User:Tristanbay/Gallery of just intonation scales: Difference between revisions

From Xenharmonic Reference
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Created gallery of JI scales (expanded from my user page)
 
Formatting and named a scale
Line 319: Line 319:
== 14-note scales ==
== 14-note scales ==
'''No-13s ultrajust'''
'''No-13s ultrajust'''
17/16
17/16
9/8
9/8
19/16
19/16
5/4
5/4
21/16
21/16
11/8
11/8
23/16
23/16
3/2
3/2
19/12
19/12
5/3
5/3
7/4
7/4
11/6
11/6
23/12
23/12
2/1
2/1


== 17-note scales ==
== 17-note scales ==
'''Walkie'''
'''Walkie'''
65/64
65/64
13/12
13/12
9/8
9/8
585/512
585/512
39/32
39/32
5/4
5/4
4/3
4/3
65/48
65/48
45/32
45/32
3/2
3/2
195/128
195/128
13/8
13/8
5/3
5/3
16/9
16/9
117/64
117/64
15/8
15/8
2/1
2/1
 
'''Mohahadene'''
'''Mohahadene'''
55/54
55/54
88/81
88/81
9/8
9/8
55/48
55/48
11/9
11/9
5/4
5/4
4/3
4/3
11/8
11/8
45/32
45/32
3/2
3/2
55/36
55/36
44/27
44/27
5/3
5/3
55/32
55/32
11/6
11/6
15/8
15/8
2/1
2/1
 
'''Dichotidene'''
'''Dichotidene'''
28/27
28/27
35/32
35/32
9/8
9/8
7/6
7/6
5/4
5/4
35/27
35/27
4/3
4/3
45/32
45/32
35/24
35/24
3/2
3/2
14/9
14/9
105/64
105/64
27/16
27/16
7/4
7/4
15/8
15/8
35/18
35/18
2/1
2/1
 
'''Just Spoogalaxy'''
'''Just Spoogalaxy'''
28/27
28/27
29/27
29/27
9/8
9/8
7/6
7/6
29/24
29/24
81/64
81/64
21/16
21/16
87/64
87/64
116/81
116/81
3/2
3/2
14/9
14/9
29/18
29/18
27/16
27/16
7/4
7/4
29/16
29/16
243/128
243/128
2/1
2/1
 
'''Cartwheel'''
'''Cartwheel'''
28/27
28/27
13/12
13/12
9/8
9/8
7/6
7/6
11/9
11/9
5/4
5/4
4/3
4/3
11/8
11/8
13/9
13/9
3/2
3/2
14/9
14/9
13/8
13/8
5/3
5/3
7/4
7/4
11/6
11/6
15/8
15/8
2/1
2/1
 
'''Ringer 17-quad'''
'''Ringer 17-quad'''
33/32
33/32
17/16
17/16
9/8
9/8
19/16
19/16
77/64
77/64
5/4
5/4
21/16
21/16
11/8
11/8
23/16
23/16
3/2
3/2
49/32
49/32
25/16
25/16
13/8
13/8
7/4
7/4
29/16
29/16
15/8
15/8
2/1
2/1
 
'''Ringer 17-tri'''
'''Ringer 17-tri'''
49/48
49/48
17/16
17/16
9/8
9/8
19/16
19/16
29/24
29/24
5/4
5/4
21/16
21/16
11/8
11/8
23/16
23/16
3/2
3/2
74/48
74/48
25/16
25/16
13/8
13/8
7/4
7/4
11/6
11/6
15/8
15/8
2/1
2/1
 
'''Schismadene'''
'''Schismadene'''
135/128
135/128
10/9
10/9
9/8
9/8
32/27
32/27
5/4
5/4
81/64
81/64
4/3
4/3
45/32
45/32
40/27
40/27
3/2
3/2
128/81
128/81
5/3
5/3
27/16
27/16
16/9
16/9
15/8
15/8
160/81
160/81
2/1
2/1
 
'''Traditional Baglama Fret Scale'''
'''Traditional Baglama Fret Scale'''
18/17
18/17
12/11
12/11
9/8
9/8
81/68
81/68
27/22
27/22
81/64
81/64
4/3
4/3
24/17
24/17
16/11
16/11
3/2
3/2
27/17
27/17
18/11
18/11
27/16
27/16
16/9
16/9
32/17
32/17
64/33
64/33
2/1
2/1
 
'''23-limit Pseudoringer'''
'''23-limit Pseudoringer'''
33/32
33/32
13/12
13/12
9/8
9/8
7/6
7/6
39/32
39/32
5/4
5/4
4/3
4/3
11/8
11/8
17/12
17/12
3/2
3/2
19/12
19/12
13/8
13/8
5/3
5/3
7/4
7/4
11/6
11/6
23/12
23/12
2/1
2/1
 
'''Zothogothic'''
'''Zothogothic'''
28/27
28/27
13/12
13/12
9/8
9/8
7/6
7/6
39/32
39/32
91/72
91/72
4/3
4/3
112/81
112/81
13/9
13/9
3/2
3/2
14/9
14/9
13/8
13/8
91/54
91/54
7/4
7/4
117/64
117/64
91/48
91/48
2/1
2/1
 
'''Zolugothic'''
'''Zolugothic'''
28/27
28/27
12/11
12/11
9/8
9/8
7/6
7/6
27/22
27/22
14/11
14/11
4/3
4/3
112/81
112/81
16/11
16/11
3/2
3/2
14/9
14/9
18/11
18/11
56/33
56/33
7/4
7/4
81/44
81/44
21/11
21/11
2/1
2/1
 
'''Persian Johnston'''
'''Persian Johnston'''
33/32
33/32
17/16
17/16
9/8
9/8
19/16
19/16
5/4
5/4
21/16
21/16
4/3
4/3
11/8
11/8
23/16
23/16
3/2
3/2
13/8
13/8
5/3
5/3
7/4
7/4
57/32
57/32
15/8
15/8
63/32
63/32
2/1
2/1
 
