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ABACABA JI scales: Difference between revisions

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ABACABA is the singular pairwise well-formed generalised step pattern, and the (4, 2, 1) SNS pattern. Scales with this step pattern are known as Cantor-2 scales. Such scales can be thought of as symmetrical tetrachordal 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.


== 729-limit ABACABA scales with steps > 20c ==
=== Tetrachord to 4/3 -> C = 9/8 (~203.91c) ===
One scale under such constraints is a degenderate case, wherein A = C: the pythagorean diatonic scale, where A = C = 9/8, and B = 256/243. This scale is well-formed, and (5, 2) SNS. Specifically it is SNS (2/1, 3/2)[7]. All other scales can be described as SNS (2/1, 2/T, A), or equivalently as SNS (2/1, T, A), where T=ABA, the outer interval of the tetrachord.
 
=== Tetrachord to 4/3 -> C = 9/8 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 12: Line 11:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|8/7
|8/7 (~231.17c)
|49/48
|49/48 (~35.70c)
|1/1 8/7 7/6 4/3 3/2 12/7 7/4 2/1
|1/1 8/7 7/6 4/3 3/2 12/7 7/4 2/1
|49
|49
|-
|-
|10/9
|10/9 (~182.40c)
|27/25
|27/25 (~133.24c)
|1/1 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|1/1 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|81
|81
|-
|-
|12/11
|12/11 (~150.64c)
|121/108
|121/108 (~196.77c)
|1/1 12/11 11/9 4/3 3/2 18/11 11/6 2/1  
|1/1 12/11 11/9 4/3 3/2 18/11 11/6 2/1  
|121
|121
|-
|-
|13/12
|13/12 (~138.57c)
|192/169
|192/169 (~220.90c)
|1/1 13/12 16/13 4/3 3/2 13/8 24/13 2/1
|1/1 13/12 16/13 4/3 3/2 13/8 24/13 2/1
|169
|169
|-
|-
|16/15
|16/15 (~111.72c)
|75/64
|75/64 (~247.74c)
|1/1 16/15 5/4 4/3 3/2 8/5 15/8 2/1
|1/1 16/15 5/4 4/3 3/2 8/5 15/8 2/1
|225
|225
|}
=== Tetrachord to 7/5 -> C = 50/49 (~34.98c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|17/15
|7/6 (~266.87c)
|300/289
|36/35 (~48.77c)
|1/1 17/15 20/17 4/3 3/2 17/10 30/17 2/1
|1/1 7/6 6/5 7/5 10/7 5/3 12/7 2/1
|289
|49
|-
|-
|19/18
|11/10 (~182.40c)
|432/361
|140/121 (~252.50c)
|1/1 19/18 24/19 4/3 3/2 19/12 36/19 2/1
|1/1 11/10 14/11 7/5 10/7 11/7 20/11 2/1
|361
|121
|-
|-
|20/19
|14/13 (~128.30c)
|361/300
|169/140 (~325.92c)
|1/1 20/19 19/15 4/3 3/2 30/19 19/10 2/1
|1/1 14/13 13/10 7/5 10/7 20/13 13/7 2/1
|361
|169          
|}
 
=== Tetrachord to 5/4 -> C = 32/25 (~427.37c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|22/21
|10/9 (~182.40c)
|147/121
|81/80 (~21.51c)
|1/1 22/21 14/11 4/3 3/2 11/7 21/11 2/1  
|1/1 10/9 9/8 5/4 8/5 16/9 9/5 2/1
|441
|81
|-
|-
|14/13
|15/14 (~119.44c)
|169/147
|49/45 (~147.43c)
|1/1 14/13 26/21 4/3 3/2 21/13 13/7 2/1  
|1/1 15/14 7/6 5/4 8/5 12/7 28/15 2/1
|441
|225
|-
|-
|23/21
|13/12 (~138.57c)
|588/529
|180/169 (~109.17c)
|1/1 23/21 28/23 4/3 3/2 23/14 42/23 2/1
|1/1 13/12 15/13 5/4 8/5 26/15 24/13 2/1
|529
|225
|}
 
=== Tetrachord to 9/7 -> C = 98/81 (~329.83c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|25/24
|9/8 (~203.91c)
|768/625
|64/63 (~27.26c)
|1/1 25/24 32/25 4/3 3/2 25/16 48/25 2/1
|1/1 9/8 8/7 9/7 14/9 7/4 16/9 2/1
|625
|81
|-
|-
|28/25
|15/14 (~119.44c)
|625/588
|28/25 (~196.20c)
|1/1 28/25 25/21 4/3 3/2 42/25 25/14 2/1
|1/1 15/14 6/5 9/7 14/9 5/3 28/15 2/1
|625
|225
|-
|9/8
|256/243
|1/1 9/8 32/27 4/3 3/2 27/16 16/9 2/1
|729
|-
|28/27
|243/196
|1/1 28/27 9/7 4/3 3/2 14/9 27/14 2/1  
|729
|-
|18/17
|289/243
|1/1 18/17 34/27 4/3 3/2 27/17 17/9 2/1
|729
|}
|}


=== Tetrachord to 7/5 -> C = 50/49 ===
=== Tetrachord to 11/8 -> C = 128/121 (~97.36c) ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 101: Line 112:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|7/6
|11/10 (~165.00c)
|36/25
|25/22 (~221.31c)
|1/1 7/6 6/5 7/5 10/7 5/3 12/7 2/1
|1/1 11/10 5/4 11/8 16/11 8/5 20/11 2/1
|49
|-
|11/10
|140/121
|1/1 11/10 14/11 7/5 10/7 11/7 20/11 2/1
|121
|121
|-
|-
|14/13
|9/8 (~203.91c)
|169/140      
|88/81 (~143.50c)
|1/1 14/13 13/10 7/5 10/7 20/13 13/7 2/1
|1/1 9/8 11/9 11/8 16/11 18/11 16/9 2/1
|169          
|121
|}
 
=== Tetrachord to 14/11 -> C = 121/98 (~364.98c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|21/20
|12/11 (~150.64c)
|80/63
|77/72 (~116.23c)
|1/1 21/20 4/3 7/5 10/7 3/2 40/21 2/1
|1/1 12/11 7/6 14/11 11/7 12/7 11/6 2/1
|441
|121
|-
|-
|16/15
|14/13 (~128.30c)
|315/256
|169/154 (~160.91c)
|1/1 16/15 21/16 7/5 10/7 32/21 15/8 2/1
|1/1 14/13 13/11 14/11 11/7 22/13 13/7 2/1
|441
|169
|}
 
=== Tetrachord to 18/13 -> C = 169/162 (~73.24c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|17/15
|14/13 (~128.30c)
|315/289
|117/98 (~306.79c)
|1/1 17/15 21/17 7/5 10/7 34/21 30/17 2/1
|1/1 14/13 9/7 18/13 13/9 14/9 13/7 2/1
|441
|169
|-
|-
|21/19
|9/8 (~203.91c)
|361/315
|128/117 (~155.56c)
|1/1 21/19 19/15 7/5 10/7 30/19 38/21 2/1
|1/1 9/8 16/13 18/13 13/9 13/8 16/9 2/1
|441
|169
|-
|-
|23/20
|15/13 (~247.74c)
|560/529
|26/25 (~67.90c)
|1/1 23/20 28/23 7/5 10/7 23/14 40/23 2/1
|1/1 15/13 6/5 18/13 13/9 5/3 26/15 2/1
|529
|225
|}
 
=== Tetrachord to 13/10 -> C = 200/169 (~291.57c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|28/25
|13/12 (~138.57c)
|125/112
|72/65 (~177.07c)
|1/1 28/25 5/4 7/5 10/7 8/5 25/14 2/1
|1/1 13/12 6/5 13/10 20/13 5/3 24/13 2/1
|625
|169
|-
|-
|28/27
|11/10 (~165.00c)
|729/560
|130/121 (~137.47c)
|1/1 28/27 27/20 7/5 10/7 40/27 27/14 2/1
|1/1 11/10 13/11 13/10 20/13 22/13 20/11 2/1
|729
|169
|}
|}


