12L 11s
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Step pattern
LLsLsLsLsLsLsLsLsLsLsLs
sLsLsLsLsLsLsLsLsLsLsLL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
21\23 to 11\12 (1095.7 ¢ to 1100.0 ¢)
Dark
1\12 to 2\23 (100.0 ¢ to 104.3 ¢)
Related to
1L 9s (antisinatonic)
With tunings
5:2 to 3:1 (quasihard)
Parent
11L 1s
Sister
11L 12s
Daughters
23L 12s, 12L 23s
Neutralized
1L 22s
2-Flought
35L 11s, 12L 34s
Equalized (L:s = 1:1)
21\23 (1095.7 ¢)
Supersoft (L:s = 4:3)
74\81 (1096.3 ¢)
Soft (L:s = 3:2)
53\58 (1096.6 ¢)
Semisoft (L:s = 5:3)
85\93 (1096.8 ¢)
Basic (L:s = 2:1)
32\35 (1097.1 ¢)
Semihard (L:s = 5:2)
75\82 (1097.6 ¢)
Hard (L:s = 3:1)
43\47 (1097.9 ¢)
Superhard (L:s = 4:1)
54\59 (1098.3 ¢)
Collapsed (L:s = 1:0)
11\12 (1100.0 ¢)
| ↖ 11L 10s | ↑ 12L 10s | 13L 10s ↗ |
| ← 11L 11s | 12L 11s | 13L 11s → |
| ↙ 11L 12s | ↓ 12L 12s | 13L 12s ↘ |
┌╥╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┐ │║║│║│║│║│║│║│║│║│║│║│║││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLsLsLsLsLsLsLsLsLsLsLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
12L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 11 small steps, repeating every octave. 12L 11s is a great-grandchild scale of 1L 9s, expanding it by 13 tones. Generators that produce this scale range from 1095.7 ¢ to 1100 ¢, or from 100 ¢ to 104.3 ¢.
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 52.2 ¢ |
| Major 1-mosstep | M1ms | L | 52.2 ¢ to 100.0 ¢ | |
| 2-mosstep | Perfect 2-mosstep | P2ms | L + s | 100.0 ¢ to 104.3 ¢ |
| Augmented 2-mosstep | A2ms | 2L | 104.3 ¢ to 200.0 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 100.0 ¢ to 156.5 ¢ |
| Major 3-mosstep | M3ms | 2L + s | 156.5 ¢ to 200.0 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 200.0 ¢ to 208.7 ¢ |
| Major 4-mosstep | M4ms | 3L + s | 208.7 ¢ to 300.0 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 2L + 3s | 200.0 ¢ to 260.9 ¢ |
| Major 5-mosstep | M5ms | 3L + 2s | 260.9 ¢ to 300.0 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 300.0 ¢ to 313.0 ¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 313.0 ¢ to 400.0 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 3L + 4s | 300.0 ¢ to 365.2 ¢ |
| Major 7-mosstep | M7ms | 4L + 3s | 365.2 ¢ to 400.0 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 4L + 4s | 400.0 ¢ to 417.4 ¢ |
| Major 8-mosstep | M8ms | 5L + 3s | 417.4 ¢ to 500.0 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 4L + 5s | 400.0 ¢ to 469.6 ¢ |
| Major 9-mosstep | M9ms | 5L + 4s | 469.6 ¢ to 500.0 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 5L + 5s | 500.0 ¢ to 521.7 ¢ |
| Major 10-mosstep | M10ms | 6L + 4s | 521.7 ¢ to 600.0 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 5L + 6s | 500.0 ¢ to 573.9 ¢ |
| Major 11-mosstep | M11ms | 6L + 5s | 573.9 ¢ to 600.0 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 6L + 6s | 600.0 ¢ to 626.1 ¢ |
| Major 12-mosstep | M12ms | 7L + 5s | 626.1 ¢ to 700.0 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 6L + 7s | 600.0 ¢ to 678.3 ¢ |
| Major 13-mosstep | M13ms | 7L + 6s | 678.3 ¢ to 700.0 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 7L + 7s | 700.0 ¢ to 730.4 ¢ |
| Major 14-mosstep | M14ms | 8L + 6s | 730.4 ¢ to 800.0 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 7L + 8s | 700.0 ¢ to 782.6 ¢ |
| Major 15-mosstep | M15ms | 8L + 7s | 782.6 ¢ to 800.0 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 8L + 8s | 800.0 ¢ to 834.8 ¢ |
| Major 16-mosstep | M16ms | 9L + 7s | 834.8 ¢ to 900.0 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 8L + 9s | 800.0 ¢ to 887.0 ¢ |
| Major 17-mosstep | M17ms | 9L + 8s | 887.0 ¢ to 900.0 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 9L + 9s | 900.0 ¢ to 939.1 ¢ |