'''Succulent Novemdecimal scale'''
'''Succulent Novemdecimal scale'''
13/12
13/12
10/9
10/9
7/6
7/6
19/16
19/16
5/4
5/4
21/16
21/16
4/3
4/3
11/8
11/8
17/12
17/12
3/2
3/2
19/12
19/12
5/3
5/3
7/4
7/4
16/9
16/9
11/6
11/6
17/9
17/9
2/1
2/1
 
'''Aberrismic Neopersian'''
'''Aberrismic Neopersian'''
64/63
64/63
13/12
13/12
9/8
9/8
8/7
8/7
39/32
39/32
26/21
26/21
4/3
4/3
256/189
256/189
13/9
13/9
3/2
3/2
32/21
32/21
13/8
13/8
104/63
104/63
12/7
12/7
117/64
117/64
13/7
13/7
2/1
2/1
 
'''Latwethagothic'''
'''Latwethagothic'''
33/32
33/32
69/64
69/64
9/8
9/8
32/27
32/27
11/9
11/9
23/18
23/18
4/3
4/3
11/8
11/8
23/16
23/16
3/2
3/2
99/64
99/64
207/128
207/128
27/16
27/16
16/9
16/9
11/6
11/6
23/12
23/12
2/1
2/1
 
'''Zalatwethagothic'''
'''Zalatwethagothic'''
33/32
33/32
69/64
69/64
9/8
9/8
7/6
7/6
11/9
11/9
23/18
23/18
21/16
21/16
11/8
11/8
23/16
23/16
3/2
3/2
14/9
14/9
44/27
44/27
46/27
46/27
7/4
7/4
11/6
11/6
23/12
23/12
2/1
2/1
 
'''Chariot'''
'''Chariot'''
19/18
19/18
13/12
13/12
10/9
10/9
7/6
7/6
11/9
11/9
5/4
5/4
4/3
4/3
11/8
11/8
17/12
17/12
3/2
3/2
19/12
19/12
13/8
13/8
5/3
5/3
7/4
7/4
11/6
11/6
23/12
23/12
2/1
2/1


== 19-note scales ==
== 19-note scales ==
'''Not-quite-ringer 19p'''
'''Not-quite-ringer 19p'''
33/32
33/32
17/16
17/16
9/8
9/8
7/6
7/6
19/16
19/16
5/4
5/4
21/16
21/16
4/3
4/3
11/8
11/8
23/16
23/16
3/2
3/2
25/16
25/16
13/8
13/8
27/16
27/16
7/4
7/4
29/16
29/16
15/8
15/8
31/16
31/16
2/1
2/1
 
'''Quasi-hemipyth detemper'''
'''Quasi-hemipyth detemper'''
28/27
28/27
13/12
13/12
9/8
9/8
7/6
7/6
32/27
32/27
11/9
11/9
21/16
21/16
4/3
4/3
11/8
11/8
13/9
13/9
3/2
3/2
14/9
14/9
13/8
13/8
27/16
27/16
7/4
7/4
16/9
16/9
11/6
11/6
63/32
63/32
2/1
2/1
 
'''19-limit dual-harmonic-segment-based'''
'''19-limit dual-harmonic-segment-based'''
25/24
25/24
13/12
13/12
9/8
9/8
7/6
7/6
19/16
19/16
5/4
5/4
21/16
21/16
4/3
4/3
11/8
11/8
17/12
17/12
3/2
3/2
25/16
25/16
13/8
13/8
27/16
27/16
7/4
7/4
57/32
57/32
15/8
15/8
63/32
63/32
2/1
2/1
 
'''Pseudo-fives scale'''
'''Pseudo-fives scale'''
33/32
33/32
77/72
77/72
9/8
9/8
7/6
7/6
77/64
77/64
11/9
11/9
21/16
21/16
4/3
4/3
11/8
11/8
77/54
77/54
3/2
3/2
14/9
14/9
77/48
77/48
44/27
44/27
7/4
7/4
16/9
16/9
11/6
11/6
154/81
154/81
2/1
2/1
 
'''Chipped Tetromino'''
'''Chipped Tetromino'''
21/20
21/20
35/32
35/32
9/8
9/8
7/6
7/6
6/5
6/5
5/4
5/4
21/16
21/16
4/3
4/3
7/5
7/5
35/24
35/24
3/2
3/2
63/40
63/40
8/5
8/5
5/3
5/3
7/4
7/4
9/5
9/5
15/8
15/8
63/32
63/32
2/1
2/1
 
'''Not-quite-ringer 19egh'''
'''Not-quite-ringer 19egh'''
17/16
17/16
35/32
35/32
9/8
9/8
19/16
19/16
39/32
39/32
5/4
5/4
21/16
21/16
11/8
11/8
45/32
45/32
23/16
23/16
3/2
3/2
25/16
25/16
13/8
13/8
27/16
27/16
7/4
7/4
29/16
29/16
15/8
15/8
31/16
31/16
2/1
2/1


== 20-note scales ==
== 20-note scales ==
'''Yatha Double Blackdye'''
'''Yatha Double Blackdye'''
65/64
65/64
13/12
13/12
10/9
10/9
9/8
9/8
65/54
65/54
39/32
39/32
5/4
5/4
4/3
4/3
65/48
65/48
13/9
13/9
40/27
40/27
3/2
3/2
130/81
130/81
13/8
13/8
5/3
5/3
27/16
27/16
65/36
65/36
117/64
117/64
15/8
15/8
2/1
2/1
 