=== Tetrachord to 5/4 -> C = 32/25 ===
=== Tetrachord to 16/13 -> C = 169/128 (~481.06c) ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 160: Line 193:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|10/9
|14/13 (~128.30c)
|81/80
|52/49 (~102.88c)
|1/1 10/9 9/8 5/4 8/5 16/9 9/5 2/1
|1/1 14/13 8/7 16/13 13/8 7/4 13/7 2/1
|81
|169
|-
|-
|15/14
|16/15 (~111.72c)
|49/45
|225/208 (~136.01c)
|1/1 15/14 7/6 5/4 8/5 12/7 28/15 2/1
|1/1 16/15 15/13 16/13 13/8 26/15 15/8 2/1
|225
|225
|}
=== Tetrachord to 15/11 -> C = 243/225 (~133.24c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|13/12
|12/11 (~150.64c)
|180/169
|55/48 (~235.68c)
|1/1 13/12 15/13 5/4 8/5 26/15 24/13 2/1
|1/1 12/11 5/4 15/11 22/15 8/5 11/6 2/1
|225
|225
|-
|-
|17/16
|15/14 (~119.44c)
|320/289
|196/165 (~298.07c)
|1/1 17/16 20/17 5/4 8/5 17/10 32/17 2/1
|1/1 15/14 14/11 15/11 22/15 11/7 28/15 2/1
|289
|225
|-
|-
|20/19
|15/13 (~247.74c)
|361/320
|169/165 (~41.47c)
|1/1 20/19 19/16 5/4 8/5 32/19 40/19 2/1
|1/1 15/13 13/11 15/11 22/15 22/13 26/15 2/1
|361
|225
|-
|}
|25/24
 
|144/125
=== Tetrachord to 6/5 -> C = 25/18 (~568.72c) ===
|1/1 25/24 6/5 5/4 8/5 5/3 48/25 2/1
|625
|-
|11/10
|125/121
|1/1 11/10 25/22 5/4 8/5 44/25 20/11 2/1
|625
|-
|21/20
|500/441
|1/1 21/20 25/21 5/4 8/5 42/25 40/21 2/1
|625
|-
|25/23
|529/500
|1/1 25/23 23/20 5/4 8/5 40/23 46/25 2/1
|625
|}
 
=== Tetrachord to 9/7 -> C = 98/81 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 214: Line 236:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|9/8
|16/15 (~111.72c)
|64/63
|135/128 (~92.18c)
|1/1 9/8 8/7 9/7 14/9 7/4 16/9 2/1
|1/1 16/15 9/8 6/5 5/3 16/9 15/8 2/1
|225
|}
 
== 729-limit ABACABA scales with period 2/1, with steps > 20c ==
One scale under such constraints is a degenerate case, wherein A = C: the [[Pythagorean]] diatonic scale, where A = C = [[9/8]], and B = [[256/243]], with a rank-2 form ABABABA. This scale is well-formed, and (5, 2) SNS. Specifically it is SNS (2/1, 3/2)[7]. The most complex interval in this scale is the Pythagorean augmented fourth — [[729/512]] — and it's inversion, the Pythagorean diminished fifth — [[1024/729]]. Accordingly, the scale is 729-limit. 729 is chosen as the limit so that the list includes all ABACABA scales with complexity up to that of the Pythagorean diatonic scale (with steps > 20c). As [[step-nested scales]], all other ABACABA scales with period 2/1 can be best described as SNS (2/1, 2/T, A), or equivalently as SNS (2/1, T, A), where T = ABA, the outer interval of the tetrachord. For ABACABA scales, 729-odd-limit implies 23-limit, and a 27-odd limit for A.
 
=== Tetrachord to 4/3 -> C = 9/8 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|8/7
|49/48
|1/1 8/7 7/6 4/3 3/2 12/7 7/4 2/1
|49
|-
|10/9
|27/25
|1/1 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|81
|81
|-
|-
|15/14
|12/11
|28/25
|121/108
|1/1 15/14 6/5 9/7 14/9 5/3 28/15 2/1
|1/1 12/11 11/9 4/3 3/2 18/11 11/6 2/1  
|225
|121
|-
|18/17
|289/252
|1/1 18/17 17/14 9/7 14/9 28/27 36/17 2/1
|289
|-
|-
|22/21
|13/12
|567/484
|192/169
|1/1 22/21 27/22 9/7 14/9 44/27 21/11 2/1
|1/1 13/12 16/13 4/3 3/2 13/8 24/13 2/1
|729
|169
|-
|-
|27/26
|16/15
|676/567
|75/64
|1/1 27/26 26/21 9/7 14/9 21/13 52/27 2/1
|1/1 16/15 5/4 4/3 3/2 8/5 15/8 2/1
|729
|225
|-
|-
|23/21
|17/15
|567/529
|300/289
|1/1 23/21 27/23 9/7 14/9 46/27 42/23 2/1
|1/1 17/15 20/17 4/3 3/2 17/10 30/17 2/1
|729
|289
|-
|-
|27/25
|19/18
|625/567
|432/361
|1/1 27/25 25/21 9/7 14/9 42/25 50/27 2/1
|1/1 19/18 24/19 4/3 3/2 19/12 36/19 2/1
|729
|361
|}
 
=== Tetrachord to 11/8 -> C = 128/121 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|11/10
|20/19
|25/22
|361/300
|1/1 11/10 5/4 11/8 16/11 8/5 20/11 2/1
|1/1 20/19 19/15 4/3 3/2 30/19 19/10 2/1
|121
|-
|9/8
|88/81
|1/1 9/8 11/9 11/8 16/11 18/11 16/9 2/1
|121
|-
|17/16
|352/289
|1/1 17/16 22/17 11/8 16/11 17/11 32/17 2/1
|289
|-
|22/19
|361/352
|1/1 22/19 19/16 11/8 16/11 32/19 19/11 2/1
|361
|361
|-
|-
|22/21
|22/21
|441/352
|147/121
|1/1 22/21 21/16 11/8 16/11 32/21 21/11 2/1
|1/1 22/21 14/11 4/3 3/2 11/7 21/11 2/1  
|441
|-
|14/13
|169/147
|1/1 14/13 26/21 4/3 3/2 21/13 13/7 2/1  
|441
|441
|}
=== Tetrachord to 14/11 -> C = 121/98 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|12/11
|23/21
|77/72
|588/529
|1/1 12/11 7/6 14/11 11/7 12/7 11/6 2/1
|1/1 23/21 28/23 4/3 3/2 23/14 42/23 2/1
|121
|529
|-
|-
|14/13
|25/24
|169/154
|768/625
|1/1 14/13 13/11 14/11 11/7 22/13 13/7 2/1
|1/1 25/24 32/25 4/3 3/2 25/16 48/25 2/1
|169
|625
|-
|23/22
|616/529
|1/1 23/22 28/23 14/11 11/7 23/14 44/23 2/1
|529
|-
|-
|28/25
|28/25
|625/616
|625/588
|1/1 28/25 25/22 14/11 11/7 44/25 25/14 2/1
|1/1 28/25 25/21 4/3 3/2 42/25 25/14 2/1
|625
|625
|-
|9/8
|256/243
|1/1 9/8 32/27 4/3 3/2 27/16 16/9 2/1
|729
|-
|-
|28/27
|28/27
|729/616
|243/196
|1/1 28/27 27/22 14/11 11/7 44/27 56/27 2/1
|1/1 28/27 9/7 4/3 3/2 14/9 27/14 2/1  
|729
|-
|18/17
|289/243
|1/1 18/17 34/27 4/3 3/2 27/17 17/9 2/1
|729
|729
|}
|}


