11L 12s
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Step pattern
LsLsLsLsLsLsLsLsLsLsLss
ssLsLsLsLsLsLsLsLsLsLsL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
2\23 to 1\11 (104.3 ¢ to 109.1 ¢)
Dark
10\11 to 21\23 (1090.9 ¢ to 1095.7 ¢)
Descends from
1L 9s (antisinatonic)
Ancestor's step ratio range
2:1 to 5:2 (minihard)
Parent
11L 1s
Sister
12L 11s
Daughters
23L 11s, 11L 23s
Neutralized
22L 1s
2-Flought
34L 12s, 11L 35s
Equalized (L:s = 1:1)
2\23 (104.3 ¢)
Supersoft (L:s = 4:3)
7\80 (105.0 ¢)
Soft (L:s = 3:2)
5\57 (105.3 ¢)
Semisoft (L:s = 5:3)
8\91 (105.5 ¢)
Basic (L:s = 2:1)
3\34 (105.9 ¢)
Semihard (L:s = 5:2)
7\79 (106.3 ¢)
Hard (L:s = 3:1)
4\45 (106.7 ¢)
Superhard (L:s = 4:1)
5\56 (107.1 ¢)
Collapsed (L:s = 1:0)
1\11 (109.1 ¢)
| ↖ 10L 11s | ↑ 11L 11s | 12L 11s ↗ |
| ← 10L 12s | 11L 12s | 12L 12s → |
| ↙ 10L 13s | ↓ 11L 13s | 12L 13s ↘ |
┌╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┬┐ │║│║│║│║│║│║│║│║│║│║│║│││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssLsLsLsLsLsLsLsLsLsLsL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
11L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 12 small steps, repeating every octave. 11L 12s is a great-grandchild scale of 1L 9s, expanding it by 13 tones. Generators that produce this scale range from 104.3 ¢ to 109.1 ¢, or from 1090.9 ¢ to 1095.7 ¢.
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 52.2 ¢ |
| Major 1-mosstep | M1ms | L | 52.2 ¢ to 109.1 ¢ | |
| 2-mosstep | Diminished 2-mosstep | d2ms | 2s | 0.0 ¢ to 104.3 ¢ |
| Perfect 2-mosstep | P2ms | L + s | 104.3 ¢ to 109.1 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 109.1 ¢ to 156.5 ¢ |
| Major 3-mosstep | M3ms | 2L + s | 156.5 ¢ to 218.2 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 109.1 ¢ to 208.7 ¢ |
| Major 4-mosstep | M4ms | 2L + 2s | 208.7 ¢ to 218.2 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 2L + 3s | 218.2 ¢ to 260.9 ¢ |
| Major 5-mosstep | M5ms | 3L + 2s | 260.9 ¢ to 327.3 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 2L + 4s | 218.2 ¢ to 313.0 ¢ |
| Major 6-mosstep | M6ms | 3L + 3s | 313.0 ¢ to 327.3 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 3L + 4s | 327.3 ¢ to 365.2 ¢ |
| Major 7-mosstep | M7ms | 4L + 3s | 365.2 ¢ to 436.4 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 3L + 5s | 327.3 ¢ to 417.4 ¢ |
| Major 8-mosstep | M8ms | 4L + 4s | 417.4 ¢ to 436.4 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 4L + 5s | 436.4 ¢ to 469.6 ¢ |
| Major 9-mosstep | M9ms | 5L + 4s | 469.6 ¢ to 545.5 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 4L + 6s | 436.4 ¢ to 521.7 ¢ |
| Major 10-mosstep | M10ms | 5L + 5s | 521.7 ¢ to 545.5 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 5L + 6s | 545.5 ¢ to 573.9 ¢ |
| Major 11-mosstep | M11ms | 6L + 5s | 573.9 ¢ to 654.5 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 5L + 7s | 545.5 ¢ to 626.1 ¢ |
| Major 12-mosstep | M12ms | 6L + 6s | 626.1 ¢ to 654.5 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 6L + 7s | 654.5 ¢ to 678.3 ¢ |
| Major 13-mosstep | M13ms | 7L + 6s | 678.3 ¢ to 763.6 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 6L + 8s | 654.5 ¢ to 730.4 ¢ |
| Major 14-mosstep | M14ms | 7L + 7s | 730.4 ¢ to 763.6 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 7L + 8s | 763.6 ¢ to 782.6 ¢ |
| Major 15-mosstep | M15ms | 8L + 7s | 782.6 ¢ to 872.7 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 7L + 9s | 763.6 ¢ to 834.8 ¢ |
| Major 16-mosstep | M16ms | 8L + 8s | 834.8 ¢ to 872.7 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 8L + 9s | 872.7 ¢ to 887.0 ¢ |
| Major 17-mosstep | M17ms | 9L + 8s | 887.0 ¢ to 981.8 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 8L + 10s | 872.7 ¢ to 939.1 ¢ |
