User:MisterShafXen/13L 52s

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13L 52s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 52 small steps, with a period of 1 large step and 4 small steps that repeats every 92.3 ¢, or 13 times every octave. 13L 52s is a great-grandchild scale of 13L 13s, expanding it by 39 tones. Generators that produce this scale range from 73.8 ¢ to 92.3 ¢, or from 0 ¢ to 18.5 ¢.

↖ 12L 51s ↑ 13L 51s 14L 51s ↗
← 12L 52s 13L 52s 14L 52s →
↙ 12L 53s ↓ 13L 53s 14L 53s ↘
Scale structure
Step pattern ...65 steps...
Equave 2/1 (1200.0 ¢)
Period 1\13 (92.3 ¢)
Generator size
Bright 4\65 to 1\13 (73.8 ¢ to 92.3 ¢)
Dark 0\13 to 1\65 (0.0 ¢ to 18.5 ¢)
TAMNAMS information
Related to 13L 13s
With tunings 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 13L 39s
Sister 52L 13s
Daughters 65L 13s, 13L 65s
Neutralized 26L 39s
2-Flought 78L 52s, 13L 117s
Equal tunings
Equalized (L:s = 1:1) 4\65 (73.8 ¢)
Supersoft (L:s = 4:3) 13\208 (75.0 ¢)
Soft (L:s = 3:2) 9\143 (75.5 ¢)
Semisoft (L:s = 5:3) 14\221 (76.0 ¢)
Basic (L:s = 2:1) 5\78 (76.9 ¢)
Semihard (L:s = 5:2) 11\169 (78.1 ¢)
Hard (L:s = 3:1) 6\91 (79.1 ¢)
Superhard (L:s = 4:1) 7\104 (80.8 ¢)
Collapsed (L:s = 1:0) 1\13 (92.3 ¢)
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Scale properties

Intervals of 13L 52s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 18.5 ¢
Augmented 1-mosstep A1ms L 18.5 ¢ to 92.3 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 36.9 ¢
Major 2-mosstep M2ms L + s 36.9 ¢ to 92.3 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 55.4 ¢
Major 3-mosstep M3ms L + 2s 55.4 ¢ to 92.3 ¢
4-mosstep Diminished 4-mosstep d4ms 4s 0.0 ¢ to 73.8 ¢
Perfect 4-mosstep P4ms L + 3s 73.8 ¢ to 92.3 ¢
5-mosstep Perfect 5-mosstep P5ms L + 4s 92.3 ¢
6-mosstep Perfect 6-mosstep P6ms L + 5s 92.3 ¢ to 110.8 ¢
Augmented 6-mosstep A6ms 2L + 4s 110.8 ¢ to 184.6 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 92.3 ¢ to 129.2 ¢
Major 7-mosstep M7ms 2L + 5s 129.2 ¢ to 184.6 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 92.3 ¢ to 147.7 ¢
Major 8-mosstep M8ms 2L + 6s 147.7 ¢ to 184.6 ¢
9-mosstep Diminished 9-mosstep d9ms L + 8s 92.3 ¢ to 166.2 ¢
Perfect 9-mosstep P9ms 2L + 7s 166.2 ¢ to 184.6 ¢
10-mosstep Perfect 10-mosstep P10ms 2L + 8s 184.6 ¢
11-mosstep Perfect 11-mosstep P11ms 2L + 9s 184.6 ¢ to 203.1 ¢
Augmented 11-mosstep A11ms 3L + 8s 203.1 ¢ to 276.9 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 184.6 ¢ to 221.5 ¢
Major 12-mosstep M12ms 3L + 9s 221.5 ¢ to 276.9 ¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 184.6 ¢ to 240.0 ¢
Major 13-mosstep M13ms 3L + 10s 240.0 ¢ to 276.9 ¢
14-mosstep Diminished 14-mosstep d14ms 2L + 12s 184.6 ¢ to 258.5 ¢
Perfect 14-mosstep P14ms 3L + 11s 258.5 ¢ to 276.9 ¢
15-mosstep Perfect 15-mosstep P15ms 3L + 12s 276.9 ¢
16-mosstep Perfect 16-mosstep P16ms 3L + 13s 276.9 ¢ to 295.4 ¢
Augmented 16-mosstep A16ms 4L + 12s 295.4 ¢ to 369.2 ¢
17-mosstep Minor 17-mosstep m17ms 3L + 14s 276.9 ¢ to 313.8 ¢
Major 17-mosstep M17ms 4L + 13s 313.8 ¢ to 369.2 ¢
18-mosstep Minor 18-mosstep m18ms 3L + 15s 276.9 ¢ to 332.3 ¢
Major 18-mosstep M18ms 4L + 14s 332.3 ¢ to 369.2 ¢
19-mosstep Diminished 19-mosstep d19ms 3L + 16s 276.9 ¢ to 350.8 ¢
Perfect 19-mosstep P19ms 4L + 15s 350.8 ¢ to 369.2 ¢
20-mosstep Perfect 20-mosstep P20ms 4L + 16s 369.2 ¢
21-mosstep Perfect 21-mosstep P21ms 4L + 17s 369.2 ¢ to 387.7 ¢
Augmented 21-mosstep A21ms 5L + 16s 387.7 ¢ to 461.5 ¢
22-mosstep Minor 22-mosstep m22ms 4L + 18s 369.2 ¢ to 406.2 ¢
Major 22-mosstep M22ms 5L + 17s 406.2 ¢ to 461.5 ¢
23-mosstep Minor 23-mosstep m23ms 4L + 19s 369.2 ¢ to 424.6 ¢
Major 23-mosstep M23ms 5L + 18s 424.6 ¢ to 461.5 ¢