=== Tetrachord to 18/13 -> C = 169/162 ===
=== Tetrachord to 7/5 -> C = 50/49 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 326: Line 342:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|14/13
|7/6
|117/98
|36/35
|1/1 14/13 9/7 18/13 13/9 14/9 13/7 2/1
|1/1 7/6 6/5 7/5 10/7 5/3 12/7 2/1
|169
|49
|-
|-
|9/8
|11/10
|128/117
|140/121
|1/1 9/8 16/13 18/13 13/9 13/8 16/9 2/1
|1/1 11/10 14/11 7/5 10/7 11/7 20/11 2/1
|169
|121
|-
|-
|15/13
|14/13
|26/25
|169/140      
|1/1 15/13 6/5 18/13 13/9 5/3 26/15 2/1
|1/1 14/13 13/10 7/5 10/7 20/13 13/7 2/1
|225
|169          
|-
|-
|18/17
|21/20
|289/234
|80/63
|1/1 18/17 17/13 18/13 13/9 26/17 17/9 2/1
|1/1 21/20 4/3 7/5 10/7 3/2 40/21 2/1
|289
|441
|-
|-
|27/26
|16/15
|104/81
|315/256
|1/1 27/26 4/3 18/13 13/9 3/2 52/27 2/1
|1/1 16/15 21/16 7/5 10/7 32/21 15/8 2/1
|729
|441
|}
 
=== Tetrachord to 13/10 -> C = 200/169 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|13/12
|17/15
|72/65
|315/289
|1/1 13/12 6/5 13/10 20/13 5/3 24/13 2/1
|1/1 17/15 21/17 7/5 10/7 34/21 30/17 2/1
|169
|441
|-
|-
|11/10
|21/19
|130/121
|361/315
|1/1 11/10 13/11 13/10 20/13 22/13 20/11 2/1
|1/1 21/19 19/15 7/5 10/7 30/19 38/21 2/1
|169
|441
|-
|-
|21/20
|23/20
|520/441
|560/529
|1/1 21/20 26/21 13/10 20/13 21/13 40/21 2/1
|1/1 23/20 28/23 7/5 10/7 23/14 40/23 2/1
|441
|529
|-
|-
|26/25
|28/25
|125/104
|125/112
|1/1 26/25 5/4 13/10 20/13 8/5 25/13 2/1
|1/1 28/25 5/4 7/5 10/7 8/5 25/14 2/1
|625
|625
|-
|28/27
|729/560
|1/1 28/27 27/20 7/5 10/7 40/27 27/14 2/1
|729
|}
|}


=== Tetrachord to 16/13 -> C = 169/128 ===
=== Tetrachord to 5/4 -> C = 32/25 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 389: Line 401:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|14/13
|10/9
|52/49
|81/80
|1/1 14/13 8/7 16/13 13/8 7/4 13/7 2/1
|1/1 10/9 9/8 5/4 8/5 16/9 9/5 2/1
|169
|81
|-
|15/14
|49/45
|1/1 15/14 7/6 5/4 8/5 12/7 28/15 2/1
|225
|-
|-
|16/15
|13/12
|225/208
|180/169
|1/1 16/15 15/13 16/13 13/8 26/15 15/8 2/1
|1/1 13/12 15/13 5/4 8/5 26/15 24/13 2/1
|225
|225
|-
|-
|27/26
|17/16
|832/729
|320/289
|1/1 27/26 32/27 16/13 13/8 27/16 52/27 2/1
|1/1 17/16 20/17 5/4 8/5 17/10 32/17 2/1
|729
|289
|}
 
=== Tetrachord to 15/11 -> C = 243/225 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|12/11
|20/19
|55/48
|361/320
|1/1 12/11 5/4 15/11 22/15 8/5 11/6 2/1
|1/1 20/19 19/16 5/4 8/5 32/19 40/19 2/1
|225
|361
|-
|-
|15/14
|25/24
|196/165
|144/125
|1/1 15/14 14/11 15/11 22/15 11/7 28/15 2/1
|1/1 25/24 6/5 5/4 8/5 5/3 48/25 2/1
|225
|625
|-
|-
|15/13
|11/10
|169/165
|125/121
|1/1 15/13 13/11 15/11 22/15 22/13 26/15 2/1
|1/1 11/10 25/22 5/4 8/5 44/25 20/11 2/1
|225
|625
|-
|-
|23/22
|21/20
|660/529
|500/441
|1/1 23/22 30/23 15/11 22/15 23/15 44/23 2/1
|1/1 21/20 25/21 5/4 8/5 42/25 40/21 2/1
|529
|625
|-
|-
|25/22
|25/23
|132/125
|529/500
|1/1 25/22 6/5 15/11 22/15 5/3 44/25 2/1
|1/1 25/23 23/20 5/4 8/5 40/23 46/25 2/1
|625
|625
|}
|}


=== Tetrachord to 6/5 -> C = 25/18 ===
=== Tetrachord to 9/7 -> C = 98/81 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 447: Line 455:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|16/15
|9/8
|135/128
|64/63
|1/1 16/15 9/8 6/5 5/3 16/9 15/8 2/1
|1/1 9/8 8/7 9/7 14/9 7/4 16/9 2/1
|225
|81
|-
|15/14
|28/25
|1/1 15/14 6/5 9/7 14/9 5/3 28/15 2/1
|225
|-
|-
|18/17
|18/17
|289/270
|289/252
|1/1 18/17 17/15 6/5 5/3 30/17 17/9 2/1
|1/1 18/17 17/14 9/7 14/9 28/27 36/17 2/1
|289
|289
|-
|-
|21/20
|22/21
|160/147
|567/484
|1/1 21/20 8/7 6/5 5/3 7/4 40/21 2/1
|1/1 22/21 27/22 9/7 14/9 44/27 21/11 2/1
|441
|729
|-
|-
|24/23
|27/26
|529/480
|676/567
|1/1 24/25 23/20 6/5 5/3 40/23 48/25 2/1
|1/1 27/26 26/21 9/7 14/9 21/13 52/27 2/1
|529
|729
|-
|-
|15/14
|23/21
|392/375
|567/529
|1/1 15/14 28/25 6/5 5/3 25/14 28/15 2/1
|1/1 23/21 27/23 9/7 14/9 46/27 42/23 2/1
|625
|729
|-
|26/25
|373/338
|1/1 26/25 15/13 6/5 5/3 26/15 52/25 2/1
|625
|-
|-
|27/25
|27/25
|250/243
|625/567
|1/1 27/25 10/9 6/5 5/3 9/5 50/27 2/1
|1/1 27/25 25/21 9/7 14/9 42/25 50/27 2/1
|729
|729
|}
|}


=== Tetrachord to 17/13 -> C = 338/289 ===
=== Tetrachord to 11/8 -> C = 128/121 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 491: Line 499:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|17/16
|11/10
|256/221
|25/22
|1/1 17/16 16/13 17/13 26/17 13/8 32/17 2/1
|1/1 11/10 5/4 11/8 16/11 8/5 20/11 2/1
|289
|121
|-
|-
|14/13
|9/8
|221/196
|88/81
|1/1 14/13 17/14 17/13 26/17 28/17 13/7 2/1
|1/1 9/8 11/9 11/8 16/11 18/11 16/9 2/1
|121
|-
|17/16
|352/289
|1/1 17/16 22/17 11/8 16/11 17/11 32/17 2/1
|289
|289
|-
|-
|17/15
|22/19
|225/221
|361/352
|1/1 17/15 15/13 17/13 26/17 26/15 30/17 2/1
|1/1 22/19 19/16 11/8 16/11 32/19 19/11 2/1
|289
|361
|-
|-
|27/26
|22/21
|884/729
|441/352
|1/1 27/26 34/27 17/13 26/17 27/17 52/27 2/1
|1/1 22/21 21/16 11/8 16/11 32/21 21/11 2/1
|729
|441
|}
|}