| Major 18-mosstep | M18ms | 9L + 9s | 939.1 ¢ to 981.8 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 9L + 10s | 981.8 ¢ to 991.3 ¢ |
| Major 19-mosstep | M19ms | 10L + 9s | 991.3 ¢ to 1090.9 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 9L + 11s | 981.8 ¢ to 1043.5 ¢ |
| Major 20-mosstep | M20ms | 10L + 10s | 1043.5 ¢ to 1090.9 ¢ | |
| 21-mosstep | Perfect 21-mosstep | P21ms | 10L + 11s | 1090.9 ¢ to 1095.7 ¢ |
| Augmented 21-mosstep | A21ms | 11L + 10s | 1095.7 ¢ to 1200.0 ¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 10L + 12s | 1090.9 ¢ to 1147.8 ¢ |
| Major 22-mosstep | M22ms | 11L + 11s | 1147.8 ¢ to 1200.0 ¢ | |
| 23-mosstep | Perfect 23-mosstep | P23ms | 11L + 12s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 33 | Augmented 20-mosdegree | A20md |
| 32 | Augmented 18-mosdegree | A18md |
| 31 | Augmented 16-mosdegree | A16md |
| 30 | Augmented 14-mosdegree | A14md |
| 29 | Augmented 12-mosdegree | A12md |
| 28 | Augmented 10-mosdegree | A10md |
| 27 | Augmented 8-mosdegree | A8md |
| 26 | Augmented 6-mosdegree | A6md |
| 25 | Augmented 4-mosdegree | A4md |
| 24 | Augmented 2-mosdegree | A2md |
| 23 | Augmented 0-mosdegree | A0md |
| 22 | Augmented 21-mosdegree | A21md |
| 21 | Major 19-mosdegree | M19md |
| 20 | Major 17-mosdegree | M17md |
| 19 | Major 15-mosdegree | M15md |
| 18 | Major 13-mosdegree | M13md |
| 17 | Major 11-mosdegree | M11md |
| 16 | Major 9-mosdegree | M9md |
| 15 | Major 7-mosdegree | M7md |
| 14 | Major 5-mosdegree | M5md |
| 13 | Major 3-mosdegree | M3md |
| 12 | Major 1-mosdegree | M1md |
| 11 | Major 22-mosdegree | M22md |
| 10 | Major 20-mosdegree | M20md |
| 9 | Major 18-mosdegree | M18md |
| 8 | Major 16-mosdegree | M16md |
| 7 | Major 14-mosdegree | M14md |
| 6 | Major 12-mosdegree | M12md |
| 5 | Major 10-mosdegree | M10md |
| 4 | Major 8-mosdegree | M8md |
| 3 | Major 6-mosdegree | M6md |
| 2 | Major 4-mosdegree | M4md |
| 1 | Perfect 2-mosdegree | P2md |
| 0 | Perfect 0-mosdegree Perfect 23-mosdegree |
P0md P23md |
| −1 | Perfect 21-mosdegree | P21md |
| −2 | Minor 19-mosdegree | m19md |
| −3 | Minor 17-mosdegree | m17md |
| −4 | Minor 15-mosdegree | m15md |
| −5 | Minor 13-mosdegree | m13md |
| −6 | Minor 11-mosdegree | m11md |
| −7 | Minor 9-mosdegree | m9md |
| −8 | Minor 7-mosdegree | m7md |
| −9 | Minor 5-mosdegree | m5md |
| −10 | Minor 3-mosdegree | m3md |
| −11 | Minor 1-mosdegree | m1md |
| −12 | Minor 22-mosdegree | m22md |
| −13 | Minor 20-mosdegree | m20md |
| −14 | Minor 18-mosdegree | m18md |
| −15 | Minor 16-mosdegree | m16md |
| −16 | Minor 14-mosdegree | m14md |
| −17 | Minor 12-mosdegree | m12md |
| −18 | Minor 10-mosdegree | m10md |
| −19 | Minor 8-mosdegree | m8md |
| −20 | Minor 6-mosdegree | m6md |
| −21 | Minor 4-mosdegree | m4md |
| −22 | Diminished 2-mosdegree | d2md |
| −23 | Diminished 23-mosdegree | d23md |
| −24 | Diminished 21-mosdegree | d21md |
| −25 | Diminished 19-mosdegree | d19md |
| −26 | Diminished 17-mosdegree | d17md |
| −27 | Diminished 15-mosdegree | d15md |
| −28 | Diminished 13-mosdegree | d13md |
| −29 | Diminished 11-mosdegree | d11md |
| −30 | Diminished 9-mosdegree | d9md |
| −31 | Diminished 7-mosdegree | d7md |
| −32 | Diminished 5-mosdegree | d5md |
| −33 | Diminished 3-mosdegree | d3md |
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 | 23 | |||
| 22|0 | 1 | LsLsLsLsLsLsLsLsLsLsLss | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Perf. |
