12L 2s
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Scale structure
Step pattern
LLLLLLsLLLLLLs
sLLLLLLsLLLLLL
Equave
2/1 (1200.0¢)
Period
1\2 (600.0¢)
Generator size
Bright
1\14 to 1\12 (85.7¢ to 100.0¢)
Dark
5\12 to 6\14 (500.0¢ to 514.3¢)
TAMNAMS information
Descends from
2L 8s (jaric)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Related MOS scales
Parent
2L 10s
Sister
2L 12s
Daughters
14L 12s, 12L 14s
Neutralized
10L 4s
2-Flought
26L 2s, 12L 16s
Equal tunings
Equalized (L:s = 1:1)
1\14 (85.7¢)
Supersoft (L:s = 4:3)
4\54 (88.9¢)
Soft (L:s = 3:2)
3\40 (90.0¢)
Semisoft (L:s = 5:3)
5\66 (90.9¢)
Basic (L:s = 2:1)
2\26 (92.3¢)
Semihard (L:s = 5:2)
5\64 (93.8¢)
Hard (L:s = 3:1)
3\38 (94.7¢)
Superhard (L:s = 4:1)
4\50 (96.0¢)
Collapsed (L:s = 1:0)
1\12 (100.0¢)
| ↖ 11L 1s | ↑ 12L 1s | 13L 1s ↗ |
| ← 11L 2s | 12L 2s | 13L 2s → |
| ↙ 11L 3s | ↓ 12L 3s | 13L 3s ↘ |
┌╥╥╥╥╥╥┬╥╥╥╥╥╥┬┐ │║║║║║║│║║║║║║││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLsLLLLLL
12L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 2 small steps, with a period of 6 large steps and 1 small step that repeats every 600.0¢, or twice every octave. 12L 2s is a grandchild scale of 2L 8s, expanding it by 4 tones. Generators that produce this scale range from 85.7¢ to 100¢, or from 500¢ to 514.3¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.
It appears as the mega chromatic scale of injera temperament, meaning that its harmonic entropy is where +4 generators equals 5/4 (simple) or +10 generators equals 5/3 (complex).
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 12|0(2) | 1 | LLLLLLsLLLLLLs |
| 10|2(2) | 2 | LLLLLsLLLLLLsL |
| 8|4(2) | 3 | LLLLsLLLLLLsLL |
| 6|6(2) | 4 | LLLsLLLLLLsLLL |
| 4|8(2) | 5 | LLsLLLLLLsLLLL |
| 2|10(2) | 6 | LsLLLLLLsLLLLL |
| 0|12(2) | 7 | sLLLLLLsLLLLLL |
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 85.7¢ |
| Perfect 1-mosstep | P1ms | L | 85.7¢ to 100.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 100.0¢ to 171.4¢ |
| Major 2-mosstep | M2ms | 2L | 171.4¢ to 200.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 200.0¢ to 257.1¢ |
| Major 3-mosstep | M3ms | 3L | 257.1¢ to 300.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 300.0¢ to 342.9¢ |
| Major 4-mosstep | M4ms | 4L | 342.9¢ to 400.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 400.0¢ to 428.6¢ |
| Major 5-mosstep | M5ms | 5L | 428.6¢ to 500.0¢ | |
| 6-mosstep | Perfect 6-mosstep | P6ms | 5L + s | 500.0¢ to 514.3¢ |
| Augmented 6-mosstep | A6ms | 6L | 514.3¢ to 600.0¢ | |
| 7-mosstep | Perfect 7-mosstep | P7ms | 6L + s | 600.0¢ |
| 8-mosstep | Diminished 8-mosstep | d8ms | 6L + 2s | 600.0¢ to 685.7¢ |
