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ABACABA JI scales: Difference between revisions

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VisualWikitext
Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
got rid of scales where P/B was above the limit
Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
corrected limits of scales (with 3/2 and 4/3 period), changed order accordingly
Line 1,634: Line 1,634:
== 729-limit (675-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. There are no 729-limit ABACABA scales with period 3/2, with steps > 20c. The list has an effective odd-limit of 675.
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) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|21/20 (~84.47c)
|160/147 (~146.71c)
|1/1 21/20 8/7 6/5 5/4 21/16 10/7 3/2
|147
|-
|24/23 (~73.68c)
|529/480 (~168.28c)
|1/1 24/23 23/20 6/5 5/4 30/23 23/16 3/2
|529
|-
|27/25 (~133.24c)
|250/243 (~49.17c)
|1/1 27/25 10/9 6/5 5/4 27/20 25/18 3/2
|625
|-
|16/15 (~111.73c)
|135/128 (~92.18c)
|1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2
|675
|-
|18/17 (~98.95c)
|289/270 (~117.73c)
|1/1 18/17 17/15 6/5 5/4 45/34 17/12 3/2
|675
|}


=== Tetrachord to 9/8 -> C = 32/27 (~294.13c) ===
=== Tetrachord to 9/8 -> C = 32/27 (~294.13c) ===
Line 1,693: Line 1,659:
|}
|}


=== Tetrachord to 7/6 -> C = 54/49 (~168.21c) ===
=== Tetrachord to 17/14 -> C = 294/289 (~29.70c) ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,701: Line 1,667:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|21/20 (~84.47c)
|17/16 (~104.96c)
|200/189 (~97.94c)
|128/117 (~115.56c)
|1/1 21/20 10/9 7/6 9/7 27/20 10/7 3/2
|1/1 17/16 8/7 17/14 28/17 21/16 24/17 3/2
|243
|357
|-
|-
|19/18 (~93.60c)
|15/14 (~119.44c)
|378/361 (~79.65c)
|238/225 (~97.24c)
|1/1 19/18 21/19 7/6 9/7 19/14 27/19 3/2
|1/1 15/14 17/15 17/14 28/17 45/34 7/5 3/2
|361
|675
|}
|}


=== Tetrachord to 15/13 -> C = 169/150 (~206.47c) ===
=== Tetrachord to 7/6 -> C = 54/49 (~168.21c) ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,720: Line 1,686:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|27/26 (~65.34c)
|19/18 (~93.60c)
|260/243 (~117.07c)
|378/361 (~79.65c)
|1/1 27/26 10/9 15/13 39/30 27/20 13/9 3/2
|1/1 19/18 21/19 7/6 9/7 19/14 27/19 3/2
|243
|361
|}
 
=== Tetrachord to 17/14 -> C = 294/289 (~29.70c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|17/16 (~104.96c)
|21/20 (~84.47c)
|128/117 (~115.56c)
|200/189 (~97.94c)
|1/1 17/16 8/7 17/14 28/17 21/16 24/17 3/2
|1/1 21/20 10/9 7/6 9/7 27/20 10/7 3/2
|289
|567
|-
|15/14 (~119.44c)
|238/225 (~97.24c)
|1/1 15/14 17/15 17/14 28/17 45/34 7/5 3/2
|675
|}
|}


Line 1,759: Line 1,711:
|}
|}


=== Tetrachord to 23/20 -> C = 600/529 (~218.03c) ===
=== Tetrachord to 6/5 -> C = 25/24 (~70.67c) ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,767: Line 1,719:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|23/22 (~76.96c)
|21/20 (~84.47c)
|121/115 (~88.05c)
|160/147 (~146.71c)
|1/1 23/22 11/10 23/20 30/23 15/11 33/23 3/2
|1/1 21/20 8/7 6/5 5/4 21/16 10/7 3/2
|441
|-
|24/23 (~73.68c)
|529/480 (~168.28c)
|1/1 24/23 23/20 6/5 5/4 30/23 23/16 3/2
|529
|529
|-
|16/15 (~111.73c)
|135/128 (~92.18c)
|1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2
|675
|-
|18/17 (~98.95c)
|289/270 (~117.73c)
|1/1 18/17 17/15 6/5 5/4 45/34 17/12 3/2
|675
|-
|27/25 (~133.24c)
|250/243 (~49.17c)
|1/1 27/25 10/9 6/5 5/4 27/20 25/18 3/2
|729
|}
|}


Line 1,784: Line 1,756:
|69/64 (~130.23c)
|69/64 (~130.23c)
|1/1 24/23 9/8 27/23 23/18 4/3 23/16 3/2
|1/1 24/23 9/8 27/23 23/18 4/3 23/16 3/2
|529
|}
=== Tetrachord to 23/20 -> C = 600/529 (~218.03c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|23/22 (~76.96c)
|121/115 (~88.05c)
|1/1 23/22 11/10 23/20 30/23 15/11 33/23 3/2
|529
|529
|}
|}
Line 1,815: Line 1,801:
|}
|}


=== Tetrachord to 11/10 -> C = 150/121 (~371.95c) ===
=== Tetrachord to 15/13 -> C = 169/150 (~206.47c) ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,823: Line 1,809:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|33/32 (~53.27c)
|27/26 (~65.34c)
|512/495 (~58.46c)
|260/243 (~117.07c)
|1/1 33/32 16/15 11/10 15/11 45/32 16/11 3/2
|1/1 27/26 10/9 15/13 39/30 27/20 13/9 3/2
|675
|243
|}
|}


Line 1,843: Line 1,829:
|126/121 (~70.10c)
|126/121 (~70.10c)
|1/1 22/21 12/11 8/7 7/6 11/9 14/11 4/3
|1/1 22/21 12/11 8/7 7/6 11/9 14/11 4/3
|147
|189
|-
|-
|24/23 (~73.68c)
|24/23 (~73.68c)
Line 1,851: Line 1,837:
|}
|}


=== Tetrachord to 10/9 -> C = 27/25 (~133.24c)===
=== Tetrachord to 26/23 -> C = 529/507 (~73.54c)===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,859: Line 1,845:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|25/24 (~70.67c)
|24/23 (~73.68c)
|128/125 (~41.06c)
|299/288 (~64.89c)
|1/1 25/24 16/15 10/9 6/5 5/4 32/25 4/3
|1/1 24/23 13/12 26/23 46/39 16/13 23/18 4/3
|625
|529
|}
|}


=== Tetrachord to 26/23 -> C = 529/507 (~73.54c) ===
=== Tetrachord to 10/9 -> C = 27/25 (~133.24c) ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,873: Line 1,859:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|24/23 (~73.68c)
|25/24 (~70.67c)
|299/288 (~64.89c)
|128/125 (~41.06c)
|1/1 24/23 13/12 26/23 46/39 16/13 23/18 4/3
|1/1 25/24 16/15 10/9 6/5 5/4 32/25 4/3
|529
|625
|}
|}


Retrieved from "https://en.xen.wiki/w/ABACABA_JI_scales"