'''Yala Double Blackdye'''
'''Yala Double Blackdye'''
55/54
55/54
33/32
33/32
10/9
10/9
9/8
9/8
55/48
55/48
11/9
11/9
5/4
5/4
4/3
4/3
110/81
110/81
11/8
11/8
40/27
40/27
3/2
3/2
55/36
55/36
99/64
99/64
5/3
5/3
27/16
27/16
55/32
55/32
11/6
11/6
15/8
15/8
2/1
2/1


== 22-note scales ==
== 22-note scales ==
'''Yala Dart'''
'''Yala Dart'''
33/32
33/32
88/81
88/81
10/9
10/9
9/8
9/8
32/27
32/27
11/9
11/9
5/4
5/4
81/64
81/64
4/3
4/3
11/8
11/8
45/32
45/32
40/27
40/27
3/2
3/2
99/64
99/64
44/27
44/27
5/3
5/3
27/16
27/16
16/9
16/9
11/6
11/6
15/8
15/8
160/81
160/81
2/1
2/1
 
'''Close-to-even Scale'''
'''Close-to-even Scale'''
33/32
33/32
17/16
17/16
35/32
35/32
9/8
9/8
7/6
7/6
29/24
29/24
5/4
5/4
31/24
31/24
4/3
4/3
11/8
11/8
17/12
17/12
35/24
35/24
3/2
3/2
14/9
14/9
29/18
29/18
5/3
5/3
31/18
31/18
16/9
16/9
11/6
11/6
17/9
17/9
35/18
35/18
2/1
2/1
 
'''Cheendene'''
'''cheen detempering'''
1053/1024
1053/1024
13/12
13/12
10/9
10/9
9/8
9/8
32/27
32/27
39/32
39/32
5/4
5/4
81/64
81/64
4/3
4/3
351/256
351/256
45/32
45/32
40/27
40/27
3/2
3/2
3159/2048
3159/2048
13/8
13/8
5/3
5/3
27/16
27/16
16/9
16/9
117/64
117/64
15/8
15/8
160/81
160/81
2/1
2/1
 
'''Compact 11-limit detemper'''
'''Compact 11-limit detemper'''
33/32
33/32
77/72
77/72
35/32
35/32
9/8
9/8
7/6
7/6
77/64
77/64
5/4
5/4
165/128
165/128
4/3
4/3
11/8
11/8
45/32
45/32
35/24
35/24
3/2
3/2
14/9
14/9
77/48
77/48
5/3
5/3
55/32
55/32
7/4
7/4
11/6
11/6
15/8
15/8
35/18
35/18
2/1
2/1


== 24-note scales ==
== 24-note scales ==
'''Car'''
'''Car'''
33/32
33/32
17/16
17/16
13/12
13/12
9/8
9/8
7/6
7/6
19/16
19/16
39/32
39/32
5/4
5/4
21/16
21/16
4/3
4/3
11/8
11/8
17/12
17/12
23/16
23/16
3/2
3/2
14/9
14/9
19/12
19/12
13/8
13/8
5/3
5/3
7/4
7/4
57/32
57/32
11/6
11/6
15/8
15/8
23/12
23/12
2/1
2/1
 
'''Sedan'''
'''Sedan'''
33/32
33/32
17/16
17/16
13/12
13/12
10/9
10/9
7/6
7/6
19/16
19/16
39/32
39/32
5/4
5/4
21/16
21/16
4/3
4/3
11/8
11/8
17/12
17/12
23/16
23/16
3/2
3/2
14/9
14/9
19/12
19/12
13/8
13/8
5/3
5/3
7/4
7/4
16/9
16/9
11/6
11/6
15/8
15/8
23/12
23/12
2/1
2/1
 
'''Modstraw'''
'''Modstraw'''
28/27
28/27
35/32
35/32
10/9
10/9
9/8
9/8
7/6
7/6
32/27
32/27
5/4
5/4
35/27
35/27
21/16
21/16
4/3
4/3
45/32
45/32
35/24
35/24
40/27
40/27
3/2
3/2
14/9
14/9
105/64
105/64
5/3
5/3
27/16
27/16
7/4
7/4
16/9
16/9
15/8
15/8
35/18
35/18
63/32
63/32
2/1
2/1
 
'''17-limit scale'''
'''17-limit scale'''
33/32
33/32
17/16
17/16
13/12
13/12
10/9
10/9
7/6
7/6
32/27
32/27
11/9
11/9
5/4
5/4
21/16
21/16
4/3
4/3
11/8
11/8
17/12
17/12
13/9
13/9
3/2
3/2
14/9
14/9
51/32
51/32
13/8
13/8
5/3
5/3
7/4
7/4
16/9
16/9
11/6
11/6
15/8
15/8
52/27
52/27
2/1
2/1
 
'''31-limit scale'''
'''31-limit scale'''
33/32
33/32
17/16
17/16
13/12
13/12
9/8
9/8
7/6
7/6
19/16
19/16
29/24
29/24
5/4
5/4
21/16
21/16
4/3
4/3
11/8
11/8
17/12
17/12
23/16
23/16
3/2
3/2
14/9
14/9
19/12
19/12
13/8
13/8
5/3
5/3
7/4
7/4
16/9
16/9
29/16
29/16
15/8
15/8
31/16
31/16
2/1
2/1
 
'''No-fives undecimal scale'''
'''No-fives undecimal scale'''
33/32
33/32
77/72
77/72
88/81
88/81
9/8
9/8
7/6
7/6
77/64
77/64
11/9
11/9
81/64
81/64
21/16
21/16
4/3
4/3
11/8
11/8
77/54
77/54
352/243
352/243
3/2
3/2
14/9
14/9
77/48
77/48
44/27
44/27
27/16
27/16
7/4
7/4
16/9
16/9
11/6
11/6
154/81
154/81
63/32
63/32
2/1
2/1
 
