12L 1s
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Scale structure
Step pattern
LLLLLLLLLLLLs
sLLLLLLLLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
1\13 to 1\12 (92.3¢ to 100.0¢)
Dark
11\12 to 12\13 (1100.0¢ to 1107.7¢)
TAMNAMS information
Descends from
1L 9s (antisinatonic)
Ancestor's step ratio range
3:1 to 4:1 (parahard)
Related MOS scales
Parent
1L 11s
Sister
1L 12s
Daughters
13L 12s, 12L 13s
Neutralized
11L 2s
2-Flought
25L 1s, 12L 14s
Equal tunings
Equalized (L:s = 1:1)
1\13 (92.3¢)
Supersoft (L:s = 4:3)
4\51 (94.1¢)
Soft (L:s = 3:2)
3\38 (94.7¢)
Semisoft (L:s = 5:3)
5\63 (95.2¢)
Basic (L:s = 2:1)
2\25 (96.0¢)
Semihard (L:s = 5:2)
5\62 (96.8¢)
Hard (L:s = 3:1)
3\37 (97.3¢)
Superhard (L:s = 4:1)
4\49 (98.0¢)
Collapsed (L:s = 1:0)
1\12 (100.0¢)
| ← 11L 1s | 12L 1s | 13L 1s → |
| ↙ 11L 2s | ↓ 12L 2s | 13L 2s ↘ |
┌╥╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║║││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLLLLLLL
12L 1s, also called quasidozenal, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 1 small step, repeating every octave. 12L 1s is a great-grandchild scale of 1L 9s, expanding it by 3 tones. Generators that produce this scale range from 92.3¢ to 100¢, or from 1100¢ to 1107.7¢. Scales of this form are always proper because there is only one small step.
Quasidozenal does not have many regular temperament applications.
However, it becomes a compressed 12edo scale when you ignore the octave (this obviously does not work when the generator is very near 12edo (within -7/24 ¢ of it), for the 13th degree of the scale registers as identical to the octave for human listeners.
And it becomes indistinct from 13edo or 1L 11s in the 1.75 ¢ above 1\13 because the large and small steps register as identical to one another for human listeners).
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 12|0 | 1 | LLLLLLLLLLLLs |
| 11|1 | 2 | LLLLLLLLLLLsL |
| 10|2 | 3 | LLLLLLLLLLsLL |
| 9|3 | 4 | LLLLLLLLLsLLL |
| 8|4 | 5 | LLLLLLLLsLLLL |
| 7|5 | 6 | LLLLLLLsLLLLL |
| 6|6 | 7 | LLLLLLsLLLLLL |
| 5|7 | 8 | LLLLLsLLLLLLL |
| 4|8 | 9 | LLLLsLLLLLLLL |
| 3|9 | 10 | LLLsLLLLLLLLL |
| 2|10 | 11 | LLsLLLLLLLLLL |
| 1|11 | 12 | LsLLLLLLLLLLL |
| 0|12 | 13 | sLLLLLLLLLLLL |
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 92.3¢ |
| Perfect 1-mosstep | P1ms | L | 92.3¢ to 100.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 100.0¢ to 184.6¢ |
| Major 2-mosstep | M2ms | 2L | 184.6¢ to 200.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 200.0¢ to 276.9¢ |
| Major 3-mosstep | M3ms | 3L | 276.9¢ to 300.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 300.0¢ to 369.2¢ |
| Major 4-mosstep | M4ms | 4L | 369.2¢ to 400.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 400.0¢ to 461.5¢ |
| Major 5-mosstep | M5ms | 5L | 461.5¢ to 500.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 500.0¢ to 553.8¢ |