24-mosstep Diminished 24-mosstep d24ms 4L + 20s 369.2 ¢ to 443.1 ¢
Perfect 24-mosstep P24ms 5L + 19s 443.1 ¢ to 461.5 ¢
25-mosstep Perfect 25-mosstep P25ms 5L + 20s 461.5 ¢
26-mosstep Perfect 26-mosstep P26ms 5L + 21s 461.5 ¢ to 480.0 ¢
Augmented 26-mosstep A26ms 6L + 20s 480.0 ¢ to 553.8 ¢
27-mosstep Minor 27-mosstep m27ms 5L + 22s 461.5 ¢ to 498.5 ¢
Major 27-mosstep M27ms 6L + 21s 498.5 ¢ to 553.8 ¢
28-mosstep Minor 28-mosstep m28ms 5L + 23s 461.5 ¢ to 516.9 ¢
Major 28-mosstep M28ms 6L + 22s 516.9 ¢ to 553.8 ¢
29-mosstep Diminished 29-mosstep d29ms 5L + 24s 461.5 ¢ to 535.4 ¢
Perfect 29-mosstep P29ms 6L + 23s 535.4 ¢ to 553.8 ¢
30-mosstep Perfect 30-mosstep P30ms 6L + 24s 553.8 ¢
31-mosstep Perfect 31-mosstep P31ms 6L + 25s 553.8 ¢ to 572.3 ¢
Augmented 31-mosstep A31ms 7L + 24s 572.3 ¢ to 646.2 ¢
32-mosstep Minor 32-mosstep m32ms 6L + 26s 553.8 ¢ to 590.8 ¢
Major 32-mosstep M32ms 7L + 25s 590.8 ¢ to 646.2 ¢
33-mosstep Minor 33-mosstep m33ms 6L + 27s 553.8 ¢ to 609.2 ¢
Major 33-mosstep M33ms 7L + 26s 609.2 ¢ to 646.2 ¢
34-mosstep Diminished 34-mosstep d34ms 6L + 28s 553.8 ¢ to 627.7 ¢
Perfect 34-mosstep P34ms 7L + 27s 627.7 ¢ to 646.2 ¢
35-mosstep Perfect 35-mosstep P35ms 7L + 28s 646.2 ¢
36-mosstep Perfect 36-mosstep P36ms 7L + 29s 646.2 ¢ to 664.6 ¢
Augmented 36-mosstep A36ms 8L + 28s 664.6 ¢ to 738.5 ¢
37-mosstep Minor 37-mosstep m37ms 7L + 30s 646.2 ¢ to 683.1 ¢
Major 37-mosstep M37ms 8L + 29s 683.1 ¢ to 738.5 ¢
38-mosstep Minor 38-mosstep m38ms 7L + 31s 646.2 ¢ to 701.5 ¢
Major 38-mosstep M38ms 8L + 30s 701.5 ¢ to 738.5 ¢
39-mosstep Diminished 39-mosstep d39ms 7L + 32s 646.2 ¢ to 720.0 ¢
Perfect 39-mosstep P39ms 8L + 31s 720.0 ¢ to 738.5 ¢
40-mosstep Perfect 40-mosstep P40ms 8L + 32s 738.5 ¢
41-mosstep Perfect 41-mosstep P41ms 8L + 33s 738.5 ¢ to 756.9 ¢
Augmented 41-mosstep A41ms 9L + 32s 756.9 ¢ to 830.8 ¢
42-mosstep Minor 42-mosstep m42ms 8L + 34s 738.5 ¢ to 775.4 ¢
Major 42-mosstep M42ms 9L + 33s 775.4 ¢ to 830.8 ¢
43-mosstep Minor 43-mosstep m43ms 8L + 35s 738.5 ¢ to 793.8 ¢
Major 43-mosstep M43ms 9L + 34s 793.8 ¢ to 830.8 ¢
44-mosstep Diminished 44-mosstep d44ms 8L + 36s 738.5 ¢ to 812.3 ¢
Perfect 44-mosstep P44ms 9L + 35s 812.3 ¢ to 830.8 ¢
45-mosstep Perfect 45-mosstep P45ms 9L + 36s 830.8 ¢
46-mosstep Perfect 46-mosstep P46ms 9L + 37s 830.8 ¢ to 849.2 ¢
Augmented 46-mosstep A46ms 10L + 36s 849.2 ¢ to 923.1 ¢
47-mosstep Minor 47-mosstep m47ms 9L + 38s 830.8 ¢ to 867.7 ¢
Major 47-mosstep M47ms 10L + 37s 867.7 ¢ to 923.1 ¢
48-mosstep Minor 48-mosstep m48ms 9L + 39s 830.8 ¢ to 886.2 ¢
Major 48-mosstep M48ms 10L + 38s 886.2 ¢ to 923.1 ¢
49-mosstep Diminished 49-mosstep d49ms 9L + 40s 830.8 ¢ to 904.6 ¢
Perfect 49-mosstep P49ms 10L + 39s 904.6 ¢ to 923.1 ¢
50-mosstep Perfect 50-mosstep P50ms 10L + 40s 923.1 ¢
51-mosstep Perfect 51-mosstep P51ms 10L + 41s 923.1 ¢ to 941.5 ¢
Augmented 51-mosstep A51ms 11L + 40s 941.5 ¢ to 1015.4 ¢
52-mosstep Minor 52-mosstep m52ms 10L + 42s 923.1 ¢ to 960.0 ¢
Major 52-mosstep M52ms 11L + 41s 960.0 ¢ to 1015.4 ¢
53-mosstep Minor 53-mosstep m53ms 10L + 43s 923.1 ¢ to 978.5 ¢
Major 53-mosstep M53ms 11L + 42s 978.5 ¢ to 1015.4 ¢
54-mosstep Diminished 54-mosstep d54ms 10L + 44s 923.1 ¢ to 996.9 ¢
Perfect 54-mosstep P54ms 11L + 43s 996.9 ¢ to 1015.4 ¢
55-mosstep Perfect 55-mosstep P55ms 11L + 44s 1015.4 ¢
56-mosstep Perfect 56-mosstep P56ms 11L + 45s 1015.4 ¢ to 1033.8 ¢
Augmented 56-mosstep A56ms 12L + 44s 1033.8 ¢ to 1107.7 ¢
57-mosstep Minor 57-mosstep m57ms 11L + 46s 1015.4 ¢ to 1052.3 ¢
Major 57-mosstep M57ms 12L + 45s 1052.3 ¢ to 1107.7 ¢
58-mosstep Minor 58-mosstep m58ms 11L + 47s 1015.4 ¢ to 1070.8 ¢
Major 58-mosstep M58ms 12L + 46s 1070.8 ¢ to 1107.7 ¢