'''37-limit scale'''
'''37-limit scale'''
31/30
31/30
16/15
16/15
11/10
11/10
17/15
17/15
7/6
7/6
6/5
6/5
37/30
37/30
19/15
19/15
13/10
13/10
4/3
4/3
11/8
11/8
17/12
17/12
35/24
35/24
3/2
3/2
31/20
31/20
8/5
8/5
33/20
33/20
17/10
17/10
7/4
7/4
9/5
9/5
37/20
37/20
19/10
19/10
39/20
39/20
2/1
2/1
 
'''Hexquad'''
'''Hexquad'''
28/27
28/27
77/72
77/72
35/32
35/32
9/8
9/8
7/6
7/6
77/64
77/64
11/9
11/9
5/4
5/4
35/27
35/27
4/3
4/3
11/8
11/8
45/32
45/32
35/24
35/24
3/2
3/2
14/9
14/9
77/48
77/48
44/27
44/27
5/3
5/3
7/4
7/4
231/128
231/128
11/6
11/6
15/8
15/8
35/18
35/18
2/1
2/1
 
'''bus-like 11-limit detemper'''
'''bus-like 11-limit detemper'''
33/32
33/32
77/72
77/72
35/32
35/32
9/8
9/8
7/6
7/6
77/64
77/64
11/9
11/9
5/4
5/4
21/16
21/16
4/3
4/3
11/8
11/8
45/32
45/32
35/24
35/24
3/2
3/2
14/9
14/9
77/48
77/48
105/64
105/64
5/3
5/3
7/4
7/4
16/9
16/9
11/6
11/6
15/8
15/8
35/18
35/18
2/1
2/1


== 26-note scales ==
== 26-note scales ==
'''Mothra Detemper'''
'''Mothra Detemper'''
135/128
135/128
15/14
15/14
35/32
35/32
9/8
9/8
8/7
8/7
7/6
7/6
315/256
315/256
5/4
5/4
9/7
9/7
21/16
21/16
4/3
4/3
45/32
45/32
10/7
10/7
35/24
35/24
3/2
3/2
32/21
32/21
45/28
45/28
105/64
105/64
5/3
5/3
12/7
12/7
7/4
7/4
945/512
945/512
15/8
15/8
40/21
40/21
63/32
63/32
2/1
2/1


== 29-note scales ==
== 29-note scales ==
'''andromeda[29] detemper'''
'''andromeda[29] detemper'''
33/32
33/32
135/128
135/128
13/12
13/12
10/9
10/9
9/8
9/8
7/6
7/6
32/27
32/27
11/9
11/9
5/4
5/4
81/64
81/64
21/16
21/16
4/3
4/3
11/8
11/8
45/32
45/32
13/9
13/9
189/128
189/128
3/2
3/2
14/9
14/9
405/256
405/256
13/8
13/8
5/3
5/3
27/16
27/16
7/4
7/4
16/9
16/9
11/6
11/6
15/8
15/8
52/27
52/27
63/32
63/32
2/1
2/1


== 31-note scales ==
== 31-note scales ==
'''Otonal Sevenice'''
'''Otonal Sevenice'''
36/35
36/35
21/20
21/20
15/14
15/14
35/32
35/32
9/8
9/8
8/7
8/7
7/6
7/6
6/5
6/5
128/105
128/105
5/4
5/4
9/7
9/7
21/16
21/16
4/3
4/3
48/35
48/35
7/5
7/5
10/7
10/7
35/24
35/24
3/2
3/2
32/21
32/21
63/40
63/40
8/5
8/5
105/64
105/64
5/3
5/3
12/7
12/7
7/4
7/4
9/5
9/5
64/35
64/35
15/8
15/8
40/21
40/21
63/32
63/32
2/1
2/1
 
'''Utonal Sevenice'''
'''Utonal Sevenice'''
36/35
36/35
21/20
21/20
15/14
15/14
35/32
35/32
9/8
9/8
8/7
8/7
7/6
7/6
6/5
6/5
315/256
315/256
5/4
5/4
9/7
9/7
21/16
21/16
4/3
4/3
48/35
48/35
7/5
7/5
10/7
10/7
35/24
35/24
3/2
3/2
32/21
32/21
63/40
63/40
8/5
8/5
105/64
105/64
5/3
5/3
12/7
12/7
7/4
7/4
9/5
9/5
64/35
64/35
15/8
15/8
40/21
40/21
63/32
63/32
2/1
2/1
 
'''Ringer 31p'''
'''Ringer 31p'''
39/38
39/38
20/19
20/19
41/38
41/38
21/19
21/19
43/38
43/38
22/19
22/19
45/38
45/38
23/19
23/19
47/38
47/38
24/19
24/19
49/38
49/38
25/19
25/19
51/38
51/38
26/19
26/19
27/19
27/19
55/38
55/38
28/19
28/19
3/2
3/2
29/19
29/19
30/19
30/19
61/38
61/38
31/19
31/19
32/19
32/19
33/19
33/19
67/38
67/38
34/19
34/19
35/19
35/19
36/19
36/19
37/19
37/19
75/38
75/38
2/1
2/1
 
'''Symmetrizine'''
'''Symmetrizine'''
64/63
64/63
28/27
28/27
16/15
16/15
12/11
12/11
9/8
9/8
8/7
8/7
7/6
7/6
6/5
6/5
11/9
11/9
5/4
5/4
9/7
9/7
21/16
21/16
4/3
4/3
11/8
11/8
45/32
45/32
64/45
64/45
16/11
16/11
3/2
3/2
32/21
32/21
14/9
14/9
8/5
8/5
18/11
18/11
5/3
5/3
12/7
12/7
7/4
7/4
16/9
16/9
11/6
11/6
15/8
15/8
27/14
27/14
63/32
63/32
2/1
2/1