| 21|1 | 3 | LsLsLsLsLsLsLsLsLsLssLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 20|2 | 5 | LsLsLsLsLsLsLsLsLssLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 19|3 | 7 | LsLsLsLsLsLsLsLssLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 18|4 | 9 | LsLsLsLsLsLsLssLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 17|5 | 11 | LsLsLsLsLsLssLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 16|6 | 13 | LsLsLsLsLssLsLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 15|7 | 15 | LsLsLsLssLsLsLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 14|8 | 17 | LsLsLssLsLsLsLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 13|9 | 19 | LsLssLsLsLsLsLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 12|10 | 21 | LssLsLsLsLsLsLsLsLsLsLs | Perf. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 11|11 | 23 | sLsLsLsLsLsLsLsLsLsLsLs | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 10|12 | 2 | sLsLsLsLsLsLsLsLsLsLssL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Perf. |
| 9|13 | 4 | sLsLsLsLsLsLsLsLsLssLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Min. | Perf. | Min. | Perf. |
| 8|14 | 6 | sLsLsLsLsLsLsLsLssLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 7|15 | 8 | sLsLsLsLsLsLsLssLsLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 6|16 | 10 | sLsLsLsLsLsLssLsLsLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 5|17 | 12 | sLsLsLsLsLssLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 4|18 | 14 | sLsLsLsLssLsLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 3|19 | 16 | sLsLsLssLsLsLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 2|20 | 18 | sLsLssLsLsLsLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 1|21 | 20 | sLssLsLsLsLsLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 0|22 | 22 | ssLsLsLsLsLsLsLsLsLsLsL | Perf. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 2\23 | 104.348 | 1095.652 | 1:1 | 1.000 | Equalized 11L 12s | |||||
| 11\126 | 104.762 | 1095.238 | 6:5 | 1.200 | ||||||
| 9\103 | 104.854 | 1095.146 | 5:4 | 1.250 | ||||||
| 16\183 | 104.918 | 1095.082 | 9:7 | 1.286 | ||||||
| 7\80 | 105.000 | 1095.000 | 4:3 | 1.333 | Supersoft 11L 12s | |||||
| 19\217 | 105.069 | 1094.931 | 11:8 | 1.375 | ||||||
| 12\137 | 105.109 | 1094.891 | 7:5 | 1.400 | ||||||
| 17\194 | 105.155 | 1094.845 | 10:7 | 1.429 | ||||||
| 5\57 | 105.263 | 1094.737 | 3:2 | 1.500 | Soft 11L 12s | |||||
| 18\205 | 105.366 | 1094.634 | 11:7 | 1.571 | ||||||
| 13\148 | 105.405 | 1094.595 | 8:5 | 1.600 | ||||||
| 21\239 | 105.439 | 1094.561 | 13:8 | 1.625 | ||||||
| 8\91 | 105.495 | 1094.505 | 5:3 | 1.667 | Semisoft 11L 12s | |||||
| 19\216 | 105.556 | 1094.444 | 12:7 | 1.714 | ||||||
| 11\125 | 105.600 | 1094.400 | 7:4 | 1.750 | ||||||
| 14\159 | 105.660 | 1094.340 | 9:5 | 1.800 | ||||||
| 3\34 | 105.882 | 1094.118 | 2:1 | 2.000 | Basic 11L 12s Scales with tunings softer than this are proper | |||||
| 13\147 | 106.122 | 1093.878 | 9:4 | 2.250 | ||||||
| 10\113 | 106.195 | 1093.805 | 7:3 | 2.333 | ||||||
| 17\192 | 106.250 | 1093.750 | 12:5 | 2.400 | ||||||
| 7\79 | 106.329 | 1093.671 | 5:2 | 2.500 | Semihard 11L 12s | |||||
| 18\203 | 106.404 | 1093.596 | 13:5 | 2.600 | ||||||
| 11\124 | 106.452 | 1093.548 | 8:3 | 2.667 | ||||||
| 15\169 | 106.509 | 1093.491 | 11:4 | 2.750 | ||||||
| 4\45 | 106.667 | 1093.333 | 3:1 | 3.000 | Hard 11L 12s | |||||
| 13\146 | 106.849 | 1093.151 | 10:3 | 3.333 | ||||||
| 9\101 | 106.931 | 1093.069 | 7:2 | 3.500 | ||||||
| 14\157 | 107.006 | 1092.994 | 11:3 | 3.667 | ||||||
| 5\56 | 107.143 | 1092.857 | 4:1 | 4.000 | Superhard 11L 12s | |||||
| 11\123 | 107.317 | 1092.683 | 9:2 | 4.500 | ||||||
| 6\67 | 107.463 | 1092.537 | 5:1 | 5.000 | ||||||
| 7\78 | 107.692 | 1092.308 | 6:1 | 6.000 | ||||||
| 1\11 | 109.091 | 1090.909 | 1:0 | → ∞ | Collapsed 11L 12s | |||||
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