13L 9s
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Step pattern
LLsLsLLsLsLLsLsLLsLsLs
sLsLsLLsLsLLsLsLLsLsLL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
5\22 to 3\13 (272.7 ¢ to 276.9 ¢)
Dark
10\13 to 17\22 (923.1 ¢ to 927.3 ¢)
Descends from
4L 5s (gramitonic)
Ancestor's step ratio range
3:2 to 2:1 (hyposoft)
Parent
9L 4s
Sister
9L 13s
Daughters
22L 13s, 13L 22s
Neutralized
4L 18s
2-Flought
35L 9s, 13L 31s
Equalized (L:s = 1:1)
5\22 (272.7 ¢)
Supersoft (L:s = 4:3)
18\79 (273.4 ¢)
Soft (L:s = 3:2)
13\57 (273.7 ¢)
Semisoft (L:s = 5:3)
21\92 (273.9 ¢)
Basic (L:s = 2:1)
8\35 (274.3 ¢)
Semihard (L:s = 5:2)
19\83 (274.7 ¢)
Hard (L:s = 3:1)
11\48 (275.0 ¢)
Superhard (L:s = 4:1)
14\61 (275.4 ¢)
Collapsed (L:s = 1:0)
3\13 (276.9 ¢)
| ↖ 12L 8s | ↑ 13L 8s | 14L 8s ↗ |
| ← 12L 9s | 13L 9s | 14L 9s → |
| ↙ 12L 10s | ↓ 13L 10s | 14L 10s ↘ |
┌╥╥┬╥┬╥╥┬╥┬╥╥┬╥┬╥╥┬╥┬╥┬┐ │║║│║│║║│║│║║│║│║║│║│║││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLsLsLLsLsLLsLsLLsLsLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
13L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 9 small steps, repeating every octave. 13L 9s is a grandchild scale of 4L 5s, expanding it by 13 tones. Generators that produce this scale range from 272.7 ¢ to 276.9 ¢, or from 923.1 ¢ to 927.3 ¢.
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0 ¢ |
| 1-mosstep | Minor 1-mosstep | m1ms | s | 0.0 ¢ to 54.5 ¢ |
| Major 1-mosstep | M1ms | L | 54.5 ¢ to 92.3 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 92.3 ¢ to 109.1 ¢ |
| Major 2-mosstep | M2ms | 2L | 109.1 ¢ to 184.6 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 92.3 ¢ to 163.6 ¢ |
| Major 3-mosstep | M3ms | 2L + s | 163.6 ¢ to 184.6 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 184.6 ¢ to 218.2 ¢ |
| Major 4-mosstep | M4ms | 3L + s | 218.2 ¢ to 276.9 ¢ | |
| 5-mosstep | Diminished 5-mosstep | d5ms | 2L + 3s | 184.6 ¢ to 272.7 ¢ |
| Perfect 5-mosstep | P5ms | 3L + 2s | 272.7 ¢ to 276.9 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 276.9 ¢ to 327.3 ¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 327.3 ¢ to 369.2 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 4L + 3s | 369.2 ¢ to 381.8 ¢ |
| Major 7-mosstep | M7ms | 5L + 2s | 381.8 ¢ to 461.5 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 4L + 4s | 369.2 ¢ to 436.4 ¢ |
| Major 8-mosstep | M8ms | 5L + 3s | 436.4 ¢ to 461.5 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 5L + 4s | 461.5 ¢ to 490.9 ¢ |
| Major 9-mosstep | M9ms | 6L + 3s | 490.9 ¢ to 553.8 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 5L + 5s | 461.5 ¢ to 545.5 ¢ |
| Major 10-mosstep | M10ms | 6L + 4s | 545.5 ¢ to 553.8 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 6L + 5s | 553.8 ¢ to 600.0 ¢ |
| Major 11-mosstep | M11ms | 7L + 4s | 600.0 ¢ to 646.2 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 7L + 5s | 646.2 ¢ to 654.5 ¢ |
| Major 12-mosstep | M12ms | 8L + 4s | 654.5 ¢ to 738.5 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 7L + 6s | 646.2 ¢ to 709.1 ¢ |
| Major 13-mosstep | M13ms | 8L + 5s | 709.1 ¢ to 738.5 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 8L + 6s | 738.5 ¢ to 763.6 ¢ |
| Major 14-mosstep | M14ms | 9L + 5s | 763.6 ¢ to 830.8 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 8L + 7s | 738.5 ¢ to 818.2 ¢ |
| Major 15-mosstep | M15ms | 9L + 6s | 818.2 ¢ to 830.8 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 9L + 7s | 830.8 ¢ to 872.7 ¢ |
| Major 16-mosstep | M16ms | 10L + 6s | 872.7 ¢ to 923.1 ¢ | |
| 17-mosstep | Perfect 17-mosstep | P17ms | 10L + 7s | 923.1 ¢ to 927.3 ¢ |