== Large scales (greater than 31 notes) ==
== Large scales (greater than 31 notes) ==
'''41-tone 5-limit JI'''
'''41-tone 5-limit JI'''
81/80
81/80
25/24
25/24
135/128
135/128
16/15
16/15
27/25
27/25
10/9
10/9
9/8
9/8
256/225
256/225
75/64
75/64
32/27
32/27
6/5
6/5
100/81
100/81
5/4
5/4
81/64
81/64
32/25
32/25
320/243
320/243
4/3
4/3
27/20
27/20
25/18
25/18
45/32
45/32
64/45
64/45
36/25
36/25
40/27
40/27
3/2
3/2
243/160
243/160
25/16
25/16
128/81
128/81
8/5
8/5
81/50
81/50
5/3
5/3
27/16
27/16
128/75
128/75
225/128
225/128
16/9
16/9
9/5
9/5
50/27
50/27
15/8
15/8
256/135
256/135
48/25
48/25
160/81
160/81
2/1
2/1
 
'''46-tone septimal JI'''
'''46-tone septimal JI'''
64/63
64/63
36/35
36/35
21/20
21/20
16/15
16/15
15/14
15/14
35/32
35/32
10/9
10/9
9/8
9/8
8/7
8/7
7/6
7/6
189/160
189/160
6/5
6/5
128/105
128/105
315/256
315/256
5/4
5/4
80/63
80/63
9/7
9/7
21/16
21/16
4/3
4/3
27/20
27/20
48/35
48/35
7/5
7/5
45/32
45/32
10/7
10/7
35/24
35/24
189/128
189/128
3/2
3/2
32/21
32/21
14/9
14/9
63/40
63/40
8/5
8/5
45/28
45/28
105/64
105/64
5/3
5/3
27/16
27/16
12/7
12/7
7/4
7/4
16/9
16/9
9/5
9/5
64/35
64/35
28/15
28/15
15/8
15/8
40/21
40/21
27/14
27/14
63/32
63/32
2/1
2/1
 
'''53-tone Semantic Scale'''
'''53-tone Semantic Scale'''
81/80
81/80
128/125
128/125
25/24
25/24
135/128
135/128
16/15
16/15
27/25
27/25
800/729
800/729
10/9
10/9
9/8
9/8
256/225
256/225
144/125
144/125
75/64
75/64
32/27
32/27
6/5
6/5
243/200
243/200
100/81
100/81
5/4
5/4
81/64
81/64
32/25
32/25
125/96
125/96
320/243
320/243
4/3
4/3
27/20
27/20
512/375
512/375
25/18
25/18
45/32
45/32
64/45
64/45
36/25
36/25
375/256
375/256
40/27
40/27
3/2
3/2
243/160
243/160
192/125
192/125
25/16
25/16
128/81
128/81
8/5
8/5
81/50
81/50
400/243
400/243
5/3
5/3
27/16
27/16
128/75
128/75
125/72
125/72
225/128
225/128
16/9
16/9
9/5
9/5
729/400
729/400
50/27
50/27
15/8
15/8
256/135
256/135
48/25
48/25
125/64
125/64
160/81
160/81
2/1
2/1
 
'''130-tone 13-limit JI'''
'''130-tone 13-limit JI'''
225/224
225/224
105/104
105/104
65/64
65/64
45/44
45/44
36/35
36/35
33/32
33/32
28/27
28/27
25/24
25/24
21/20
21/20
135/128
135/128
35/33
35/33
16/15
16/15
15/14
15/14
14/13
14/13
13/12
13/12
12/11
12/11
35/32
35/32
11/10
11/10
72/65
72/65
10/9
10/9
28/25
28/25
9/8
9/8
112/99
112/99
25/22
25/22
8/7
8/7
55/48
55/48
15/13
15/13
65/56
65/56
7/6
7/6
168/143
168/143
13/11
13/11
32/27
32/27
25/21
25/21
6/5
6/5
135/112
135/112
40/33
40/33
128/105
128/105
11/9
11/9
16/13
16/13
26/21
26/21
56/45
56/45
5/4
5/4
63/50
63/50
81/64
81/64
14/11
14/11
32/25
32/25
9/7
9/7
84/65
84/65
13/10
13/10
72/55
72/55
21/16
21/16
33/25
33/25
143/108
143/108
4/3
4/3
75/56
75/56
27/20
27/20
65/48
65/48
15/11
15/11
48/35
48/35
11/8
11/8
18/13
18/13
25/18
25/18
7/5
7/5
45/32
45/32
99/70
99/70
64/45
64/45
10/7
10/7
36/25
36/25
13/9
13/9
16/11
16/11
35/24
35/24
22/15
22/15
96/65
96/65
40/27
40/27
112/75
112/75
3/2
3/2
448/297
448/297
50/33
50/33
32/21
32/21
55/36
55/36
20/13
20/13
65/42
65/42
14/9
14/9
25/16
25/16
11/7
11/7
128/81
128/81
100/63
100/63
8/5
8/5
45/28
45/28
21/13
21/13
13/8
13/8
18/11
18/11
105/64
105/64
33/20
33/20
224/135
224/135
5/3
5/3
42/25
42/25
27/16
27/16
22/13
22/13
143/84
143/84
12/7
12/7
112/65
112/65
26/15
26/15
96/55
96/55
7/4
7/4
44/25
44/25
99/56
99/56
16/9
16/9
25/14
25/14
9/5
9/5
65/36
65/36
20/11
20/11
64/35
64/35
11/6
11/6
24/13
24/13
13/7
13/7
28/15
28/15
15/8
15/8
66/35
66/35
256/135
256/135
40/21
40/21
48/25
48/25
27/14
27/14
64/33
64/33
35/18
35/18
49/25
49/25
63/32
63/32
99/50
99/50
143/72
143/72
2/1
2/1

Revision as of 04:52, 4 January 2026

All of the scales below are constant structure and repeat at 2/1.