59-mosstep Diminished 59-mosstep d59ms 11L + 48s 1015.4 ¢ to 1089.2 ¢
Perfect 59-mosstep P59ms 12L + 47s 1089.2 ¢ to 1107.7 ¢
60-mosstep Perfect 60-mosstep P60ms 12L + 48s 1107.7 ¢
61-mosstep Perfect 61-mosstep P61ms 12L + 49s 1107.7 ¢ to 1126.2 ¢
Augmented 61-mosstep A61ms 13L + 48s 1126.2 ¢ to 1200.0 ¢
62-mosstep Minor 62-mosstep m62ms 12L + 50s 1107.7 ¢ to 1144.6 ¢
Major 62-mosstep M62ms 13L + 49s 1144.6 ¢ to 1200.0 ¢
63-mosstep Minor 63-mosstep m63ms 12L + 51s 1107.7 ¢ to 1163.1 ¢
Major 63-mosstep M63ms 13L + 50s 1163.1 ¢ to 1200.0 ¢
64-mosstep Diminished 64-mosstep d64ms 12L + 52s 1107.7 ¢ to 1181.5 ¢
Perfect 64-mosstep P64ms 13L + 51s 1181.5 ¢ to 1200.0 ¢
65-mosstep Perfect 65-mosstep P65ms 13L + 52s 1200.0 ¢
Harmonic entropy info for 13L 52s
Interval Range in cents Average of HE
(from HE Calc)		 Min of HE
Perfect 0-mosstep 0.0 ¢ ~2.4654 nats ~2.4654 nats
Perfect 1-mosstep 0.0 ¢ to 18.5 ¢ ~3.1769 nats ~2.8939 nats
Augmented 1-mosstep 18.5 ¢ to 92.3 ¢ ~4.3816 nats ~3.8895 nats
Minor 2-mosstep 0.0 ¢ to 36.9 ¢ ~4.3347 nats ~3.8895 nats
Major 2-mosstep 36.9 ¢ to 92.3 ¢ ~4.7786 nats ~4.7292 nats
Minor 3-mosstep 0.0 ¢ to 55.4 ¢ ~4.7516 nats ~4.5802 nats
Major 3-mosstep 55.4 ¢ to 92.3 ¢ ~4.7801 nats ~4.7560 nats
Diminished 4-mosstep 0.0 ¢ to 73.8 ¢ ~4.7813 nats ~4.7560 nats
Perfect 4-mosstep 73.8 ¢ to 92.3 ¢ ~4.7292 nats ~4.7189 nats
Perfect 5-mosstep 92.3 ¢ ~4.6898 nats ~4.6898 nats
Perfect 6-mosstep 92.3 ¢ to 110.8 ¢ ~4.6665 nats ~4.6638 nats
Augmented 6-mosstep 110.8 ¢ to 184.6 ¢ ~4.6471 nats ~4.6333 nats
Minor 7-mosstep 92.3 ¢ to 129.2 ¢ ~4.6496 nats ~4.6443 nats
Major 7-mosstep 129.2 ¢ to 184.6 ¢ ~4.6322 nats ~4.6233 nats
Minor 8-mosstep 92.3 ¢ to 147.7 ¢ ~4.6346 nats ~4.6284 nats
Major 8-mosstep 147.7 ¢ to 184.6 ¢ ~4.6189 nats ~4.6124 nats
Diminished 9-mosstep 92.3 ¢ to 166.2 ¢ ~4.6211 nats ~4.6124 nats
Perfect 9-mosstep 166.2 ¢ to 184.6 ¢ ~4.6053 nats ~4.6025 nats
Perfect 10-mosstep 184.6 ¢ ~4.5938 nats ~4.5938 nats
Perfect 11-mosstep 184.6 ¢ to 203.1 ¢ ~4.5856 nats ~4.5850 nats
Augmented 11-mosstep 203.1 ¢ to 276.9 ¢ ~4.5843 nats ~4.5840 nats
Minor 12-mosstep 184.6 ¢ to 221.5 ¢ ~4.5843 nats ~4.5841 nats
Major 12-mosstep 221.5 ¢ to 276.9 ¢ ~4.5850 nats ~4.5841 nats
Minor 13-mosstep 184.6 ¢ to 240.0 ¢ ~4.5849 nats ~4.5840 nats
Major 13-mosstep 240.0 ¢ to 276.9 ¢ ~4.5839 nats ~4.5779 nats
Diminished 14-mosstep 184.6 ¢ to 258.5 ¢ ~4.5833 nats ~4.5779 nats
Perfect 14-mosstep 258.5 ¢ to 276.9 ¢ ~4.5674 nats ~4.5642 nats
Perfect 15-mosstep 276.9 ¢ ~4.5696 nats ~4.5696 nats
Perfect 16-mosstep 276.9 ¢ to 295.4 ¢ ~4.5792 nats ~4.5771 nats
Augmented 16-mosstep 295.4 ¢ to 369.2 ¢ ~4.5504 nats ~4.5382 nats
Minor 17-mosstep 276.9 ¢ to 313.8 ¢ ~4.5492 nats ~4.5399 nats
Major 17-mosstep 313.8 ¢ to 369.2 ¢ ~4.5554 nats ~4.5388 nats
Minor 18-mosstep 276.9 ¢ to 332.3 ¢ ~4.5505 nats ~4.5382 nats
Major 18-mosstep 332.3 ¢ to 369.2 ¢ ~4.6013 nats ~4.5877 nats
Diminished 19-mosstep 276.9 ¢ to 350.8 ¢ ~4.5920 nats ~4.5488 nats
Perfect 19-mosstep 350.8 ¢ to 369.2 ¢ ~4.6173 nats ~4.6120 nats
Perfect 20-mosstep 369.2 ¢ ~4.5624 nats ~4.5624 nats
Perfect 21-mosstep 369.2 ¢ to 387.7 ¢ ~4.4892 nats ~4.4849 nats
Augmented 21-mosstep 387.7 ¢ to 461.5 ¢ ~4.5355 nats ~4.4916 nats
Minor 22-mosstep 369.2 ¢ to 406.2 ¢ ~4.5231 nats ~4.4916 nats
Major 22-mosstep 406.2 ¢ to 461.5 ¢ ~4.5944 nats ~4.5778 nats
Minor 23-mosstep 369.2 ¢ to 424.6 ¢ ~4.5881 nats ~4.5482 nats
Major 23-mosstep 424.6 ¢ to 461.5 ¢ ~4.6021 nats ~4.6003 nats
Diminished 24-mosstep 369.2 ¢ to 443.1 ¢ ~4.6014 nats ~4.5972 nats
Perfect 24-mosstep 443.1 ¢ to 461.5 ¢ ~4.6072 nats ~4.6044 nats
Perfect 25-mosstep 461.5 ¢ ~4.6179 nats ~4.6179 nats