| Augmented 17-mosstep | A17ms | 11L + 6s | 927.3 ¢ to 1015.4 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 10L + 8s | 923.1 ¢ to 981.8 ¢ |
| Major 18-mosstep | M18ms | 11L + 7s | 981.8 ¢ to 1015.4 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 11L + 8s | 1015.4 ¢ to 1036.4 ¢ |
| Major 19-mosstep | M19ms | 12L + 7s | 1036.4 ¢ to 1107.7 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 11L + 9s | 1015.4 ¢ to 1090.9 ¢ |
| Major 20-mosstep | M20ms | 12L + 8s | 1090.9 ¢ to 1107.7 ¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 12L + 9s | 1107.7 ¢ to 1145.5 ¢ |
| Major 21-mosstep | M21ms | 13L + 8s | 1145.5 ¢ to 1200.0 ¢ | |
| 22-mosstep | Perfect 22-mosstep | P22ms | 13L + 9s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 34 | Augmented 16-mosdegree | A16md |
| 33 | Augmented 11-mosdegree | A11md |
| 32 | Augmented 6-mosdegree | A6md |
| 31 | Augmented 1-mosdegree | A1md |
| 30 | Augmented 18-mosdegree | A18md |
| 29 | Augmented 13-mosdegree | A13md |
| 28 | Augmented 8-mosdegree | A8md |
| 27 | Augmented 3-mosdegree | A3md |
| 26 | Augmented 20-mosdegree | A20md |
| 25 | Augmented 15-mosdegree | A15md |
| 24 | Augmented 10-mosdegree | A10md |
| 23 | Augmented 5-mosdegree | A5md |
| 22 | Augmented 0-mosdegree | A0md |
| 21 | Augmented 17-mosdegree | A17md |
| 20 | Major 12-mosdegree | M12md |
| 19 | Major 7-mosdegree | M7md |
| 18 | Major 2-mosdegree | M2md |
| 17 | Major 19-mosdegree | M19md |
| 16 | Major 14-mosdegree | M14md |
| 15 | Major 9-mosdegree | M9md |
| 14 | Major 4-mosdegree | M4md |
| 13 | Major 21-mosdegree | M21md |
| 12 | Major 16-mosdegree | M16md |
| 11 | Major 11-mosdegree | M11md |
| 10 | Major 6-mosdegree | M6md |
| 9 | Major 1-mosdegree | M1md |
| 8 | Major 18-mosdegree | M18md |
| 7 | Major 13-mosdegree | M13md |
| 6 | Major 8-mosdegree | M8md |
| 5 | Major 3-mosdegree | M3md |
| 4 | Major 20-mosdegree | M20md |
| 3 | Major 15-mosdegree | M15md |
| 2 | Major 10-mosdegree | M10md |
| 1 | Perfect 5-mosdegree | P5md |
| 0 | Perfect 0-mosdegree Perfect 22-mosdegree |
P0md P22md |
| −1 | Perfect 17-mosdegree | P17md |
| −2 | Minor 12-mosdegree | m12md |
| −3 | Minor 7-mosdegree | m7md |
| −4 | Minor 2-mosdegree | m2md |
| −5 | Minor 19-mosdegree | m19md |
| −6 | Minor 14-mosdegree | m14md |
| −7 | Minor 9-mosdegree | m9md |
| −8 | Minor 4-mosdegree | m4md |
| −9 | Minor 21-mosdegree | m21md |
| −10 | Minor 16-mosdegree | m16md |
| −11 | Minor 11-mosdegree | m11md |
| −12 | Minor 6-mosdegree | m6md |
| −13 | Minor 1-mosdegree | m1md |
| −14 | Minor 18-mosdegree | m18md |
| −15 | Minor 13-mosdegree | m13md |
| −16 | Minor 8-mosdegree | m8md |
| −17 | Minor 3-mosdegree | m3md |
| −18 | Minor 20-mosdegree | m20md |
| −19 | Minor 15-mosdegree | m15md |
| −20 | Minor 10-mosdegree | m10md |
| −21 | Diminished 5-mosdegree | d5md |
| −22 | Diminished 22-mosdegree | d22md |
| −23 | Diminished 17-mosdegree | d17md |
| −24 | Diminished 12-mosdegree | d12md |
| −25 | Diminished 7-mosdegree | d7md |
| −26 | Diminished 2-mosdegree | d2md |
| −27 | Diminished 19-mosdegree | d19md |
| −28 | Diminished 14-mosdegree | d14md |
| −29 | Diminished 9-mosdegree | d9md |
| −30 | Diminished 4-mosdegree | d4md |
| −31 | Diminished 21-mosdegree | d21md |
| −32 | Diminished 16-mosdegree | d16md |
| −33 | Diminished 11-mosdegree | d11md |
| −34 | Diminished 6-mosdegree | d6md |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | |||
| 21|0 | 1 | LLsLsLLsLsLLsLsLLsLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 20|1 | 6 | LLsLsLLsLsLLsLsLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 19|2 | 11 | LLsLsLLsLsLsLLsLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 18|3 | 16 | LLsLsLsLLsLsLLsLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 17|4 | 21 | LsLLsLsLLsLsLLsLsLLsLs | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 16|5 | 4 | LsLLsLsLLsLsLLsLsLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. |