=== Tetrachord to 22/17 -> C = 289/242 ===
=== Tetrachord to 14/11 -> C = 121/98 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 520: Line 533:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|18/17
|12/11
|187/162
|77/72
|1/1 18/17 11/9 22/17 17/11 18/11 17/9 2/1
|1/1 12/11 7/6 14/11 11/7 12/7 11/6 2/1
|289
|121
|-
|-
|11/10
|14/13
|200/187
|169/154
|1/1 11/10 20/17 22/17 17/11 17/10 20/11 2/1
|1/1 14/13 13/11 14/11 11/7 22/13 13/7 2/1
|289
|169
|-
|-
|19/17
|23/22
|374/361
|616/529
|1/1 19/17 22/19 22/17 17/11 19/11 34/19 2/1
|1/1 23/22 28/23 14/11 11/7 23/14 44/23 2/1
|361
|529
|-
|-
|22/21
|28/25
|441/374
|625/616
|1/1 22/21 21/17 22/17 17/11 34/21 21/11 2/1
|1/1 28/25 25/22 14/11 11/7 44/25 25/14 2/1
|441
|625
|-
|28/27
|729/616
|1/1 28/27 27/22 14/11 11/7 44/27 56/27 2/1
|729
|}
|}


=== Tetrachord to 17/14 -> C = 392/289 ===
=== Tetrachord to 18/13 -> C = 169/162 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 549: Line 567:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|17/16
|14/13
|117/98
|1/1 14/13 9/7 18/13 13/9 14/9 13/7 2/1
|169
|-
|9/8
|128/117
|128/117
|1/1 17/16 8/7 17/14 28/17 7/4 32/17 2/1
|1/1 9/8 16/13 18/13 13/9 13/8 16/9 2/1
|289
|169
|-
|-
|15/14
|15/13
|238/225
|26/25
|1/1 15/14 17/15 17/14 28/17 30/17 28/15 2/1
|1/1 15/13 6/5 18/13 13/9 5/3 26/15 2/1
|289
|225
|}
 
=== Tetrachord to 20/17 -> C = 289/200 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|18/17
|18/17
|85/81
|289/234
|1/1 18/17 10/9 20/17 17/10 9/5 17/9 2/1
|1/1 18/17 17/13 18/13 13/9 26/17 17/9 2/1
|289
|289
|-
|-
|20/19
|27/26
|361/340
|104/81
|1/1 20/19 19/17 20/17 17/10 34/19 19/10 2/1
|1/1 27/26 4/3 18/13 13/9 3/2 52/27 2/1
|361
|729
|}
|}


=== Tetrachord to 19/15 -> C = 540/361 ===
=== Tetrachord to 13/10 -> C = 200/169 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 587: Line 601:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|19/18
|13/12
|108/95
|72/65
|1/1 19/18 6/5 19/15 30/19 5/3 36/19 2/1
|1/1 13/12 6/5 13/10 20/13 5/3 24/13 2/1
|361
|169
|-
|11/10
|130/121
|1/1 11/10 13/11 13/10 20/13 22/13 20/11 2/1
|169
|-
|-
|16/15
|21/20
|285/256
|520/441
|1/1 16/15 19/16 19/15 30/19 32/19 15/8 2/1
|1/1 21/20 26/21 13/10 20/13 21/13 40/21 2/1
|361
|441
|-
|-
|19/17
|26/25
|289/285
|125/104
|1/1 19/17 17/15 19/15 30/19 30/17 34/19 2/1
|1/1 26/25 5/4 13/10 20/13 8/5 25/13 2/1
|361
|625
|}
|}


=== Tetrachord to 24/19 -> C = 361/288 ===
=== Tetrachord to 16/13 -> C = 169/128 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 611: Line 630:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|20/19
|14/13
|57/50
|52/49
|1/1 20/19 6/5 24/19 19/12 5/3 19/10 2/1
|1/1 14/13 8/7 16/13 13/8 7/4 13/7 2/1
|361
|169
|-
|-
|12/11
|16/15
|121/114
|225/208
|1/1 12/11 22/19 24/19 19/12 19/11 11/6 2/1
|1/1 16/15 15/13 16/13 13/8 26/15 15/8 2/1
|361
|225
|-
|-
|21/19
|27/26
|152/147
|832/729
|1/1 21/19 8/7 24/19 19/12 7/4 38/21 2/1
|1/1 27/26 32/27 16/13 13/8 27/16 52/27 2/1
|441
|729
|-
|24/23
|529/456
|1/1 24/23 23/19 24/19 19/12 38/23 23/12 2/1
|529
|}
|}


=== Tetrachord to 19/16 -> C = 512/361 ===
=== Tetrachord to 15/11 -> C = 243/225 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 640: Line 654:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|19/18
|12/11
|81/76
|55/48
|1/1 19/18 9/8 19/16 32/19 16/9 36/19 2/1
|1/1 12/11 5/4 15/11 22/15 8/5 11/6 2/1
|361
|225
|-
|15/14
|196/165
|1/1 15/14 14/11 15/11 22/15 11/7 28/15 2/1
|225
|-
|-
|17/16
|15/13
|304/289
|169/165
|1/1 17/16 19/17 19/16 32/19 34/19 32/17 2/1
|1/1 15/13 13/11 15/11 22/15 22/13 26/15 2/1
|361
|225
|-
|23/22
|660/529
|1/1 23/22 30/23 15/11 22/15 23/15 44/23 2/1
|529
|-
|25/22
|132/125
|1/1 25/22 6/5 15/11 22/15 5/3 44/25 2/1
|625
|}
|}


=== Tetrachord to 11/9 -> C = 162/121 ===
=== Tetrachord to 6/5 -> C = 25/18 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 659: Line 688:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|19/18
|16/15
|396/391
|135/128
|1/1 19/18 22/19 11/9 18/11 19/11 36/19 2/1
|1/1 16/15 9/8 6/5 5/3 16/9 15/8 2/1
|361
|225
|-
|-
|22/21
|18/17
|49/44
|289/270
|1/1 22/21 7/6 11/9 18/11 12/7 21/11 2/1
|1/1 18/17 17/15 6/5 5/3 30/17 17/9 2/1
|289
|-
|21/20
|160/147
|1/1 21/20 8/7 6/5 5/3 7/4 40/21 2/1
|441
|441
|}
=== Tetrachord to 22/19 -> C = 361/242 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|20/19
|24/23
|209/200
|529/480
|1/1 20/19 11/10 22/19 19/11 20/11 19/10 2/1
|1/1 24/25 23/20 6/5 5/3 40/23 48/25 2/1
|361
|529
|-
|-
|22/21
|15/14
|441/418
|392/375
|1/1 22/21 21/19 22/19 19/11 38/21 21/11 2/1
|1/1 15/14 28/25 6/5 5/3 25/14 28/15 2/1
|441
|625
|-
|26/25
|373/338
|1/1 26/25 15/13 6/5 5/3 26/15 52/25 2/1
|625
|-
|27/25
|250/243
|1/1 27/25 10/9 6/5 5/3 9/5 50/27 2/1
|729
|}
|}


=== Tetrachord to 21/16 -> C = 512/441 ===
=== Tetrachord to 17/13 -> C = 338/289 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 697: Line 732:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|9/8
|17/16
|28/27
|256/221
|1/1 9/8 7/6 21/16 32/21 12/7 16/9 2/1
|1/1 17/16 16/13 17/13 26/17 13/8 32/17 2/1
|441
|289
|-
|-
|21/20
|14/13
|25/21
|221/196
|1/1 21/20 5/4 21/16 32/21 8/5 40/21 2/1
|1/1 14/13 17/14 17/13 26/17 28/17 13/7 2/1
|441
|289
|-
|-
|17/16
|17/15
|336/289
|225/221
|1/1 17/16 21/17 21/16 32/21 34/21 32/17 2/1
|1/1 17/15 15/13 17/13 26/17 26/15 30/17 2/1
|441
|289
|-
|-
|21/19
|27/26
|361/336
|884/729
|1/1 21/19 19/16 21/16 32/21 32/19 38/21 2/1
|1/1 27/26 34/27 17/13 26/17 27/17 52/27 2/1
|441
|729
|}
|}