Perfect 26-mosstep 461.5 ¢ to 480.0 ¢ ~4.5462 nats ~4.5248 nats
Augmented 26-mosstep 480.0 ¢ to 553.8 ¢ ~4.4086 nats ~4.3680 nats
Minor 27-mosstep 461.5 ¢ to 498.5 ¢ ~4.4023 nats ~4.3705 nats
Major 27-mosstep 498.5 ¢ to 553.8 ¢ ~4.4275 nats ~4.3711 nats
Minor 28-mosstep 461.5 ¢ to 516.9 ¢ ~4.4112 nats ~4.3686 nats
Major 28-mosstep 516.9 ¢ to 553.8 ¢ ~4.5700 nats ~4.5307 nats
Diminished 29-mosstep 461.5 ¢ to 535.4 ¢ ~4.5410 nats ~4.4076 nats
Perfect 29-mosstep 535.4 ¢ to 553.8 ¢ ~4.6305 nats ~4.6291 nats
Perfect 30-mosstep 553.8 ¢ ~4.6181 nats ~4.6181 nats
Perfect 31-mosstep 553.8 ¢ to 572.3 ¢ ~4.5854 nats ~4.5795 nats
Augmented 31-mosstep 572.3 ¢ to 646.2 ¢ ~4.5659 nats ~4.5596 nats
Minor 32-mosstep 553.8 ¢ to 590.8 ¢ ~4.5615 nats ~4.5596 nats
Major 32-mosstep 590.8 ¢ to 646.2 ¢ ~4.5811 nats ~4.5694 nats
Minor 33-mosstep 553.8 ¢ to 609.2 ¢ ~4.5776 nats ~4.5614 nats
Major 33-mosstep 609.2 ¢ to 646.2 ¢ ~4.5979 nats ~4.5951 nats
Diminished 34-mosstep 553.8 ¢ to 627.7 ¢ ~4.5948 nats ~4.5799 nats
Perfect 34-mosstep 627.7 ¢ to 646.2 ¢ ~4.6085 nats ~4.6059 nats
Perfect 35-mosstep 646.2 ¢ ~4.6329 nats ~4.6329 nats
Perfect 36-mosstep 646.2 ¢ to 664.6 ¢ ~4.6519 nats ~4.6498 nats
Augmented 36-mosstep 664.6 ¢ to 738.5 ¢ ~4.4930 nats ~4.2378 nats
Minor 37-mosstep 646.2 ¢ to 683.1 ¢ ~4.5487 nats ~4.4795 nats
Major 37-mosstep 683.1 ¢ to 738.5 ¢ ~4.2367 nats ~4.1228 nats
Minor 38-mosstep 646.2 ¢ to 701.5 ¢ ~4.2732 nats ~4.1486 nats
Major 38-mosstep 701.5 ¢ to 738.5 ¢ ~4.1688 nats ~4.1228 nats
Diminished 39-mosstep 646.2 ¢ to 720.0 ¢ ~4.1919 nats ~4.1219 nats
Perfect 39-mosstep 720.0 ¢ to 738.5 ¢ ~4.4434 nats ~4.3959 nats
Perfect 40-mosstep 738.5 ¢ ~4.6332 nats ~4.6332 nats
Perfect 41-mosstep 738.5 ¢ to 756.9 ¢ ~4.6420 nats ~4.6380 nats
Augmented 41-mosstep 756.9 ¢ to 830.8 ¢ ~4.6155 nats ~4.6034 nats
Minor 42-mosstep 738.5 ¢ to 775.4 ¢ ~4.6172 nats ~4.6114 nats
Major 42-mosstep 775.4 ¢ to 830.8 ¢ ~4.6016 nats ~4.5914 nats
Minor 43-mosstep 738.5 ¢ to 793.8 ¢ ~4.6040 nats ~4.5985 nats
Major 43-mosstep 793.8 ¢ to 830.8 ¢ ~4.5844 nats ~4.5747 nats
Diminished 44-mosstep 738.5 ¢ to 812.3 ¢ ~4.5873 nats ~4.5747 nats
Perfect 44-mosstep 812.3 ¢ to 830.8 ¢ ~4.5715 nats ~4.5709 nats
Perfect 45-mosstep 830.8 ¢ ~4.5928 nats ~4.5928 nats
Perfect 46-mosstep 830.8 ¢ to 849.2 ¢ ~4.6143 nats ~4.6125 nats
Augmented 46-mosstep 849.2 ¢ to 923.1 ¢ ~4.5510 nats ~4.4505 nats
Minor 47-mosstep 830.8 ¢ to 867.7 ¢ ~4.5730 nats ~4.5438 nats
Major 47-mosstep 867.7 ¢ to 923.1 ¢ ~4.4537 nats ~4.4218 nats
Minor 48-mosstep 830.8 ¢ to 886.2 ¢ ~4.4658 nats ~4.4235 nats
Major 48-mosstep 886.2 ¢ to 923.1 ¢ ~4.4498 nats ~4.4244 nats
Diminished 49-mosstep 830.8 ¢ to 904.6 ¢ ~4.4541 nats ~4.4218 nats
Perfect 49-mosstep 904.6 ¢ to 923.1 ¢ ~4.5616 nats ~4.5454 nats
Perfect 50-mosstep 923.1 ¢ ~4.6161 nats ~4.6161 nats
Perfect 51-mosstep 923.1 ¢ to 941.5 ¢ ~4.6104 nats ~4.6073 nats
Augmented 51-mosstep 941.5 ¢ to 1015.4 ¢ ~4.5667 nats ~4.5308 nats
Minor 52-mosstep 923.1 ¢ to 960.0 ¢ ~4.5737 nats ~4.5577 nats
Major 52-mosstep 960.0 ¢ to 1015.4 ¢ ~4.5363 nats ~4.5308 nats
Minor 53-mosstep 923.1 ¢ to 978.5 ¢ ~4.5374 nats ~4.5306 nats
Major 53-mosstep 978.5 ¢ to 1015.4 ¢ ~4.5610 nats ~4.5471 nats
Diminished 54-mosstep 923.1 ¢ to 996.9 ¢ ~4.5562 nats ~4.5308 nats
Perfect 54-mosstep 996.9 ¢ to 1015.4 ¢ ~4.5870 nats ~4.5863 nats
Perfect 55-mosstep 1015.4 ¢ ~4.5784 nats ~4.5784 nats
Perfect 56-mosstep 1015.4 ¢ to 1033.8 ¢ ~4.5896 nats ~4.5849 nats
Augmented 56-mosstep 1033.8 ¢ to 1107.7 ¢ ~4.6052 nats ~4.6004 nats
Minor 57-mosstep 1015.4 ¢ to 1052.3 ¢ ~4.6053 nats ~4.6004 nats
Major 57-mosstep 1052.3 ¢ to 1107.7 ¢ ~4.6079 nats ~4.6077 nats