| Major 18-mosstep | M18ms | 10L + 8s | 939.1 ¢ to 1000.0 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 9L + 10s | 900.0 ¢ to 991.3 ¢ |
| Major 19-mosstep | M19ms | 10L + 9s | 991.3 ¢ to 1000.0 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 10L + 10s | 1000.0 ¢ to 1043.5 ¢ |
| Major 20-mosstep | M20ms | 11L + 9s | 1043.5 ¢ to 1100.0 ¢ | |
| 21-mosstep | Diminished 21-mosstep | d21ms | 10L + 11s | 1000.0 ¢ to 1095.7 ¢ |
| Perfect 21-mosstep | P21ms | 11L + 10s | 1095.7 ¢ to 1100.0 ¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 11L + 11s | 1100.0 ¢ to 1147.8 ¢ |
| Major 22-mosstep | M22ms | 12L + 10s | 1147.8 ¢ to 1200.0 ¢ | |
| 23-mosstep | Perfect 23-mosstep | P23ms | 12L + 11s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 34 | Augmented 1-mosdegree | A1md |
| 33 | Augmented 3-mosdegree | A3md |
| 32 | Augmented 5-mosdegree | A5md |
| 31 | Augmented 7-mosdegree | A7md |
| 30 | Augmented 9-mosdegree | A9md |
| 29 | Augmented 11-mosdegree | A11md |
| 28 | Augmented 13-mosdegree | A13md |
| 27 | Augmented 15-mosdegree | A15md |
| 26 | Augmented 17-mosdegree | A17md |
| 25 | Augmented 19-mosdegree | A19md |
| 24 | Augmented 21-mosdegree | A21md |
| 23 | Augmented 0-mosdegree | A0md |
| 22 | Augmented 2-mosdegree | A2md |
| 21 | Major 4-mosdegree | M4md |
| 20 | Major 6-mosdegree | M6md |
| 19 | Major 8-mosdegree | M8md |
| 18 | Major 10-mosdegree | M10md |
| 17 | Major 12-mosdegree | M12md |
| 16 | Major 14-mosdegree | M14md |
| 15 | Major 16-mosdegree | M16md |
| 14 | Major 18-mosdegree | M18md |
| 13 | Major 20-mosdegree | M20md |
| 12 | Major 22-mosdegree | M22md |
| 11 | Major 1-mosdegree | M1md |
| 10 | Major 3-mosdegree | M3md |
| 9 | Major 5-mosdegree | M5md |
| 8 | Major 7-mosdegree | M7md |
| 7 | Major 9-mosdegree | M9md |
| 6 | Major 11-mosdegree | M11md |
| 5 | Major 13-mosdegree | M13md |
| 4 | Major 15-mosdegree | M15md |
| 3 | Major 17-mosdegree | M17md |
| 2 | Major 19-mosdegree | M19md |
| 1 | Perfect 21-mosdegree | P21md |
| 0 | Perfect 0-mosdegree Perfect 23-mosdegree |
P0md P23md |
| −1 | Perfect 2-mosdegree | P2md |
| −2 | Minor 4-mosdegree | m4md |
| −3 | Minor 6-mosdegree | m6md |
| −4 | Minor 8-mosdegree | m8md |
| −5 | Minor 10-mosdegree | m10md |
| −6 | Minor 12-mosdegree | m12md |
| −7 | Minor 14-mosdegree | m14md |
| −8 | Minor 16-mosdegree | m16md |
| −9 | Minor 18-mosdegree | m18md |
| −10 | Minor 20-mosdegree | m20md |
| −11 | Minor 22-mosdegree | m22md |
| −12 | Minor 1-mosdegree | m1md |
| −13 | Minor 3-mosdegree | m3md |
| −14 | Minor 5-mosdegree | m5md |
| −15 | Minor 7-mosdegree | m7md |
| −16 | Minor 9-mosdegree | m9md |
| −17 | Minor 11-mosdegree | m11md |
| −18 | Minor 13-mosdegree | m13md |
| −19 | Minor 15-mosdegree | m15md |
| −20 | Minor 17-mosdegree | m17md |
| −21 | Minor 19-mosdegree | m19md |
| −22 | Diminished 21-mosdegree | d21md |
| −23 | Diminished 23-mosdegree | d23md |
| −24 | Diminished 2-mosdegree | d2md |
| −25 | Diminished 4-mosdegree | d4md |
| −26 | Diminished 6-mosdegree | d6md |
| −27 | Diminished 8-mosdegree | d8md |
| −28 | Diminished 10-mosdegree | d10md |
| −29 | Diminished 12-mosdegree | d12md |
| −30 | Diminished 14-mosdegree | d14md |
| −31 | Diminished 16-mosdegree | d16md |
| −32 | Diminished 18-mosdegree | d18md |
| −33 | Diminished 20-mosdegree | d20md |
| −34 | Diminished 22-mosdegree | d22md |