=== Tetrachord to 7/6 -> C = 72/49 ===
=== Tetrachord to 22/17 -> C = 289/242 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 726: Line 761:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|21/20
|18/17
|200/189
|187/162
|1/1 21/20 10/9 7/6 12/7 9/5 40/21 2/1
|1/1 18/17 11/9 22/17 17/11 18/11 17/9 2/1
|441
|289
|-
|-
|19/18
|11/10
|378/361
|200/187
|1/1 19/18 21/19 7/6 12/7 38/21 36/19 2/1
|1/1 11/10 20/17 22/17 17/11 17/10 20/11 2/1
|441
|289
|-
|-
|25/24
|19/17
|672/625
|374/361
|1/1 25/24 28/25 7/6 12/7 25/14 48/25 2/1
|1/1 19/17 22/19 22/17 17/11 19/11 34/19 2/1
|625
|361
|-
|-
|28/27
|22/21
|243/224
|441/374
|1/1 28/27 9/8 7/6 12/7 16/9 27/14 2/1
|1/1 22/21 21/17 22/17 17/11 34/21 21/11 2/1
|729
|441
|}
|}


=== Tetrachord to 26/21 -> C = 441/338 ===
=== Tetrachord to 17/14 -> C = 392/289 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 755: Line 790:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|13/12
|17/16
|96/91
|128/117
|1/1 13/12 8/7 26/21 21/13 7/4 24/13 2/1
|1/1 17/16 8/7 17/14 28/17 7/4 32/17 2/1
|441
|289
|-
|-
|22/21
|15/14
|273/242
|238/225
|1/1 22/21 13/11 26/21 21/13 22/13 21/11 2/1
|1/1 15/14 17/15 17/14 28/17 30/17 28/15 2/1
|441
|289
|-
|}
|23/21
 
|546/529
=== Tetrachord to 20/17 -> C = 289/200 ===
|1/1 23/21 26/23 26/21 21/13 23/13 42/23 2/1
|529
|-
|26/25
|625/546
|1/1 26/25 25/21 26/21 21/13 42/25 25/13 2/1
|625
|}
 
=== Tetrachord to 21/17 -> C = 578/451 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 785: Line 810:
|-
|-
|18/17
|18/17
|119/108
|85/81
|1/1 18/17 7/6 21/17 34/21 12/7 17/9 2/1
|1/1 18/17 10/9 20/17 17/10 9/5 17/9 2/1
|441
|289
|-
|-
|21/20
|20/19
|400/357
|361/340
|1/1 21/20 20/17 21/17 34/21 17/10 40/21 2/1
|1/1 20/19 19/17 20/17 17/10 34/19 19/10 2/1
|441
|361
|}
|}


=== Tetrachord to 8/7 -> C = 49/32 ===
=== Tetrachord to 19/15 -> C = 540/361 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 803: Line 828:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|22/21
|19/18
|126/121
|108/95
|1/1 22/21 12/11 8/7 7/4 11/6 21/11 2/1
|1/1 19/18 6/5 19/15 30/19 5/3 36/19 2/1
|441
|361
|-
|16/15
|285/256
|1/1 16/15 19/16 19/15 30/19 32/19 15/8 2/1
|361
|-
|-
|24/23
|19/17
|529/504
|289/285
|1/1 24/23 23/21 8/7 7/4 42/23 23/12 2/1
|1/1 19/17 17/15 19/15 30/19 30/17 34/19 2/1
|529
|361
|}
|}


=== Tetrachord to 32/23 -> C = 529/512 ===
=== Tetrachord to 24/19 -> C = 361/288 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 822: Line 852:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|24/23
|20/19
|23/18
|57/50
|1/1 24/23 4/3 32/23 23/16 3/2 23/12 2/1
|1/1 20/19 6/5 24/19 19/12 5/3 19/10 2/1
|529
|361
|-
|-
|8/7
|12/11
|49/46
|121/114
|1/1 8/7 28/23 32/23 23/16 23/14 7/4 2/1
|1/1 12/11 22/19 24/19 19/12 19/11 11/6 2/1
|529
|361
|-
|-
|26/23
|21/19
|184/169
|152/147
|1/1 26/23 16/13 32/23 23/16 13/8 23/13 2/1
|1/1 21/19 8/7 24/19 19/12 7/4 38/21 2/1
|529
|441
|-
|-
|16/15
|24/23
|225/184
|529/456
|1/1 16/15 30/23 32/23 23/16 23/15 15/8 2/1
|1/1 24/23 23/19 24/19 19/12 38/23 23/12 2/1
|529
|529
|}
=== Tetrachord to 19/16 -> C = 512/361 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|19/18
|81/76
|1/1 19/18 9/8 19/16 32/19 16/9 36/19 2/1
|361
|-
|-
|25/23
|17/16
|736/625
|304/289
|1/1 25/23 32/25 32/23 23/16 50/32 46/25 2/1
|1/1 17/16 19/17 19/16 32/19 34/19 32/17 2/1
|625
|361
|-
|27/23
|736/729
|1/1 27/23 32/27 32/23 23/16 27/16 46/27 2/1
|729
|}
|}


=== Tetrachord to 30/23 -> C = 529/540 ===
=== Tetrachord to 11/9 -> C = 162/121 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 861: Line 900:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|24/23
|19/18
|115/96
|396/391
|1/1 24/23 5/4 30/23 23/15 8/5 23/12 2/1
|1/1 19/18 22/19 11/9 18/11 19/11 36/19 2/1
|529
|361
|-
|-
|25/23
|22/21
|138/125
|49/44
|1/1 25/23 6/5 30/23 23/15 5/3 46/25 2/1
|1/1 22/21 7/6 11/9 18/11 12/7 21/11 2/1
|529
|441
|}
 
=== Tetrachord to 22/19 -> C = 361/242 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|26/23
|20/19
|345/338
|209/200
|1/1 26/23 15/13 30/23 23/15 26/15 23/13 2/1
|1/1 20/19 11/10 22/19 19/11 20/11 19/10 2/1
|529
|361
|-
|-
|15/14
|22/21
|392/345
|441/418
|1/1 15/14 28/23 30/23 23/15 23/14 28/15 2/1
|1/1 22/21 21/19 22/19 19/11 38/21 21/11 2/1
|529
|441
|-
|10/9
|243/230
|1/1 10/9 27/23 30/23 23/15 46/27 9/5 2/1
|729
|}
|}


=== Tetrachord to 23/18 -> C = 648/529 ===
=== Tetrachord to 21/16 -> C = 512/441 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 895: Line 938:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|10/9
|9/8
|207/200
|28/27
|1/1 10/9 23/20 23/18 36/23 40/23 9/5 2/1
|1/1 9/8 7/6 21/16 32/21 12/7 16/9 2/1
|529
|441
|-
|-
|23/22
|21/20
|242/207
|25/21
|1/1 23/22 11/9 23/18 36/23 18/11 44/23 2/1
|1/1 21/20 5/4 21/16 32/21 8/5 40/21 2/1
|529
|441
|-
|-
|19/18
|17/16
|414/361
|336/289
|1/1 19/18 23/19 23/18 36/23 38/23 36/19 2/1
|1/1 17/16 21/17 21/16 32/21 34/21 32/17 2/1
|529
|441
|-
|-
|23/21
|21/19
|49/46
|361/336
|1/1 23/21 7/6 23/18 36/23 12/7 42/23 2/1
|1/1 21/19 19/16 21/16 32/21 32/19 38/21 2/1
|529
|441
|}
|}