Minor 58-mosstep 1015.4 ¢ to 1070.8 ¢ ~4.6078 nats ~4.6074 nats
Major 58-mosstep 1070.8 ¢ to 1107.7 ¢ ~4.6087 nats ~4.6080 nats
Diminished 59-mosstep 1015.4 ¢ to 1089.2 ¢ ~4.6086 nats ~4.6078 nats
Perfect 59-mosstep 1089.2 ¢ to 1107.7 ¢ ~4.6133 nats ~4.6121 nats
Perfect 60-mosstep 1107.7 ¢ ~4.6254 nats ~4.6254 nats
Perfect 61-mosstep 1107.7 ¢ to 1126.2 ¢ ~4.6497 nats ~4.6428 nats
Augmented 61-mosstep 1126.2 ¢ to 1200.0 ¢ ~4.6968 nats ~4.6693 nats
Minor 62-mosstep 1107.7 ¢ to 1144.6 ¢ ~4.6904 nats ~4.6693 nats
Major 62-mosstep 1144.6 ¢ to 1200.0 ¢ ~4.7137 nats ~4.6550 nats
Minor 63-mosstep 1107.7 ¢ to 1163.1 ¢ ~4.7210 nats ~4.7055 nats
Major 63-mosstep 1163.1 ¢ to 1200.0 ¢ ~4.5371 nats ~4.3119 nats
Diminished 64-mosstep 1107.7 ¢ to 1181.5 ¢ ~4.5529 nats ~4.3119 nats
Perfect 64-mosstep 1181.5 ¢ to 1200.0 ¢ ~3.8919 nats ~3.7059 nats
Perfect 65-mosstep 1200.0 ¢ ~3.3273 nats ~3.3273 nats
Simple Tunings of 13L 52s
Scale degree Abbrev. Basic (2:1)
78edo 		Hard (3:1)
91edo 		Soft (3:2)
143edo
Steps ¢ Steps ¢ Steps ¢
Perfect 0-mosdegree P0md 0\78 0.0 0\91 0.0 0\143 0.0
Perfect 1-mosdegree P1md 1\78 15.4 1\91 13.2 2\143 16.8
Augmented 1-mosdegree A1md 2\78 30.8 3\91 39.6 3\143 25.2
Minor 2-mosdegree m2md 2\78 30.8 2\91 26.4 4\143 33.6
Major 2-mosdegree M2md 3\78 46.2 4\91 52.7 5\143 42.0
Minor 3-mosdegree m3md 3\78 46.2 3\91 39.6 6\143 50.3
Major 3-mosdegree M3md 4\78 61.5 5\91 65.9 7\143 58.7
Diminished 4-mosdegree d4md 4\78 61.5 4\91 52.7 8\143 67.1
Perfect 4-mosdegree P4md 5\78 76.9 6\91 79.1 9\143 75.5
Perfect 5-mosdegree P5md 6\78 92.3 7\91 92.3 11\143 92.3
Perfect 6-mosdegree P6md 7\78 107.7 8\91 105.5 13\143 109.1
Augmented 6-mosdegree A6md 8\78 123.1 10\91 131.9 14\143 117.5
Minor 7-mosdegree m7md 8\78 123.1 9\91 118.7 15\143 125.9
Major 7-mosdegree M7md 9\78 138.5 11\91 145.1 16\143 134.3
Minor 8-mosdegree m8md 9\78 138.5 10\91 131.9 17\143 142.7
Major 8-mosdegree M8md 10\78 153.8 12\91 158.2 18\143 151.0
Diminished 9-mosdegree d9md 10\78 153.8 11\91 145.1 19\143 159.4
Perfect 9-mosdegree P9md 11\78 169.2 13\91 171.4 20\143 167.8
Perfect 10-mosdegree P10md 12\78 184.6 14\91 184.6 22\143 184.6
Perfect 11-mosdegree P11md 13\78 200.0 15\91 197.8 24\143 201.4
Augmented 11-mosdegree A11md 14\78 215.4 17\91 224.2 25\143 209.8
Minor 12-mosdegree m12md 14\78 215.4 16\91 211.0 26\143 218.2
Major 12-mosdegree M12md 15\78 230.8 18\91 237.4 27\143 226.6
Minor 13-mosdegree m13md 15\78 230.8 17\91 224.2 28\143 235.0
Major 13-mosdegree M13md 16\78 246.2 19\91 250.5 29\143 243.4
Diminished 14-mosdegree d14md 16\78 246.2 18\91 237.4 30\143 251.7
Perfect 14-mosdegree P14md 17\78 261.5 20\91 263.7 31\143 260.1
Perfect 15-mosdegree P15md 18\78 276.9 21\91 276.9 33\143 276.9
Perfect 16-mosdegree P16md 19\78 292.3 22\91 290.1 35\143 293.7
Augmented 16-mosdegree A16md 20\78 307.7 24\91 316.5 36\143 302.1
Minor 17-mosdegree m17md 20\78 307.7 23\91 303.3 37\143 310.5
Major 17-mosdegree M17md 21\78 323.1 25\91 329.7 38\143 318.9
Minor 18-mosdegree m18md 21\78 323.1 24\91 316.5 39\143 327.3
Major 18-mosdegree M18md 22\78 338.5 26\91 342.9 40\143 335.7
Diminished 19-mosdegree d19md 22\78 338.5 25\91 329.7 41\143 344.1
Perfect 19-mosdegree P19md 23\78 353.8 27\91 356.0 42\143 352.4
Perfect 20-mosdegree P20md 24\78 369.2 28\91 369.2 44\143 369.2
Perfect 21-mosdegree P21md 25\78 384.6 29\91 382.4 46\143 386.0
Augmented 21-mosdegree A21md 26\78 400.0 31\91 408.8 47\143 394.4
Minor 22-mosdegree m22md 26\78 400.0 30\91 395.6 48\143 402.8
Major 22-mosdegree M22md 27\78 415.4 32\91 422.0 49\143 411.2
Minor 23-mosdegree m23md 27\78 415.4 31\91 408.8 50\143 419.6
Major 23-mosdegree M23md 28\78 430.8 33\91 435.2 51\143 428.0