Boutique scales (less than 12 notes)

24:26:28:30:32:33:36:39:42:45:48 

13/12
7/6
5/4
4/3
11/8
3/2
13/8
7/4
15/8
2/1

24:27:28:30:33:36:39:42:45:48 

9/8
7/6
5/4
11/8
3/2
13/8
7/4
15/8
2/1

60:63:64:70:80:84:96:105:120 

35/32
5/4
21/16
4/3
35/24
5/3
7/4
2/1

56:60:64:70:84:90:96:105:112 

35/32
7/6
5/4
4/3
35/24
7/4
15/8
2/1

18:20:22:24:27:30:33:36 

10/9
11/9
4/3
3/2
5/3
11/6
2/1

14:16:18:20:21:24:27:28 

8/7
9/7
10/7
3/2
12/7
27/14
2/1

27:28:33:36:39:42:45:54 

28/27
11/9
4/3
13/9
14/9
5/3
2/1

7:8:9:10:11:12:13:14 

8/7
9/7
10/7
11/7
12/7
13/7
2/1

56:60:64:70:72:80:84:90:96:105:112 

15/14
8/7
5/4
9/7
10/7
3/2
45/28
12/7
15/8
2/1

52:58:64:71:78:86:95:104 

71/64
39/32
43/32
95/64
13/8
29/16
2/1

48:52:58:64:72:78:87:96 

13/12
29/24
4/3
3/2
13/8
29/16
2/1

33:36:40:42:44:48:54:60:63:66 

12/11
40/33
14/11
4/3
16/11
18/11
20/11
21/11
2/1

720:780:840:910:945:1008:1092:1170:1260:1365:1440 

13/12
7/6
91/72
21/16
7/5
91/60
13/8
7/4
91/48
2/1

12-note scales

Antitonic 17-limit 

17/16
39/32
5/4
21/16
11/8
3/2
51/32
13/8
5/3
7/4
11/6
2/1

Bicycle 

13/12
9/8
7/6
5/4
4/3
11/8
3/2
13/8
5/3
7/4
11/6
2/1

Duodene 

16/15
9/8
6/5
5/4
4/3
45/32
3/2
8/5
5/3
9/5
15/8
2/1

Septimal Catgirl 

28/27
9/8
7/6
5/4
4/3
45/32
3/2
14/9
5/3
7/4
15/8
2/1

North Dakota 

33/32
10/9
7/6
5/4
4/3
11/8
3/2
14/9
5/3
7/4
11/6
2/1

Johnston Piano Scale (Ringer 12) 

15/14
8/7
17/14
9/7
19/14
10/7
3/2
11/7
12/7
13/7
27/14
2/1

Ephemeral Soup Scale 

77/72
9/8
77/64
21/16
693/512
189/128
3/2
77/48
7/4
231/128
63/32
2/1

Once Upon A Time Scale 

10/9
9/8
5/4
9/7
21/16
35/24
3/2
5/3
12/7
7/4
35/18
2/1

Centaur 

21/20
9/8
7/6
5/4
4/3
7/5
3/2
14/9
5/3
7/4
15/8
2/1

Pental Diachrome 

10/9
9/8
5/4
81/64
4/3
40/27
3/2
5/3
27/16
15/8
160/81
2/1

Margo Scale 

104/99
9/8
13/11
14/11
4/3
63/44
3/2
52/33
56/33
16/9
21/11
2/1

Meta-Slendro 

50/49
8/7
57/49
64/49
65/49
72/49
74/49
151/98
12/7
86/49
96/49
2/1

Succulent Undecimal Scale 

10/9
7/6
5/4
21/16
4/3
11/8
3/2
5/3
7/4
16/9
11/6
2/1

14-note scales

No-13s ultrajust 

17/16
9/8
19/16
5/4
21/16
11/8
23/16
3/2
19/12
5/3
7/4
11/6
23/12
2/1

17-note scales

Walkie 

65/64
13/12
9/8
585/512
39/32
5/4
4/3
65/48
45/32
3/2
195/128
13/8
5/3
16/9
117/64
15/8
2/1

Mohahadene 

55/54
88/81
9/8
55/48
11/9
5/4
4/3
11/8
45/32
3/2
55/36
44/27
5/3
55/32
11/6
15/8
2/1

Dichotidene 

28/27
35/32
9/8
7/6
5/4
35/27
4/3
45/32
35/24
3/2
14/9
105/64
27/16
7/4
15/8
35/18
2/1

Just Spoogalaxy 

28/27
29/27
9/8
7/6
29/24
81/64
21/16
87/64
116/81
3/2
14/9
29/18
27/16
7/4
29/16
243/128
2/1

Cartwheel 

28/27
13/12
9/8
7/6
11/9
5/4
4/3
11/8
13/9
3/2
14/9
13/8
5/3
7/4
11/6
15/8
2/1

Ringer 17-quad 

33/32
17/16
9/8
19/16
77/64
5/4
21/16
11/8
23/16
3/2
49/32
25/16
13/8
7/4
29/16
15/8
2/1

Ringer 17-tri 

49/48
17/16
9/8
19/16
29/24
5/4
21/16
11/8
23/16
3/2
74/48
25/16
13/8
7/4
11/6
15/8
2/1

Schismadene 

135/128
10/9
9/8
32/27
5/4
81/64
4/3
45/32
40/27
3/2
128/81
5/3
27/16
16/9
15/8
160/81
2/1

Traditional Baglama Fret Scale 

18/17
12/11
9/8
81/68
27/22
81/64
4/3
24/17
16/11
3/2
27/17
18/11
27/16
16/9
32/17
64/33
2/1

23-limit Pseudoringer 

33/32
13/12
9/8
7/6
39/32
5/4
4/3
11/8
17/12
3/2
19/12
13/8
5/3
7/4
11/6
23/12
2/1