| Perfect 8-mosstep | P8ms | 7L + s | 685.7¢ to 700.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 7L + 2s | 700.0¢ to 771.4¢ |
| Major 9-mosstep | M9ms | 8L + s | 771.4¢ to 800.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 8L + 2s | 800.0¢ to 857.1¢ |
| Major 10-mosstep | M10ms | 9L + s | 857.1¢ to 900.0¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 9L + 2s | 900.0¢ to 942.9¢ |
| Major 11-mosstep | M11ms | 10L + s | 942.9¢ to 1000.0¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 10L + 2s | 1000.0¢ to 1028.6¢ |
| Major 12-mosstep | M12ms | 11L + s | 1028.6¢ to 1100.0¢ | |
| 13-mosstep | Perfect 13-mosstep | P13ms | 11L + 2s | 1100.0¢ to 1114.3¢ |
| Augmented 13-mosstep | A13ms | 12L + s | 1114.3¢ to 1200.0¢ | |
| 14-mosstep | Perfect 14-mosstep | P14ms | 12L + 2s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\14 | 85.714 | 514.286 | 1:1 | 1.000 | Equalized 12L 2s | |||||
| 6\82 | 87.805 | 512.195 | 6:5 | 1.200 | ||||||
| 5\68 | 88.235 | 511.765 | 5:4 | 1.250 | ||||||
| 9\122 | 88.525 | 511.475 | 9:7 | 1.286 | ||||||
| 4\54 | 88.889 | 511.111 | 4:3 | 1.333 | Supersoft 12L 2s | |||||
| 11\148 | 89.189 | 510.811 | 11:8 | 1.375 | ||||||
| 7\94 | 89.362 | 510.638 | 7:5 | 1.400 | ||||||
| 10\134 | 89.552 | 510.448 | 10:7 | 1.429 | ||||||
| 3\40 | 90.000 | 510.000 | 3:2 | 1.500 | Soft 12L 2s | |||||
| 11\146 | 90.411 | 509.589 | 11:7 | 1.571 | ||||||
| 8\106 | 90.566 | 509.434 | 8:5 | 1.600 | ||||||
| 13\172 | 90.698 | 509.302 | 13:8 | 1.625 | ||||||
| 5\66 | 90.909 | 509.091 | 5:3 | 1.667 | Semisoft 12L 2s | |||||
| 12\158 | 91.139 | 508.861 | 12:7 | 1.714 | ||||||
| 7\92 | 91.304 | 508.696 | 7:4 | 1.750 | ||||||
| 9\118 | 91.525 | 508.475 | 9:5 | 1.800 | ||||||
| 2\26 | 92.308 | 507.692 | 2:1 | 2.000 | Basic 12L 2s | |||||
| 9\116 | 93.103 | 506.897 | 9:4 | 2.250 | ||||||
| 7\90 | 93.333 | 506.667 | 7:3 | 2.333 | ||||||
| 12\154 | 93.506 | 506.494 | 12:5 | 2.400 | ||||||
| 5\64 | 93.750 | 506.250 | 5:2 | 2.500 | Semihard 12L 2s | |||||
| 13\166 | 93.976 | 506.024 | 13:5 | 2.600 | ||||||
| 8\102 | 94.118 | 505.882 | 8:3 | 2.667 | ||||||
| 11\140 | 94.286 | 505.714 | 11:4 | 2.750 | ||||||
| 3\38 | 94.737 | 505.263 | 3:1 | 3.000 | Hard 12L 2s Injera | |||||
| 10\126 | 95.238 | 504.762 | 10:3 | 3.333 | ||||||
| 7\88 | 95.455 | 504.545 | 7:2 | 3.500 | ||||||
| 11\138 | 95.652 | 504.348 | 11:3 | 3.667 | ||||||
| 4\50 | 96.000 | 504.000 | 4:1 | 4.000 | Superhard 12L 2s | |||||
| 9\112 | 96.429 | 503.571 | 9:2 | 4.500 | ||||||
| 5\62 | 96.774 | 503.226 | 5:1 | 5.000 | ||||||
| 6\74 | 97.297 | 502.703 | 6:1 | 6.000 | ||||||
| 1\12 | 100.000 | 500.000 | 1:0 | → ∞ | Collapsed 12L 2s | |||||