Diminished 24-mosdegree d24md 28\78 430.8 32\91 422.0 52\143 436.4
Perfect 24-mosdegree P24md 29\78 446.2 34\91 448.4 53\143 444.8
Perfect 25-mosdegree P25md 30\78 461.5 35\91 461.5 55\143 461.5
Perfect 26-mosdegree P26md 31\78 476.9 36\91 474.7 57\143 478.3
Augmented 26-mosdegree A26md 32\78 492.3 38\91 501.1 58\143 486.7
Minor 27-mosdegree m27md 32\78 492.3 37\91 487.9 59\143 495.1
Major 27-mosdegree M27md 33\78 507.7 39\91 514.3 60\143 503.5
Minor 28-mosdegree m28md 33\78 507.7 38\91 501.1 61\143 511.9
Major 28-mosdegree M28md 34\78 523.1 40\91 527.5 62\143 520.3
Diminished 29-mosdegree d29md 34\78 523.1 39\91 514.3 63\143 528.7
Perfect 29-mosdegree P29md 35\78 538.5 41\91 540.7 64\143 537.1
Perfect 30-mosdegree P30md 36\78 553.8 42\91 553.8 66\143 553.8
Perfect 31-mosdegree P31md 37\78 569.2 43\91 567.0 68\143 570.6
Augmented 31-mosdegree A31md 38\78 584.6 45\91 593.4 69\143 579.0
Minor 32-mosdegree m32md 38\78 584.6 44\91 580.2 70\143 587.4
Major 32-mosdegree M32md 39\78 600.0 46\91 606.6 71\143 595.8
Minor 33-mosdegree m33md 39\78 600.0 45\91 593.4 72\143 604.2
Major 33-mosdegree M33md 40\78 615.4 47\91 619.8 73\143 612.6
Diminished 34-mosdegree d34md 40\78 615.4 46\91 606.6 74\143 621.0
Perfect 34-mosdegree P34md 41\78 630.8 48\91 633.0 75\143 629.4
Perfect 35-mosdegree P35md 42\78 646.2 49\91 646.2 77\143 646.2
Perfect 36-mosdegree P36md 43\78 661.5 50\91 659.3 79\143 662.9
Augmented 36-mosdegree A36md 44\78 676.9 52\91 685.7 80\143 671.3
Minor 37-mosdegree m37md 44\78 676.9 51\91 672.5 81\143 679.7
Major 37-mosdegree M37md 45\78 692.3 53\91 698.9 82\143 688.1
Minor 38-mosdegree m38md 45\78 692.3 52\91 685.7 83\143 696.5
Major 38-mosdegree M38md 46\78 707.7 54\91 712.1 84\143 704.9
Diminished 39-mosdegree d39md 46\78 707.7 53\91 698.9 85\143 713.3
Perfect 39-mosdegree P39md 47\78 723.1 55\91 725.3 86\143 721.7
Perfect 40-mosdegree P40md 48\78 738.5 56\91 738.5 88\143 738.5
Perfect 41-mosdegree P41md 49\78 753.8 57\91 751.6 90\143 755.2
Augmented 41-mosdegree A41md 50\78 769.2 59\91 778.0 91\143 763.6
Minor 42-mosdegree m42md 50\78 769.2 58\91 764.8 92\143 772.0
Major 42-mosdegree M42md 51\78 784.6 60\91 791.2 93\143 780.4
Minor 43-mosdegree m43md 51\78 784.6 59\91 778.0 94\143 788.8
Major 43-mosdegree M43md 52\78 800.0 61\91 804.4 95\143 797.2
Diminished 44-mosdegree d44md 52\78 800.0 60\91 791.2 96\143 805.6
Perfect 44-mosdegree P44md 53\78 815.4 62\91 817.6 97\143 814.0
Perfect 45-mosdegree P45md 54\78 830.8 63\91 830.8 99\143 830.8
Perfect 46-mosdegree P46md 55\78 846.2 64\91 844.0 101\143 847.6
Augmented 46-mosdegree A46md 56\78 861.5 66\91 870.3 102\143 855.9
Minor 47-mosdegree m47md 56\78 861.5 65\91 857.1 103\143 864.3
Major 47-mosdegree M47md 57\78 876.9 67\91 883.5 104\143 872.7
Minor 48-mosdegree m48md 57\78 876.9 66\91 870.3 105\143 881.1
Major 48-mosdegree M48md 58\78 892.3 68\91 896.7 106\143 889.5
Diminished 49-mosdegree d49md 58\78 892.3 67\91 883.5 107\143 897.9
Perfect 49-mosdegree P49md 59\78 907.7 69\91 909.9 108\143 906.3
Perfect 50-mosdegree P50md 60\78 923.1 70\91 923.1 110\143 923.1
Perfect 51-mosdegree P51md 61\78 938.5 71\91 936.3 112\143 939.9
Augmented 51-mosdegree A51md 62\78 953.8 73\91 962.6 113\143 948.3
Minor 52-mosdegree m52md 62\78 953.8 72\91 949.5 114\143 956.6
Major 52-mosdegree M52md 63\78 969.2 74\91 975.8 115\143 965.0
Minor 53-mosdegree m53md 63\78 969.2 73\91 962.6 116\143 973.4
Major 53-mosdegree M53md 64\78 984.6 75\91 989.0 117\143 981.8
Diminished 54-mosdegree d54md 64\78 984.6 74\91 975.8 118\143 990.2
Perfect 54-mosdegree P54md 65\78 1000.0 76\91 1002.2 119\143 998.6
Perfect 55-mosdegree P55md 66\78 1015.4 77\91 1015.4 121\143 1015.4