=== Tetrachord to 28/23 -> C = 529/392 ===
=== Tetrachord to 7/6 -> C = 72/49 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 924: Line 967:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|24/23
|21/20
|161/144
|200/189
|1/1 24/23 7/6 28/23 23/14 12/7 23/12 2/1
|1/1 21/20 10/9 7/6 12/7 9/5 40/21 2/1
|529
|441
|-
|-
|14/13
|19/18
|169/161
|378/361
|1/1 14/13 26/23 28/23 23/14 23/13 13/7 2/1
|1/1 19/18 21/19 7/6 12/7 38/21 36/19 2/1
|529
|441
|-
|-
|25/23
|25/24
|644/625
|672/625
|1/1 25/23 28/25 28/23 23/14 25/14 46/25 2/1
|1/1 25/24 28/25 7/6 12/7 25/14 48/25 2/1
|625
|625
|-
|-
|28/27
|28/27
|729/644
|243/224
|1/1 28/27 27/23 28/23 23/14 46/27 27/15 2/1
|1/1 28/27 9/8 7/6 12/7 16/9 27/14 2/1
|729
|729
|}
|}


=== Tetrachord to 5/4 -> C = 32/25 ===
=== Tetrachord to 26/21 -> C = 441/338 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 953: Line 996:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|23/22
|13/12
|121/115
|96/91
|1/1 23/22 11/10 23/20 40/23 20/11 44/23 2/1
|1/1 13/12 8/7 26/21 21/13 7/4 24/13 2/1
|441
|-
|22/21
|273/242
|1/1 22/21 13/11 26/21 21/13 22/13 21/11 2/1
|441
|-
|23/21
|546/529
|1/1 23/21 26/23 26/21 21/13 23/13 42/23 2/1
|529
|529
|-
|-
|21/20
|26/25
|460/441
|625/546
|1/1 21/20 23/21 23/20 40/23 42/23 40/21 2/1
|1/1 26/25 25/21 26/21 21/13 42/25 25/13 2/1
|529
|625
|}
|}


=== Tetrachord to 23/19 -> C = 722/529 ===
=== Tetrachord to 21/17 -> C = 578/451 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 972: Line 1,025:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|20/19
|18/17
|437/400
|119/108
|1/1 20/19 23/20 23/19 38/23 40/23 19/10 2/1
|1/1 18/17 7/6 21/17 34/21 12/7 17/9 2/1
|529
|441
|-
|-
|23/22
|21/20
|484/437
|400/357
|1/1 23/22 22/19 23/19 38/23 19/11 44/23 2/1
|1/1 21/20 20/17 21/17 34/21 17/10 40/21 2/1
|529
|441
|}
|}


=== Tetrachord to 13/11 -> C = 242/169 ===
=== Tetrachord to 8/7 -> C = 49/32 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 991: Line 1,044:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|23/22
|22/21
|572/529
|126/121
|1/1 23/22 26/23 13/11 22/13 23/13 44/23 2/1
|1/1 22/21 12/11 8/7 7/4 11/6 21/11 2/1
|529
|441
|-
|-
|26/25
|24/23
|625/572
|529/504
|1/1 26/25 25/22 13/11 22/13 44/25 25/13 2/1
|1/1 24/23 23/21 8/7 7/4 42/23 23/12 2/1
|625
|529
|}
|}


=== Tetrachord to 26/23 -> C = 529/338 ===
=== Tetrachord to 32/23 -> C = 529/512 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,011: Line 1,064:
|-
|-
|24/23
|24/23
|299/288
|23/18
|1/1 24/23 13/12 26/23 23/13 24/13 23/12 2/1
|1/1 24/23 4/3 32/23 23/16 3/2 23/12 2/1
|529
|-
|8/7
|49/46
|1/1 8/7 28/23 32/23 23/16 23/14 7/4 2/1
|529
|529
|-
|-
|26/25
|26/23
|625/598
|184/169
|1/1 26/25 25/23 26/23 23/13 46/25 25/13 2/1
|1/1 26/23 16/13 32/23 23/16 13/8 23/13 2/1
|625
|529
|}
|-
 
|16/15
=== Tetrachord to 25/18 -> C = 648/625 ===
|225/184
|1/1 16/15 30/23 32/23 23/16 23/15 15/8 2/1
|529
|-
|25/23
|736/625
|1/1 25/23 32/25 32/23 23/16 50/32 46/25 2/1
|625
|-
|27/23
|736/729
|1/1 27/23 32/27 32/23 23/16 27/16 46/27 2/1
|729
|}
 
=== Tetrachord to 30/23 -> C = 529/540 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,029: Line 1,102:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|10/9
|24/23
|9/8
|115/96
|1/1 10/9 5/4 25/18 36/25 8/5 9/5 2/1
|1/1 24/23 5/4 30/23 23/15 8/5 23/12 2/1
|625
|529
|-
|-
|25/24
|25/23
|32/25
|138/125
|1/1 25/24 4/3 25/18 36/25 3/2 48/25 2/1
|1/1 25/23 6/5 30/23 23/15 5/3 46/25 2/1
|625
|529
|-
|-
|7/6
|26/23
|50/49
|345/338
|1/1 7/6 25/21 25/18 32/25 42/25 12/7 2/1
|1/1 26/23 15/13 30/23 23/15 26/15 23/13 2/1
|625
|529
|-
|-
|25/22
|15/14
|242/225
|392/345
|1/1 25/22 11/9 25/18 36/25 18/11 44/25 2/1
|1/1 15/14 28/23 30/23 23/15 23/14 28/15 2/1
|625
|529
|-
|-
|19/18
|10/9
|450/361
|243/230
|1/1 19/18 25/19 25/18 36/25 38/25 36/19 2/1
|1/1 10/9 27/23 30/23 23/15 46/27 9/5 2/1
|625
|729
|-
|25/23
|529/450
|1/1 25/23 23/18 25/18 36/25 36/23 46/25 2/1
|625
|}
|}


=== Tetrachord to 25/19 -> C = 722/625 ===
=== Tetrachord to 23/18 -> C = 648/529 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,068: Line 1,136:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|20/19
|10/9
|19/16
|207/200
|1/1 20/19 5/4 25/19 38/25 8/5 19/10 2/1
|1/1 10/9 23/20 23/18 36/23 40/23 9/5 2/1
|625
|529
|-
|-
|21/19
|23/22
|475/441
|242/207
|1/1 21/19 25/21 25/19 38/25 42/25 38/21 2/1
|1/1 23/22 11/9 23/18 36/23 18/11 44/23 2/1
|625
|529
|-
|-
|25/24
|19/18
|567/475
|414/361
|1/1 25/24 24/19 25/19 38/25 19/12 48/25 2/1
|1/1 19/18 23/19 23/18 36/23 38/23 36/19 2/1
|625
|529
|-
|-
|25/22
|23/21
|484/475
|49/46
|1/1 25/22 22/19 25/19 38/25 19/11 44/25 2/1
|1/1 23/21 7/6 23/18 36/23 12/7 42/23 2/1
|625
|529
|-
|25/23
|529/475
|1/1 25/23 23/19 25/19 38/25 38/23 46/25 2/1
|625
|}
|}


=== Tetrachord to 34/25 -> C = 625/578 ===
=== Tetrachord to 28/23 -> C = 529/392 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,102: Line 1,165:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|17/15
|24/23
|18/17
|161/144
|1/1 17/15 6/5 34/25 25/17 5/3 30/17 2/1
|1/1 24/23 7/6 28/23 23/14 12/7 23/12 2/1
|625
|529
|-
|-
|17/16
|14/13
|512/425
|169/161
|1/1 17/16 32/25 34/25 25/17 25/16 32/17 2/1
|1/1 14/13 26/23 28/23 23/14 23/13 13/7 2/1
|625
|529
|-
|-
|28/25
|25/23
|425/392
|644/625
|1/1 28/25 17/14 34/25 25/17 28/17 25/14 2/1
|1/1 25/23 28/25 28/23 23/14 25/14 46/25 2/1
|625
|625
|-
|-
|26/25
|28/27
|425/338
|729/644
|1/1 26/25 17/13 34/25 25/17 26/17 25/13 2/1
|1/1 28/27 27/23 28/23 23/14 46/27 27/15 2/1
|625
|-
|27/25
|850/729
|1/1 27/25 34/27 34/25 25/17 27/17 50/27 2/1
|729
|729
|}
|}


