11L 1s
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Scale structure
Step pattern
LLLLLLLLLLLs
sLLLLLLLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
1\12 to 1\11 (100.0¢ to 109.1¢)
Dark
10\11 to 11\12 (1090.9¢ to 1100.0¢)
TAMNAMS information
Descends from
1L 9s (antisinatonic)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Related MOS scales
Parent
1L 10s
Sister
1L 11s
Daughters
12L 11s, 11L 12s
Neutralized
10L 2s
2-Flought
23L 1s, 11L 13s
Equal tunings
Equalized (L:s = 1:1)
1\12 (100.0¢)
Supersoft (L:s = 4:3)
4\47 (102.1¢)
Soft (L:s = 3:2)
3\35 (102.9¢)
Semisoft (L:s = 5:3)
5\58 (103.4¢)
Basic (L:s = 2:1)
2\23 (104.3¢)
Semihard (L:s = 5:2)
5\57 (105.3¢)
Hard (L:s = 3:1)
3\34 (105.9¢)
Superhard (L:s = 4:1)
4\45 (106.7¢)
Collapsed (L:s = 1:0)
1\11 (109.1¢)
| ← 10L 1s | 11L 1s | 12L 1s → |
| ↙ 10L 2s | ↓ 11L 2s | 12L 2s ↘ |
┌╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLLLLLL
11L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 1 small step, repeating every octave. 11L 1s is a grandchild scale of 1L 9s, expanding it by 2 tones. Generators that produce this scale range from 100¢ to 109.1¢, or from 1090.9¢ to 1100¢. Scales of this form are always proper because there is only one small step. The 11L 1s MOS scale, with its diatonic minor second generator, is the dodecatonic scale of ripple (9:8 = +2 generators-6:5 = +3 generators) temperaments. However, it feels markedly more hendecatonic to listeners used to the equally divided chromatic scale because of its unbroken chain of eleven equal steps–never mind that the 12th degree is actually less than the octave. This hendecatonic feel is especially pronounced above 2\23, where the octave feels like a comma shift of the 12th degree rather than an independent note.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 11|0 | 1 | LLLLLLLLLLLs |
| 10|1 | 2 | LLLLLLLLLLsL |
| 9|2 | 3 | LLLLLLLLLsLL |
| 8|3 | 4 | LLLLLLLLsLLL |
| 7|4 | 5 | LLLLLLLsLLLL |
| 6|5 | 6 | LLLLLLsLLLLL |
| 5|6 | 7 | LLLLLsLLLLLL |
| 4|7 | 8 | LLLLsLLLLLLL |
| 3|8 | 9 | LLLsLLLLLLLL |
| 2|9 | 10 | LLsLLLLLLLLL |
| 1|10 | 11 | LsLLLLLLLLLL |
| 0|11 | 12 | sLLLLLLLLLLL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Diminished 1-mosstep | d1ms | s | 0.0¢ to 100.0¢ |
| Perfect 1-mosstep | P1ms | L | 100.0¢ to 109.1¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 109.1¢ to 200.0¢ |
| Major 2-mosstep | M2ms | 2L | 200.0¢ to 218.2¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 218.2¢ to 300.0¢ |
| Major 3-mosstep | M3ms | 3L | 300.0¢ to 327.3¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 327.3¢ to 400.0¢ |
| Major 4-mosstep | M4ms | 4L | 400.0¢ to 436.4¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 436.4¢ to 500.0¢ |
| Major 5-mosstep | M5ms | 5L | 500.0¢ to 545.5¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 545.5¢ to 600.0¢ |
| Major 6-mosstep | M6ms | 6L | 600.0¢ to 654.5¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 6L + s | 654.5¢ to 700.0¢ |
| Major 7-mosstep | M7ms | 7L | 700.0¢ to 763.6¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 7L + s | 763.6¢ to 800.0¢ |
| Major 8-mosstep | M8ms | 8L | 800.0¢ to 872.7¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 8L + s | 872.7¢ to 900.0¢ |
| Major 9-mosstep | M9ms | 9L | 900.0¢ to 981.8¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 9L + s | 981.8¢ to 1000.0¢ |
| Major 10-mosstep | M10ms | 10L | 1000.0¢ to 1090.9¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 10L + s | 1090.9¢ to 1100.0¢ |
| Augmented 11-mosstep | A11ms | 11L | 1100.0¢ to 1200.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 11L + s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\12 | 100.000 | 1100.000 | 1:1 | 1.000 | Equalized 11L 1s Ripple (100.838¢) | |||||
| 6\71 | 101.408 | 1098.592 | 6:5 | 1.200 | ||||||
| 5\59 | 101.695 | 1098.305 | 5:4 | 1.250 | ||||||
| 9\106 | 101.887 | 1098.113 | 9:7 | 1.286 | ||||||
| 4\47 | 102.128 | 1097.872 | 4:3 | 1.333 | Supersoft 11L 1s | |||||
| 11\129 | 102.326 | 1097.674 | 11:8 | 1.375 | ||||||
| 7\82 | 102.439 | 1097.561 | 7:5 | 1.400 | ||||||
| 10\117 | 102.564 | 1097.436 | 10:7 | 1.429 | ||||||
| 3\35 | 102.857 | 1097.143 | 3:2 | 1.500 | Soft 11L 1s | |||||
| 11\128 | 103.125 | 1096.875 | 11:7 | 1.571 | ||||||
| 8\93 | 103.226 | 1096.774 | 8:5 | 1.600 | ||||||
| 13\151 | 103.311 | 1096.689 | 13:8 | 1.625 | ||||||
| 5\58 | 103.448 | 1096.552 | 5:3 | 1.667 | Semisoft 11L 1s | |||||
| 12\139 | 103.597 | 1096.403 | 12:7 | 1.714 | ||||||
| 7\81 | 103.704 | 1096.296 | 7:4 | 1.750 | ||||||
| 9\104 | 103.846 | 1096.154 | 9:5 | 1.800 | ||||||
| 2\23 | 104.348 | 1095.652 | 2:1 | 2.000 | Basic 11L 1s | |||||
| 9\103 | 104.854 | 1095.146 | 9:4 | 2.250 | ||||||
| 7\80 | 105.000 | 1095.000 | 7:3 | 2.333 | ||||||
| 12\137 | 105.109 | 1094.891 | 12:5 | 2.400 | ||||||
| 5\57 | 105.263 | 1094.737 | 5:2 | 2.500 | Semihard 11L 1s | |||||
| 13\148 | 105.405 | 1094.595 | 13:5 | 2.600 | ||||||
| 8\91 | 105.495 | 1094.505 | 8:3 | 2.667 | ||||||
| 11\125 | 105.600 | 1094.400 | 11:4 | 2.750 | ||||||
| 3\34 | 105.882 | 1094.118 | 3:1 | 3.000 | Hard 11L 1s | |||||
| 10\113 | 106.195 | 1093.805 | 10:3 | 3.333 | ||||||
| 7\79 | 106.329 | 1093.671 | 7:2 | 3.500 | ||||||
| 11\124 | 106.452 | 1093.548 | 11:3 | 3.667 | ||||||
| 4\45 | 106.667 | 1093.333 | 4:1 | 4.000 | Superhard 11L 1s | |||||
| 9\101 | 106.931 | 1093.069 | 9:2 | 4.500 | ||||||
| 5\56 | 107.143 | 1092.857 | 5:1 | 5.000 | ||||||
| 6\67 | 107.463 | 1092.537 | 6:1 | 6.000 | ||||||
| 1\11 | 109.091 | 1090.909 | 1:0 | → ∞ | Collapsed 11L 1s | |||||