Perfect 56-mosdegree P56md 67\78 1030.8 78\91 1028.6 123\143 1032.2
Augmented 56-mosdegree A56md 68\78 1046.2 80\91 1054.9 124\143 1040.6
Minor 57-mosdegree m57md 68\78 1046.2 79\91 1041.8 125\143 1049.0
Major 57-mosdegree M57md 69\78 1061.5 81\91 1068.1 126\143 1057.3
Minor 58-mosdegree m58md 69\78 1061.5 80\91 1054.9 127\143 1065.7
Major 58-mosdegree M58md 70\78 1076.9 82\91 1081.3 128\143 1074.1
Diminished 59-mosdegree d59md 70\78 1076.9 81\91 1068.1 129\143 1082.5
Perfect 59-mosdegree P59md 71\78 1092.3 83\91 1094.5 130\143 1090.9
Perfect 60-mosdegree P60md 72\78 1107.7 84\91 1107.7 132\143 1107.7
Perfect 61-mosdegree P61md 73\78 1123.1 85\91 1120.9 134\143 1124.5
Augmented 61-mosdegree A61md 74\78 1138.5 87\91 1147.3 135\143 1132.9
Minor 62-mosdegree m62md 74\78 1138.5 86\91 1134.1 136\143 1141.3
Major 62-mosdegree M62md 75\78 1153.8 88\91 1160.4 137\143 1149.7
Minor 63-mosdegree m63md 75\78 1153.8 87\91 1147.3 138\143 1158.0
Major 63-mosdegree M63md 76\78 1169.2 89\91 1173.6 139\143 1166.4
Diminished 64-mosdegree d64md 76\78 1169.2 88\91 1160.4 140\143 1174.8
Perfect 64-mosdegree P64md 77\78 1184.6 90\91 1186.8 141\143 1183.2
Perfect 65-mosdegree P65md 78\78 1200.0 91\91 1200.0 143\143 1200.0
Generator chain of 13L 52s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
5 Augmented 0-mosdegree A0md Augmented 5-mosdegree A5md Augmented 10-mosdegree A10md Augmented 15-mosdegree A15md Augmented 20-mosdegree A20md Augmented 25-mosdegree A25md Augmented 30-mosdegree A30md Augmented 35-mosdegree A35md Augmented 40-mosdegree A40md Augmented 45-mosdegree A45md Augmented 50-mosdegree A50md Augmented 55-mosdegree A55md Augmented 60-mosdegree A60md
4 Augmented 1-mosdegree A1md Augmented 6-mosdegree A6md Augmented 11-mosdegree A11md Augmented 16-mosdegree A16md Augmented 21-mosdegree A21md Augmented 26-mosdegree A26md Augmented 31-mosdegree A31md Augmented 36-mosdegree A36md Augmented 41-mosdegree A41md Augmented 46-mosdegree A46md Augmented 51-mosdegree A51md Augmented 56-mosdegree A56md Augmented 61-mosdegree A61md
3 Major 2-mosdegree M2md Major 7-mosdegree M7md Major 12-mosdegree M12md Major 17-mosdegree M17md Major 22-mosdegree M22md Major 27-mosdegree M27md Major 32-mosdegree M32md Major 37-mosdegree M37md Major 42-mosdegree M42md Major 47-mosdegree M47md Major 52-mosdegree M52md Major 57-mosdegree M57md Major 62-mosdegree M62md
2 Major 3-mosdegree M3md Major 8-mosdegree M8md Major 13-mosdegree M13md Major 18-mosdegree M18md Major 23-mosdegree M23md Major 28-mosdegree M28md Major 33-mosdegree M33md Major 38-mosdegree M38md Major 43-mosdegree M43md Major 48-mosdegree M48md Major 53-mosdegree M53md Major 58-mosdegree M58md Major 63-mosdegree M63md
1 Perfect 4-mosdegree P4md Perfect 9-mosdegree P9md Perfect 14-mosdegree P14md Perfect 19-mosdegree P19md Perfect 24-mosdegree P24md Perfect 29-mosdegree P29md Perfect 34-mosdegree P34md Perfect 39-mosdegree P39md Perfect 44-mosdegree P44md Perfect 49-mosdegree P49md Perfect 54-mosdegree P54md Perfect 59-mosdegree P59md Perfect 64-mosdegree P64md
0 Perfect 0-mosdegree
Perfect 5-mosdegree		 P0md
P5md		 Perfect 5-mosdegree
Perfect 10-mosdegree		 P5md
P10md		 Perfect 10-mosdegree
Perfect 15-mosdegree		 P10md
P15md		 Perfect 15-mosdegree
Perfect 20-mosdegree		 P15md
P20md		 Perfect 20-mosdegree
Perfect 25-mosdegree		 P20md
P25md		 Perfect 25-mosdegree
Perfect 30-mosdegree		 P25md
P30md		 Perfect 30-mosdegree
Perfect 35-mosdegree		 P30md
P35md		 Perfect 35-mosdegree
Perfect 40-mosdegree		 P35md
P40md		 Perfect 40-mosdegree
Perfect 45-mosdegree		 P40md
P45md		 Perfect 45-mosdegree
Perfect 50-mosdegree		 P45md
P50md		 Perfect 50-mosdegree
Perfect 55-mosdegree		 P50md
P55md		 Perfect 55-mosdegree