=== Tetrachord to 32/25 -> C = 32/25 ===
=== Tetrachord to 23/20 -> C = 800/529 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,136: Line 1,194:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|16/15
|23/22
|9/8
|121/115
|1/1 16/15 6/5 32/25 25/16 5/3 15/8 2/1
|1/1 23/22 11/10 23/20 40/23 20/11 44/23 2/1
|625
|529
|-
|-
|28/25
|21/20
|50/49
|460/441
|1/1 28/25 8/7 32/25 25/16 7/4 25/14 2/1
|1/1 21/20 23/21 23/20 40/23 42/23 40/21 2/1
|625
|529
|-
|}
|26/25
 
|200/169
=== Tetrachord to 23/19 -> C = 722/529 ===
|1/1 26/25 16/13 32/25 25/16 13/8 25/13 2/1
{| class="wikitable"
|625
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|20/19
|437/400
|1/1 20/19 23/20 23/19 38/23 40/23 19/10 2/1
|529
|-
|-
|27/25
|23/22
|800/729
|484/437
|1/1 27/25 32/27 32/25 25/16 27/16 50/27 2/1
|1/1 23/22 22/19 23/19 38/23 19/11 44/23 2/1
|729
|529
|}
|}


=== Tetrachord to 25/21 -> C = 882/625 ===
=== Tetrachord to 13/11 -> C = 242/169 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,165: Line 1,232:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|25/24
|23/22
|192/175
|572/529
|1/1 25/24 8/7 25/21 42/25 7/4 48/25 2/1
|1/1 23/22 26/23 13/11 22/13 23/13 44/23 2/1
|625
|529
|-
|-
|22/21
|26/25
|525/484
|625/572
|1/1 22/21 25/22 25/21 42/25 44/25 21/11 2/1
|1/1 26/25 25/22 13/11 22/13 44/25 25/13 2/1
|625
|625
|}
|}


=== Tetrachord to 25/22 -> C = 968/625 ===
=== Tetrachord to 26/23 -> C = 529/338 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,184: Line 1,251:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|25/24
|24/23
|288/275
|299/288
|1/1 25/24 12/11 25/22 44/25 11/6 48/25 2/1
|1/1 24/23 13/12 26/23 23/13 24/13 23/12 2/1
|625
|529
|-
|-
|23/22
|26/25
|550/529
|625/598
|1/1 23/22 25/23 25/22 44/24 46/25 44/23 2/1
|1/1 26/25 25/23 26/23 23/13 46/25 25/13 2/1
|625
|625
|}
|}


=== Tetrachord to 28/25 -> C = 625/392 ===
=== Tetrachord to 25/18 -> C = 648/625 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,203: Line 1,270:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|26/25
|10/9
|175/169
|9/8
|1/1 26/25 14/13 28/25 25/14 13/7 52/25 2/1
|1/1 10/9 5/4 25/18 36/25 8/5 9/5 2/1
|625
|625
|-
|-
|28/27
|25/24
|729/700
|32/25
|1/1 28/27 27/25 28/25 25/14 50/27 27/14 2/1
|1/1 25/24 4/3 25/18 36/25 3/2 48/25 2/1
|729
|625
|}
 
=== Tetrachord to 27/20 -> C = 800/729 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|9/8
|7/6
|16/15
|50/49
|1/1 9/8 6/5 27/20 40/27 5/3 16/9 2/1
|1/1 7/6 25/21 25/18 32/25 42/25 12/7 2/1
|729
|625
|-
|-
|21/20
|25/22
|60/49
|242/225
|1/1 21/20 9/7 27/20 40/27 14/9 40/21 2/1
|1/1 25/22 11/9 25/18 36/25 18/11 44/25 2/1
|729
|625
|-
|-
|27/25
|19/18
|125/108
|450/361
|1/1 27/25 5/4 27/20 40/27 8/5 50/27 2/1
|1/1 19/18 25/19 25/18 36/25 38/25 36/19 2/1
|729
|625
|-
|-
|11/10
|25/23
|135/121
|529/450
|1/1 11/10 27/22 27/20 40/27 44/27 20/11 2/1
|1/1 25/23 23/18 25/18 36/25 36/23 46/25 2/1
|729
|625
|-
|27/26
|169/135
|1/1 27/26 13/10 27/20 40/27 20/13 52/27 2/1
|729
|-
|23/20
|540/529
|1/1 23/20 27/23 27/20 40/27 46/27 40/23 2/1
|729
|}
|}


=== Tetrachord to 27/22 -> C = 968/729 ===
=== Tetrachord to 25/19 -> C = 722/625 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,261: Line 1,309:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|12/11
|20/19
|33/32
|19/16
|1/1 12/11 9/8 27/22 44/27 16/9 11/6 2/1
|1/1 20/19 5/4 25/19 38/25 8/5 19/10 2/1
|729
|625
|-
|-
|27/26
|21/19
|338/297
|475/441
|1/1 27/26 13/11 27/22 44/27 22/13 52/27 2/1
|1/1 21/19 25/21 25/19 38/25 42/25 38/21 2/1
|729
|625
|-
|25/24
|567/475
|1/1 25/24 24/19 25/19 38/25 19/12 48/25 2/1
|625
|-
|-
|27/25
|25/22
|625/594
|484/475
|1/1 27/25 25/22 27/22 44/27 44/25 50/27 2/1
|1/1 25/22 22/19 25/19 38/25 19/11 44/25 2/1
|729
|625
|-
|-
|23/22
|25/23
|594/529
|529/475
|1/1 23/22 27/23 27/22 44/27 46/27 44/23 2/1
|1/1 25/23 23/19 25/19 38/25 38/23 46/25 2/1
|729
|625
|}
|}


=== Tetrachord to 34/27 -> C = 729/578 ===
=== Tetrachord to 34/25 -> C = 625/578 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,290: Line 1,343:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|10/9
|17/15
|51/50
|18/17
|1/1 10/9 17/15 34/27 27/17 30/17 9/5 2/1
|1/1 17/15 6/5 34/25 25/17 5/3 30/17 2/1
|729
|625
|-
|28/27
|459/392
|1/1 28/27 17/14 34/27 27/17 28/17 27/14 2/1
|729
|-
|-
|17/16
|17/16
|512/459
|512/425
|1/1 17/16 32/27 34/27 27/17 27/16 32/17 2/1
|1/1 17/16 32/25 34/25 25/17 25/16 32/17 2/1
|729
|625
|}
 
=== Tetrachord to 32/27 -> C = 729/512 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|-
|16/15
|28/25
|25/24
|425/392
|1/1 16/15 10/9 32/27 27/16 9/5 15/8 2/1
|1/1 28/25 17/14 34/25 25/17 28/17 25/14 2/1
|729
|625
|-
|26/25
|425/338
|1/1 26/25 17/13 34/25 25/17 26/17 25/13 2/1
|625
|-
|-
|28/27
|27/25
|54/49
|850/729
|1/1 28/27 8/7 32/27 27/16 7/4 27/14 2/1
|1/1 27/25 34/27 34/25 25/17 27/17 50/27 2/1
|729
|729
|}
|}


=== Tetrachord to 9/8 -> C = 128/81 ===
=== Tetrachord to 32/25 -> C = 32/25 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,333: Line 1,377:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|25/24
|16/15
|648/625
|9/8
|1/1 25/24 27/25 9/8 16/9 50/27 48/25 2/1
|1/1 16/15 6/5 32/25 25/16 5/3 15/8 2/1
|729
|625
|-
|28/25
|50/49
|1/1 28/25 8/7 32/25 25/16 7/4 25/14 2/1
|625
|-
|26/25
|200/169
|1/1 26/25 16/13 32/25 25/16 13/8 25/13 2/1
|625
|-
|-
|27/26
|27/25
|169/162
|800/729
|1/1 27/26 13/12 9/8 16/9 24/13 52/27 2/1
|1/1 27/25 32/27 32/25 25/16 27/16 50/27 2/1
|729
|729
|}
|}