Zothogothic 

28/27
13/12
9/8
7/6
39/32
91/72
4/3
112/81
13/9
3/2
14/9
13/8
91/54
7/4
117/64
91/48
2/1

Zolugothic 

28/27
12/11
9/8
7/6
27/22
14/11
4/3
112/81
16/11
3/2
14/9
18/11
56/33
7/4
81/44
21/11
2/1

Persian Johnston 

33/32
17/16
9/8
19/16
5/4
21/16
4/3
11/8
23/16
3/2
13/8
5/3
7/4
57/32
15/8
63/32
2/1

Succulent Novemdecimal scale 

13/12
10/9
7/6
19/16
5/4
21/16
4/3
11/8
17/12
3/2
19/12
5/3
7/4
16/9
11/6
17/9
2/1

Aberrismic Neopersian 

64/63
13/12
9/8
8/7
39/32
26/21
4/3
256/189
13/9
3/2
32/21
13/8
104/63
12/7
117/64
13/7
2/1

Latwethagothic 

33/32
69/64
9/8
32/27
11/9
23/18
4/3
11/8
23/16
3/2
99/64
207/128
27/16
16/9
11/6
23/12
2/1

Zalatwethagothic 

33/32
69/64
9/8
7/6
11/9
23/18
21/16
11/8
23/16
3/2
14/9
44/27
46/27
7/4
11/6
23/12
2/1

Chariot 

19/18
13/12
10/9
7/6
11/9
5/4
4/3
11/8
17/12
3/2
19/12
13/8
5/3
7/4
11/6
23/12
2/1

19-note scales

Not-quite-ringer 19p 

33/32
17/16
9/8
7/6
19/16
5/4
21/16
4/3
11/8
23/16
3/2
25/16
13/8
27/16
7/4
29/16
15/8
31/16
2/1

Quasi-hemipyth detemper 

28/27
13/12
9/8
7/6
32/27
11/9
21/16
4/3
11/8
13/9
3/2
14/9
13/8
27/16
7/4
16/9
11/6
63/32
2/1

19-limit dual-harmonic-segment-based 

25/24
13/12
9/8
7/6
19/16
5/4
21/16
4/3
11/8
17/12
3/2
25/16
13/8
27/16
7/4
57/32
15/8
63/32
2/1

Pseudo-fives scale 

33/32
77/72
9/8
7/6
77/64
11/9
21/16
4/3
11/8
77/54
3/2
14/9
77/48
44/27
7/4
16/9
11/6
154/81
2/1

Chipped Tetromino 

21/20
35/32
9/8
7/6
6/5
5/4
21/16
4/3
7/5
35/24
3/2
63/40
8/5
5/3
7/4
9/5
15/8
63/32
2/1

Not-quite-ringer 19egh 

17/16
35/32
9/8
19/16
39/32
5/4
21/16
11/8
45/32
23/16
3/2
25/16
13/8
27/16
7/4
29/16
15/8
31/16
2/1

20-note scales

Yatha Double Blackdye 

65/64
13/12
10/9
9/8
65/54
39/32
5/4
4/3
65/48
13/9
40/27
3/2
130/81
13/8
5/3
27/16
65/36
117/64
15/8
2/1

Yala Double Blackdye 

55/54
33/32
10/9
9/8
55/48
11/9
5/4
4/3
110/81
11/8
40/27
3/2
55/36
99/64
5/3
27/16
55/32
11/6
15/8
2/1

22-note scales

Yala Dart 

33/32
88/81
10/9
9/8
32/27
11/9
5/4
81/64
4/3
11/8
45/32
40/27
3/2
99/64
44/27
5/3
27/16
16/9
11/6
15/8
160/81
2/1

Close-to-even Scale 

33/32
17/16
35/32
9/8
7/6
29/24
5/4
31/24
4/3
11/8
17/12
35/24
3/2
14/9
29/18
5/3
31/18
16/9
11/6
17/9
35/18
2/1

Cheendene 

1053/1024
13/12
10/9
9/8
32/27
39/32
5/4
81/64
4/3
351/256
45/32
40/27
3/2
3159/2048
13/8
5/3
27/16
16/9
117/64
15/8
160/81
2/1

Compact 11-limit detemper 

33/32
77/72
35/32
9/8
7/6
77/64
5/4
165/128
4/3
11/8
45/32
35/24
3/2
14/9
77/48
5/3
55/32
7/4
11/6
15/8
35/18
2/1

24-note scales

Car 

33/32
17/16
13/12
9/8
7/6
19/16
39/32
5/4
21/16
4/3
11/8
17/12
23/16
3/2
14/9
19/12
13/8
5/3
7/4
57/32
11/6
15/8
23/12
2/1

Sedan 

33/32
17/16
13/12
10/9
7/6
19/16
39/32
5/4
21/16
4/3
11/8
17/12
23/16
3/2
14/9
19/12
13/8
5/3
7/4
16/9
11/6
15/8
23/12
2/1

Modstraw 

28/27
35/32
10/9
9/8
7/6
32/27
5/4
35/27
21/16
4/3
45/32
35/24
40/27
3/2
14/9
105/64
5/3
27/16
7/4
16/9
15/8
35/18
63/32
2/1

17-limit scale 

33/32
17/16
13/12
10/9
7/6
32/27
11/9
5/4
21/16
4/3
11/8
17/12
13/9
3/2
14/9
51/32
13/8
5/3
7/4
16/9
11/6
15/8
52/27
2/1

31-limit scale 

33/32
17/16
13/12
9/8
7/6
19/16
29/24
5/4
21/16
4/3
11/8
17/12
23/16
3/2
14/9
19/12
13/8
5/3
7/4
16/9
29/16
15/8
31/16
2/1