Perfect 60-mosdegree		 P55md
P60md		 Perfect 60-mosdegree
Perfect 65-mosdegree		 P60md
P65md
−1 Perfect 1-mosdegree P1md Perfect 6-mosdegree P6md Perfect 11-mosdegree P11md Perfect 16-mosdegree P16md Perfect 21-mosdegree P21md Perfect 26-mosdegree P26md Perfect 31-mosdegree P31md Perfect 36-mosdegree P36md Perfect 41-mosdegree P41md Perfect 46-mosdegree P46md Perfect 51-mosdegree P51md Perfect 56-mosdegree P56md Perfect 61-mosdegree P61md
−2 Minor 2-mosdegree m2md Minor 7-mosdegree m7md Minor 12-mosdegree m12md Minor 17-mosdegree m17md Minor 22-mosdegree m22md Minor 27-mosdegree m27md Minor 32-mosdegree m32md Minor 37-mosdegree m37md Minor 42-mosdegree m42md Minor 47-mosdegree m47md Minor 52-mosdegree m52md Minor 57-mosdegree m57md Minor 62-mosdegree m62md
−3 Minor 3-mosdegree m3md Minor 8-mosdegree m8md Minor 13-mosdegree m13md Minor 18-mosdegree m18md Minor 23-mosdegree m23md Minor 28-mosdegree m28md Minor 33-mosdegree m33md Minor 38-mosdegree m38md Minor 43-mosdegree m43md Minor 48-mosdegree m48md Minor 53-mosdegree m53md Minor 58-mosdegree m58md Minor 63-mosdegree m63md
−4 Diminished 4-mosdegree d4md Diminished 9-mosdegree d9md Diminished 14-mosdegree d14md Diminished 19-mosdegree d19md Diminished 24-mosdegree d24md Diminished 29-mosdegree d29md Diminished 34-mosdegree d34md Diminished 39-mosdegree d39md Diminished 44-mosdegree d44md Diminished 49-mosdegree d49md Diminished 54-mosdegree d54md Diminished 59-mosdegree d59md Diminished 64-mosdegree d64md
−5 Diminished 5-mosdegree d5md Diminished 10-mosdegree d10md Diminished 15-mosdegree d15md Diminished 20-mosdegree d20md Diminished 25-mosdegree d25md Diminished 30-mosdegree d30md Diminished 35-mosdegree d35md Diminished 40-mosdegree d40md Diminished 45-mosdegree d45md Diminished 50-mosdegree d50md Diminished 55-mosdegree d55md Diminished 60-mosdegree d60md Diminished 65-mosdegree d65md
Modes of 13L 52s
UDP Cyclic
order		 Step
pattern
52|0(13) 1 LssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssss
39|13(13) 5 sLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLsss
26|26(13) 4 ssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLss
13|39(13) 3 sssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLs
0|52(13) 2 ssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssLssssL

Scale tree

Scale tree and tuning spectrum of 13L 52s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\65 73.846 18.462 1:1 1.000 Equalized 13L 52s
21\338 74.556 17.751 6:5 1.200
17\273 74.725 17.582 5:4 1.250
30\481 74.844 17.464 9:7 1.286
13\208 75.000 17.308 4:3 1.333 Supersoft 13L 52s
35\559 75.134 17.174 11:8 1.375
22\351 75.214 17.094 7:5 1.400
31\494 75.304 17.004 10:7 1.429
9\143 75.524 16.783 3:2 1.500 Soft 13L 52s
32\507 75.740 16.568 11:7 1.571
23\364 75.824 16.484 8:5 1.600
37\585 75.897 16.410 13:8 1.625
14\221 76.018 16.290 5:3 1.667 Semisoft 13L 52s
33\520 76.154 16.154 12:7 1.714
19\299 76.254 16.054 7:4 1.750
24\377 76.393 15.915 9:5 1.800
5\78 76.923 15.385 2:1 2.000 Basic 13L 52s
Scales with tunings softer than this are proper
21\325 77.538 14.769 9:4 2.250
16\247 77.733 14.575 7:3 2.333
27\416 77.885 14.423 12:5 2.400
11\169 78.107 14.201 5:2 2.500 Semihard 13L 52s
28\429 78.322 13.986 13:5 2.600
17\260 78.462 13.846 8:3 2.667
23\351 78.632 13.675 11:4 2.750
6\91 79.121 13.187 3:1 3.000 Hard 13L 52s
19\286 79.720 12.587 10:3 3.333
13\195 80.000 12.308 7:2 3.500
20\299 80.268 12.040 11:3 3.667
7\104 80.769 11.538 4:1 4.000 Superhard 13L 52s
15\221 81.448 10.860 9:2 4.500
8\117 82.051 10.256 5:1 5.000
9\130 83.077 9.231 6:1 6.000
1\13 92.308 0.000 1:0 → ∞ Collapsed 13L 52s
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