=== Tetrachord to 27/23 -> C = 1058/729 ===
=== Tetrachord to 25/21 -> C = 882/625 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,352: Line 1,406:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|24/23
|25/24
|69/64
|192/175
|1/1 24/23 9/8 27/23 46/27 16/9 23/12 2/1
|1/1 25/24 8/7 25/21 42/25 7/4 48/25 2/1
|729
|625
|-
|-
|27/26
|22/21
|676/621
|525/484
|1/1 27/26 26/23 27/23 46/27 23/13 52/27 2/1
|1/1 22/21 25/22 25/21 42/25 44/25 21/11 2/1
|729
|625
|}
|}


=== Tetrachord to 15/13 -> C = 338/225 ===
=== Tetrachord to 25/22 -> C = 968/625 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,371: Line 1,425:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|27/26
|25/24
|260/243
|288/275
|1/1 27/26 10/9 15/13 26/15 9/5 52/27 2/1
|1/1 25/24 12/11 25/22 44/25 11/6 48/25 2/1
|729
|625
|-
|23/22
|550/529
|1/1 23/22 25/23 25/22 44/25 46/25 44/23 2/1
|625
|}
|}


=== Tetrachord to 10/9 -> C = 81/50 ===
=== Tetrachord to 28/25 -> C = 625/392 ===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,385: Line 1,444:
!odd-limit of scale intervals
!odd-limit of scale intervals
|-
|-
|28/27
|26/25
|405/392
|175/169
|1/1 28/27 15/14 10/9 9/5 28/15 27/14 2/1
|1/1 26/25 14/13 28/25 25/14 13/7 52/25 2/1
|625
|-
|28/27
|729/700
|1/1 28/27 27/25 28/25 25/14 50/27 27/14 2/1
|729
|}
 
=== Tetrachord to 27/20 -> C = 800/729 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|9/8
|16/15
|1/1 9/8 6/5 27/20 40/27 5/3 16/9 2/1
|729
|729
|-
|21/20
|60/49
|1/1 21/20 9/7 27/20 40/27 14/9 40/21 2/1
|729
|-
|27/25
|125/108
|1/1 27/25 5/4 27/20 40/27 8/5 50/27 2/1
|729
|-
|11/10
|135/121
|1/1 11/10 27/22 27/20 40/27 44/27 20/11 2/1
|729
|-
|27/26
|169/135
|1/1 27/26 13/10 27/20 40/27 20/13 52/27 2/1
|729
|-
|23/20
|540/529
|1/1 23/20 27/23 27/20 40/27 46/27 40/23 2/1
|729
|}
=== Tetrachord to 27/22 -> C = 968/729 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|12/11
|33/32
|1/1 12/11 9/8 27/22 44/27 16/9 11/6 2/1
|729
|-
|27/26
|338/297
|1/1 27/26 13/11 27/22 44/27 22/13 52/27 2/1
|729
|-
|27/25
|625/594
|1/1 27/25 25/22 27/22 44/27 44/25 50/27 2/1
|729
|-
|23/22
|594/529
|1/1 23/22 27/23 27/22 44/27 46/27 44/23 2/1
|729
|}
=== Tetrachord to 34/27 -> C = 729/578 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|10/9
|51/50
|1/1 10/9 17/15 34/27 27/17 30/17 9/5 2/1
|729
|-
|28/27
|459/392
|1/1 28/27 17/14 34/27 27/17 28/17 27/14 2/1
|729
|-
|17/16
|512/459
|1/1 17/16 32/27 34/27 27/17 27/16 32/17 2/1
|729
|}
=== Tetrachord to 32/27 -> C = 729/512 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|16/15
|25/24
|1/1 16/15 10/9 32/27 27/16 9/5 15/8 2/1
|729
|-
|28/27
|54/49
|1/1 28/27 8/7 32/27 27/16 7/4 27/14 2/1
|729
|}
=== Tetrachord to 9/8 -> C = 128/81 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|25/24
|648/625
|1/1 25/24 27/25 9/8 16/9 50/27 48/25 2/1
|729
|-
|27/26
|169/162
|1/1 27/26 13/12 9/8 16/9 24/13 52/27 2/1
|729
|}
=== Tetrachord to 27/23 -> C = 1058/729 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|24/23
|69/64
|1/1 24/23 9/8 27/23 46/27 16/9 23/12 2/1
|729
|-
|27/26
|676/621
|1/1 27/26 26/23 27/23 46/27 23/13 52/27 2/1
|729
|}
=== Tetrachord to 15/13 -> C = 338/225 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|27/26
|260/243
|1/1 27/26 10/9 15/13 26/15 9/5 52/27 2/1
|729
|}
=== Tetrachord to 10/9 -> C = 81/50 ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|28/27
|405/392
|1/1 28/27 15/14 10/9 9/5 28/15 27/14 2/1
|729
|}
== 729-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.
=== Tetrachord to 9/8 -> C = 32/27 (~294.13c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|21/20 (~84.47c)
|50/49 (~34.98c)
|1/1 21/20 15/14 9/8 4/3 7/5 10/7 2/1
|147
|-
|27/26 (~65.34c)
|169/162 (~73.24c)
|1/1 27/26 13/12 9/8 4/3 18/13 13/9 3/2
|243
|-
|25/24 (~70.67c)
|648/625 (~62.57c)
|1/1 25/24 27/25 9/8 4/3 25/18 36/25 3/2
|625
|}
=== Tetrachord to 17/14 -> C = 294/289 (~29.70c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|17/16 (~104.96c)
|128/117 (~115.56c)
|1/1 17/16 8/7 17/14 28/17 21/16 24/17 3/2
|357
|-
|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
|}
=== Tetrachord to 7/6 -> C = 54/49 (~168.21c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|19/18 (~93.60c)
|378/361 (~79.65c)
|1/1 19/18 21/19 7/6 9/7 19/14 27/19 3/2
|361
|-
|21/20 (~84.47c)
|200/189 (~97.94c)
|1/1 21/20 10/9 7/6 9/7 27/20 10/7 3/2
|567
|}
=== Tetrachord to 19/16 -> C = 384/361 (~106.93c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|19/18 (~93.60c)
|81/76 (~110.31c)
|1/1 19/18 9/8 19/16 24/19 4/3 27/19 3/2
|361
|}
=== 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
|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
|-
|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
|}
=== Tetrachord to 27/23 -> C = 529/486 (~146.77c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|24/23 (~73.68c)
|69/64 (~130.23c)
|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
|}
=== Tetrachord to 25/22 -> C = 726/625 (~259.34c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|25/24 (~70.67c)
|288/275 (~79.96c)
|1/1 25/24 12/11 25/22 33/25 11/8 36/25 3/2
|625
|}
=== Tetrachord to 10/9 -> C = 243/200 (~337.15c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|25/24 (~70.67c)
|128/125 (~41.06c)
|1/1 25/24 16/15 10/9 27/20 45/32 36/25 3/2
|675
|}
=== Tetrachord to 15/13 -> C = 169/150 (~206.47c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|27/26 (~65.34c)
|260/243 (~117.07c)
|1/1 27/26 10/9 15/13 39/30 27/20 13/9 3/2
|729
|}
== 729-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
|189
|-
|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 10/9 -> C = 27/25 (~133.24c) ===
{| class="wikitable"
|+
!A
!B
!Scale
!odd-limit of scale intervals
|-
|25/24 (~70.67c)
|128/125 (~41.06c)
|1/1 25/24 16/15 10/9 6/5 5/4 32/25 4/3
|625
|}
=== 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
|}
|}


{{Navbox scale gallery}}
[[Category: Just intonation scales]]
[[Category: Just intonation scales]]
[[Category: Step-nested scales]]
[[Category: Step-nested scales]]
[[Category:Wakalixes]]
[[Category:Lists of scales]]
Retrieved from "https://en.xen.wiki/w/ABACABA_JI_scales"