| 15|6 | 9 | LsLLsLsLLsLsLsLLsLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. |
| 14|7 | 14 | LsLLsLsLsLLsLsLLsLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. |
| 13|8 | 19 | LsLsLLsLsLLsLsLLsLsLLs | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. |
| 12|9 | 2 | LsLsLLsLsLLsLsLLsLsLsL | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Perf. |
| 11|10 | 7 | LsLsLLsLsLLsLsLsLLsLsL | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. |
| 10|11 | 12 | LsLsLLsLsLsLLsLsLLsLsL | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. |
| 9|12 | 17 | LsLsLsLLsLsLLsLsLLsLsL | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. |
| 8|13 | 22 | sLLsLsLLsLsLLsLsLLsLsL | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. |
| 7|14 | 5 | sLLsLsLLsLsLLsLsLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. |
| 6|15 | 10 | sLLsLsLLsLsLsLLsLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. |
| 5|16 | 15 | sLLsLsLsLLsLsLLsLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. |
| 4|17 | 20 | sLsLLsLsLLsLsLLsLsLLsL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. |
| 3|18 | 3 | sLsLLsLsLLsLsLLsLsLsLL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
| 2|19 | 8 | sLsLLsLsLLsLsLsLLsLsLL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
| 1|20 | 13 | sLsLLsLsLsLLsLsLLsLsLL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
| 0|21 | 18 | sLsLsLLsLsLLsLsLLsLsLL | Perf. | Min. | Min. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 5\22 | 272.727 | 927.273 | 1:1 | 1.000 | Equalized 13L 9s | |||||
| 28\123 | 273.171 | 926.829 | 6:5 | 1.200 | ||||||
| 23\101 | 273.267 | 926.733 | 5:4 | 1.250 | ||||||
| 41\180 | 273.333 | 926.667 | 9:7 | 1.286 | ||||||
| 18\79 | 273.418 | 926.582 | 4:3 | 1.333 | Supersoft 13L 9s | |||||
| 49\215 | 273.488 | 926.512 | 11:8 | 1.375 | ||||||
| 31\136 | 273.529 | 926.471 | 7:5 | 1.400 | ||||||
| 44\193 | 273.575 | 926.425 | 10:7 | 1.429 | ||||||
| 13\57 | 273.684 | 926.316 | 3:2 | 1.500 | Soft 13L 9s | |||||
| 47\206 | 273.786 | 926.214 | 11:7 | 1.571 | ||||||
| 34\149 | 273.826 | 926.174 | 8:5 | 1.600 | ||||||
| 55\241 | 273.859 | 926.141 | 13:8 | 1.625 | ||||||
| 21\92 | 273.913 | 926.087 | 5:3 | 1.667 | Semisoft 13L 9s | |||||
| 50\219 | 273.973 | 926.027 | 12:7 | 1.714 | ||||||
| 29\127 | 274.016 | 925.984 | 7:4 | 1.750 | ||||||
| 37\162 | 274.074 | 925.926 | 9:5 | 1.800 | ||||||
| 8\35 | 274.286 | 925.714 | 2:1 | 2.000 | Basic 13L 9s Scales with tunings softer than this are proper | |||||
| 35\153 | 274.510 | 925.490 | 9:4 | 2.250 | ||||||
| 27\118 | 274.576 | 925.424 | 7:3 | 2.333 | ||||||
| 46\201 | 274.627 | 925.373 | 12:5 | 2.400 | ||||||
| 19\83 | 274.699 | 925.301 | 5:2 | 2.500 | Semihard 13L 9s | |||||
| 49\214 | 274.766 | 925.234 | 13:5 | 2.600 | ||||||
| 30\131 | 274.809 | 925.191 | 8:3 | 2.667 | ||||||
| 41\179 | 274.860 | 925.140 | 11:4 | 2.750 | ||||||
| 11\48 | 275.000 | 925.000 | 3:1 | 3.000 | Hard 13L 9s | |||||
| 36\157 | 275.159 | 924.841 | 10:3 | 3.333 | ||||||
| 25\109 | 275.229 | 924.771 | 7:2 | 3.500 | ||||||
| 39\170 | 275.294 | 924.706 | 11:3 | 3.667 | ||||||
| 14\61 | 275.410 | 924.590 | 4:1 | 4.000 | Superhard 13L 9s | |||||
| 31\135 | 275.556 | 924.444 | 9:2 | 4.500 | ||||||
| 17\74 | 275.676 | 924.324 | 5:1 | 5.000 | ||||||
| 20\87 | 275.862 | 924.138 | 6:1 | 6.000 | ||||||
| 3\13 | 276.923 | 923.077 | 1:0 | → ∞ | Collapsed 13L 9s | |||||
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