No-fives undecimal scale 

33/32
77/72
88/81
9/8
7/6
77/64
11/9
81/64
21/16
4/3
11/8
77/54
352/243
3/2
14/9
77/48
44/27
27/16
7/4
16/9
11/6
154/81
63/32
2/1

37-limit scale 

31/30
16/15
11/10
17/15
7/6
6/5
37/30
19/15
13/10
4/3
11/8
17/12
35/24
3/2
31/20
8/5
33/20
17/10
7/4
9/5
37/20
19/10
39/20
2/1

Hexquad 

28/27
77/72
35/32
9/8
7/6
77/64
11/9
5/4
35/27
4/3
11/8
45/32
35/24
3/2
14/9
77/48
44/27
5/3
7/4
231/128
11/6
15/8
35/18
2/1

bus-like 11-limit detemper 

33/32
77/72
35/32
9/8
7/6
77/64
11/9
5/4
21/16
4/3
11/8
45/32
35/24
3/2
14/9
77/48
105/64
5/3
7/4
16/9
11/6
15/8
35/18
2/1

26-note scales

Mothra Detemper 

135/128
15/14
35/32
9/8
8/7
7/6
315/256
5/4
9/7
21/16
4/3
45/32
10/7
35/24
3/2
32/21
45/28
105/64
5/3
12/7
7/4
945/512
15/8
40/21
63/32
2/1

29-note scales

andromeda[29] detemper 

33/32
135/128
13/12
10/9
9/8
7/6
32/27
11/9
5/4
81/64
21/16
4/3
11/8
45/32
13/9
189/128
3/2
14/9
405/256
13/8
5/3
27/16
7/4
16/9
11/6
15/8
52/27
63/32
2/1

31-note scales

Otonal Sevenice 

36/35
21/20
15/14
35/32
9/8
8/7
7/6
6/5
128/105
5/4
9/7
21/16
4/3
48/35
7/5
10/7
35/24
3/2
32/21
63/40
8/5
105/64
5/3
12/7
7/4
9/5
64/35
15/8
40/21
63/32
2/1

Utonal Sevenice 

36/35
21/20
15/14
35/32
9/8
8/7
7/6
6/5
315/256
5/4
9/7
21/16
4/3
48/35
7/5
10/7
35/24
3/2
32/21
63/40
8/5
105/64
5/3
12/7
7/4
9/5
64/35
15/8
40/21
63/32
2/1

Ringer 31p 

39/38
20/19
41/38
21/19
43/38
22/19
45/38
23/19
47/38
24/19
49/38
25/19
51/38
26/19
27/19
55/38
28/19
3/2
29/19
30/19
61/38
31/19
32/19
33/19
67/38
34/19
35/19
36/19
37/19
75/38
2/1

Symmetrizine 

64/63
28/27
16/15
12/11
9/8
8/7
7/6
6/5
11/9
5/4
9/7
21/16
4/3
11/8
45/32
64/45
16/11
3/2
32/21
14/9
8/5
18/11
5/3
12/7
7/4
16/9
11/6
15/8
27/14
63/32
2/1

Large scales (greater than 31 notes)

41-tone 5-limit JI 

81/80
25/24
135/128
16/15
27/25
10/9
9/8
256/225
75/64
32/27
6/5
100/81
5/4
81/64
32/25
320/243
4/3
27/20
25/18
45/32
64/45
36/25
40/27
3/2
243/160
25/16
128/81
8/5
81/50
5/3
27/16
128/75
225/128
16/9
9/5
50/27
15/8
256/135
48/25
160/81
2/1

46-tone septimal JI 

64/63
36/35
21/20
16/15
15/14
35/32
10/9
9/8
8/7
7/6
189/160
6/5
128/105
315/256
5/4
80/63
9/7
21/16
4/3
27/20
48/35
7/5
45/32
10/7
35/24
189/128
3/2
32/21
14/9
63/40
8/5
45/28
105/64
5/3
27/16
12/7
7/4
16/9
9/5
64/35
28/15
15/8
40/21
27/14
63/32
2/1

53-tone Semantic Scale 

81/80
128/125
25/24
135/128
16/15
27/25
800/729
10/9
9/8
256/225
144/125
75/64
32/27
6/5
243/200
100/81
5/4
81/64
32/25
125/96
320/243
4/3
27/20
512/375
25/18
45/32
64/45
36/25
375/256
40/27
3/2
243/160
192/125
25/16
128/81
8/5
81/50
400/243
5/3
27/16
128/75
125/72
225/128
16/9
9/5
729/400
50/27
15/8
256/135
48/25
125/64
160/81
2/1

130-tone 13-limit JI 

225/224
105/104
65/64
45/44
36/35
33/32
28/27
25/24
21/20
135/128
35/33
16/15
15/14
14/13
13/12
12/11
35/32
11/10
72/65
10/9
28/25
9/8
112/99
25/22
8/7
55/48
15/13
65/56
7/6
168/143
13/11
32/27
25/21
6/5
135/112
40/33
128/105
11/9
16/13
26/21
56/45
5/4
63/50
81/64
14/11
32/25
9/7
84/65
13/10
72/55
21/16
33/25
143/108
4/3
75/56
27/20
65/48
15/11
48/35
11/8
18/13
25/18
7/5
45/32
99/70
64/45
10/7
36/25
13/9
16/11
35/24
22/15
96/65
40/27
112/75
3/2
448/297
50/33
32/21
55/36
20/13
65/42
14/9
25/16
11/7
128/81
100/63
8/5
45/28
21/13
13/8
18/11
105/64
33/20
224/135
5/3
42/25
27/16
22/13
143/84
12/7
112/65
26/15
96/55
7/4
44/25
99/56
16/9
25/14
9/5
65/36
20/11
64/35
11/6
24/13
13/7
28/15
15/8
66/35
256/135
40/21
48/25
27/14
64/33
35/18
49/25
63/32
99/50
143/72
2/1
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