| Major 6-mosstep | M6ms | 6L | 553.8¢ to 600.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 6L + s | 600.0¢ to 646.2¢ |
| Major 7-mosstep | M7ms | 7L | 646.2¢ to 700.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 7L + s | 700.0¢ to 738.5¢ |
| Major 8-mosstep | M8ms | 8L | 738.5¢ to 800.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 8L + s | 800.0¢ to 830.8¢ |
| Major 9-mosstep | M9ms | 9L | 830.8¢ to 900.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 9L + s | 900.0¢ to 923.1¢ |
| Major 10-mosstep | M10ms | 10L | 923.1¢ to 1000.0¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 10L + s | 1000.0¢ to 1015.4¢ |
| Major 11-mosstep | M11ms | 11L | 1015.4¢ to 1100.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 11L + s | 1100.0¢ to 1107.7¢ |
| Augmented 12-mosstep | A12ms | 12L | 1107.7¢ to 1200.0¢ | |
| 13-mosstep | Perfect 13-mosstep | P13ms | 12L + s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\13 | 92.308 | 1107.692 | 1:1 | 1.000 | Equalized 12L 1s | |||||
| 6\77 | 93.506 | 1106.494 | 6:5 | 1.200 | ||||||
| 5\64 | 93.750 | 1106.250 | 5:4 | 1.250 | ||||||
| 9\115 | 93.913 | 1106.087 | 9:7 | 1.286 | ||||||
| 4\51 | 94.118 | 1105.882 | 4:3 | 1.333 | Supersoft 12L 1s | |||||
| 11\140 | 94.286 | 1105.714 | 11:8 | 1.375 | ||||||
| 7\89 | 94.382 | 1105.618 | 7:5 | 1.400 | ||||||
| 10\127 | 94.488 | 1105.512 | 10:7 | 1.429 | ||||||
| 3\38 | 94.737 | 1105.263 | 3:2 | 1.500 | Soft 12L 1s | |||||
| 11\139 | 94.964 | 1105.036 | 11:7 | 1.571 | ||||||
| 8\101 | 95.050 | 1104.950 | 8:5 | 1.600 | ||||||
| 13\164 | 95.122 | 1104.878 | 13:8 | 1.625 | ||||||
| 5\63 | 95.238 | 1104.762 | 5:3 | 1.667 | Semisoft 12L 1s | |||||
| 12\151 | 95.364 | 1104.636 | 12:7 | 1.714 | ||||||
| 7\88 | 95.455 | 1104.545 | 7:4 | 1.750 | ||||||
| 9\113 | 95.575 | 1104.425 | 9:5 | 1.800 | ||||||
| 2\25 | 96.000 | 1104.000 | 2:1 | 2.000 | Basic 12L 1s | |||||
| 9\112 | 96.429 | 1103.571 | 9:4 | 2.250 | ||||||
| 7\87 | 96.552 | 1103.448 | 7:3 | 2.333 | ||||||
| 12\149 | 96.644 | 1103.356 | 12:5 | 2.400 | ||||||
| 5\62 | 96.774 | 1103.226 | 5:2 | 2.500 | Semihard 12L 1s | |||||
| 13\161 | 96.894 | 1103.106 | 13:5 | 2.600 | ||||||
| 8\99 | 96.970 | 1103.030 | 8:3 | 2.667 | ||||||
| 11\136 | 97.059 | 1102.941 | 11:4 | 2.750 | ||||||
| 3\37 | 97.297 | 1102.703 | 3:1 | 3.000 | Hard 12L 1s | |||||
| 10\123 | 97.561 | 1102.439 | 10:3 | 3.333 | ||||||
| 7\86 | 97.674 | 1102.326 | 7:2 | 3.500 | ||||||
| 11\135 | 97.778 | 1102.222 | 11:3 | 3.667 | ||||||
| 4\49 | 97.959 | 1102.041 | 4:1 | 4.000 | Superhard 12L 1s | |||||
| 9\110 | 98.182 | 1101.818 | 9:2 | 4.500 | ||||||
| 5\61 | 98.361 | 1101.639 | 5:1 | 5.000 | ||||||
| 6\73 | 98.630 | 1101.370 | 6:1 | 6.000 | ||||||
| 1\12 | 100.000 | 1100.000 | 1:0 | → ∞ | Collapsed 12L 1s | |||||
 |
Todo: cleanup, add etymology Clean up lead section, find out who first proposed the name quasidozenal |