with a 9/8 remainder). The remaining 9/8 interval may be filled in a number of different ways. There are no 729-limit ABACABA scales with period 4/3, with steps > 20c. The list has an effective odd-limit of 675. | |||
=== Tetrachord to 8/7 -> C = 49/48 (~35.70c) === | |||
{| class="wikitable" | |||
|+ | |||
!A | |||
!B | |||
!Scale | |||
!odd-limit of scale intervals | |||
|- | |||
|22/21 (~80.54c) | |||
|126/121 (~70.10c) | |||
|1/1 22/21 12/11 8/7 7/6 11/9 14/11 4/3 | |||
|147 | |||
|- | |||
|24/23 (~73.68c) | |||
|529/504 (~83.81c) | |||
|1/1 24/23 23/21 8/7 7/6 28/23 23/18 4/3 | |||
|529 | |||
|} | |||
=== Tetrachord to 26/23 -> C = 529/507 (~73.54c) === | |||
{| class="wikitable" | |||
|+ | |||
!A | |||
!B | |||
!Scale | |||
!odd-limit of scale intervals | |||
|- | |||
|24/23 (~73.68c) | |||
|299/288 (~64.89c) | |||
|1/1 24/23 13/12 26/23 46/39 16/13 23/18 4/3 | |||
|529 | |||
|} | |||
=== Tetrachord to 28/25 -> C = 625/588 (~105.65c) === | |||
{| class="wikitable" | |||
|+ | |||
!A | |||
!B | |||
!Scale | |||
!odd-limit of scale intervals | |||
|- | |||
|26/25 (~67.90c) | |||
|175/169 (~60.40c) | |||
|1/1 26/25 14/13 28/25 25/21 26/21 50/39 4/3 | |||
|625 | |||
|} | |||
=== Tetrachord to 10/9 -> C = 27/25 (~133.24c) === | |||
{| class="wikitable" | |||
|+ | |||
!A | |||
!B | |||
!Scale | |||
!odd-limit of scale intervals | |||
|- | |||
|28/27 (~62.96c) | |||
|405/392 (~56.48c) | |||
|1/1 28/27 15/14 10/9 6/5 56/45 9/7 4/3 | |||
|675 | |||
|} | |} | ||