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 | LLsLsLsLsLsLsLsLsLsLsLs | Perf. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 21|1 | 22 | LsLLsLsLsLsLsLsLsLsLsLs | 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 | 20 | LsLsLLsLsLsLsLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 19|3 | 18 | LsLsLsLLsLsLsLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 18|4 | 16 | LsLsLsLsLLsLsLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 17|5 | 14 | LsLsLsLsLsLLsLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 16|6 | 12 | LsLsLsLsLsLsLLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 15|7 | 10 | LsLsLsLsLsLsLsLLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 14|8 | 8 | LsLsLsLsLsLsLsLsLLsLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 13|9 | 6 | LsLsLsLsLsLsLsLsLsLLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 12|10 | 4 | LsLsLsLsLsLsLsLsLsLsLLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Perf. |
| 11|11 | 2 | LsLsLsLsLsLsLsLsLsLsLsL | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 10|12 | 23 | sLLsLsLsLsLsLsLsLsLsLsL | Perf. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 9|13 | 21 | sLsLLsLsLsLsLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 8|14 | 19 | sLsLsLLsLsLsLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 7|15 | 17 | sLsLsLsLLsLsLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 6|16 | 15 | sLsLsLsLsLLsLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 5|17 | 13 | sLsLsLsLsLsLLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 4|18 | 11 | sLsLsLsLsLsLsLLsLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 3|19 | 9 | sLsLsLsLsLsLsLsLLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 2|20 | 7 | sLsLsLsLsLsLsLsLsLLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 1|21 | 5 | sLsLsLsLsLsLsLsLsLsLLsL | 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 | 3 | sLsLsLsLsLsLsLsLsLsLsLL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Dim. | Min. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 21\23 | 1095.652 | 104.348 | 1:1 | 1.000 | Equalized 12L 11s | |||||
| 116\127 | 1096.063 | 103.937 | 6:5 | 1.200 | ||||||
| 95\104 | 1096.154 | 103.846 | 5:4 | 1.250 | ||||||
| 169\185 | 1096.216 | 103.784 | 9:7 | 1.286 | ||||||
| 74\81 | 1096.296 | 103.704 | 4:3 | 1.333 | Supersoft 12L 11s | |||||
| 201\220 | 1096.364 | 103.636 | 11:8 | 1.375 | ||||||
| 127\139 | 1096.403 | 103.597 | 7:5 | 1.400 | ||||||
| 180\197 | 1096.447 | 103.553 | 10:7 | 1.429 | ||||||
| 53\58 | 1096.552 | 103.448 | 3:2 | 1.500 | Soft 12L 11s | |||||
| 191\209 | 1096.651 | 103.349 | 11:7 | 1.571 | ||||||
| 138\151 | 1096.689 | 103.311 | 8:5 | 1.600 | ||||||
| 223\244 | 1096.721 | 103.279 | 13:8 | 1.625 | ||||||
| 85\93 | 1096.774 | 103.226 | 5:3 | 1.667 | Semisoft 12L 11s | |||||
| 202\221 | 1096.833 | 103.167 | 12:7 | 1.714 | ||||||
| 117\128 | 1096.875 | 103.125 | 7:4 | 1.750 | ||||||
| 149\163 | 1096.933 | 103.067 | 9:5 | 1.800 | ||||||
| 32\35 | 1097.143 | 102.857 | 2:1 | 2.000 | Basic 12L 11s Scales with tunings softer than this are proper | |||||
| 139\152 | 1097.368 | 102.632 | 9:4 | 2.250 | ||||||
| 107\117 | 1097.436 | 102.564 | 7:3 | 2.333 | ||||||
| 182\199 | 1097.487 | 102.513 | 12:5 | 2.400 | ||||||
| 75\82 | 1097.561 | 102.439 | 5:2 | 2.500 | Semihard 12L 11s | |||||
| 193\211 | 1097.630 | 102.370 | 13:5 | 2.600 | ||||||
| 118\129 | 1097.674 | 102.326 | 8:3 | 2.667 | ||||||
| 161\176 | 1097.727 | 102.273 | 11:4 | 2.750 | ||||||
| 43\47 | 1097.872 | 102.128 | 3:1 | 3.000 | Hard 12L 11s | |||||
| 140\153 | 1098.039 | 101.961 | 10:3 | 3.333 | ||||||
| 97\106 | 1098.113 | 101.887 | 7:2 | 3.500 | ||||||
| 151\165 | 1098.182 | 101.818 | 11:3 | 3.667 | ||||||
| 54\59 | 1098.305 | 101.695 | 4:1 | 4.000 | Superhard 12L 11s | |||||
| 119\130 | 1098.462 | 101.538 | 9:2 | 4.500 | ||||||
| 65\71 | 1098.592 | 101.408 | 5:1 | 5.000 | ||||||
| 76\83 | 1098.795 | 101.205 | 6:1 | 6.000 | ||||||
| 11\12 | 1100.000 | 100.000 | 1:0 | → ∞ | Collapsed 12L 11s | |||||
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