1L 12s
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Scale structure
Step pattern
Lssssssssssss
ssssssssssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
12\13 to 1\1 (1107.7¢ to 1200.0¢)
Dark
0\1 to 1\13 (0.0¢ to 92.3¢)
TAMNAMS information
Descends from
1L 9s (antisinatonic)
Required step ratio range
4:1 to 1:0 (ultrahard)
Related MOS scales
Parent
1L 11s
Sister
12L 1s
Daughters
13L 1s
1L 13s
Equal tunings
Equalized (L:s = 1:1)
12\13 (1107.7¢)
Supersoft (L:s = 4:3)
37\40 (1110.0¢)
Soft (L:s = 3:2)
25\27 (1111.1¢)
Semisoft (L:s = 5:3)
38\41 (1112.2¢)
Basic (L:s = 2:1)
13\14 (1114.3¢)
Semihard (L:s = 5:2)
27\29 (1117.2¢)
Hard (L:s = 3:1)
14\15 (1120.0¢)
Superhard (L:s = 4:1)
15\16 (1125.0¢)
Collapsed (L:s = 1:0)
1\1 (1200.0¢)
Todo: cleanup
Rewrite intro, add links to temperaments
| ↑1L 11s | 2L 11s↗ | |
| 1L 12s | 2L 12s→ | |
| ↓1L 13s | 2L 13s↘ |
┌╥┬┬┬┬┬┬┬┬┬┬┬┬┐ │║│││││││││││││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssssssssssL
1L 13s
1L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 12 small steps, repeating every octave. 1L 12s is a great-grandchild scale of 1L 9s, expanding it by 3 tones. Generators that produce this scale range from 1107.7¢ to 1200¢, or from 0¢ to 92.3¢.
This MOS, also called the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.
Modes
| UDP | Rotational order | Step pattern |
|---|---|---|
| 12|0 | 1 | Lssssssssssss |
| 11|1 | 13 | sLsssssssssss |
| 10|2 | 12 | ssLssssssssss |
| 9|3 | 11 | sssLsssssssss |
| 8|4 | 10 | ssssLssssssss |
| 7|5 | 9 | sssssLsssssss |
| 6|6 | 8 | ssssssLssssss |
| 5|7 | 7 | sssssssLsssss |
| 4|8 | 6 | ssssssssLssss |
| 3|9 | 5 | sssssssssLsss |
| 2|10 | 4 | ssssssssssLss |
| 1|11 | 3 | sssssssssssLs |
| 0|12 | 2 | ssssssssssssL |
Scale tree
| Generator (edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 12\13 | 1107.692 | 92.308 | 1:1 | 1.000 | Equalized 1L 12s | |||||
| 61\66 | 1109.091 | 90.909 | 6:5 | 1.200 | ||||||
| 49\53 | 1109.434 | 90.566 | 5:4 | 1.250 | ||||||
| 86\93 | 1109.677 | 90.323 | 9:7 | 1.286 | ||||||
| 37\40 | 1110.000 | 90.000 | 4:3 | 1.333 | Supersoft 1L 12s | |||||
| 99\107 | 1110.280 | 89.720 | 11:8 | 1.375 | ||||||
| 62\67 | 1110.448 | 89.552 | 7:5 | 1.400 | ||||||
| 87\94 | 1110.638 | 89.362 | 10:7 | 1.429 | ||||||
| 25\27 | 1111.111 | 88.889 | 3:2 | 1.500 | Soft 1L 12s | |||||
| 88\95 | 1111.579 | 88.421 | 11:7 | 1.571 | ||||||
| 63\68 | 1111.765 | 88.235 | 8:5 | 1.600 | ||||||
| 101\109 | 1111.927 | 88.073 | 13:8 | 1.625 | ||||||
| 38\41 | 1112.195 | 87.805 | 5:3 | 1.667 | Semisoft 1L 12s | |||||
| 89\96 | 1112.500 | 87.500 | 12:7 | 1.714 | ||||||
| 51\55 | 1112.727 | 87.273 | 7:4 | 1.750 | ||||||
| 64\69 | 1113.043 | 86.957 | 9:5 | 1.800 | ||||||
| 13\14 | 1114.286 | 85.714 | 2:1 | 2.000 | Basic 1L 12s Scales with tunings softer than this are proper | |||||
| 53\57 | 1115.789 | 84.211 | 9:4 | 2.250 | ||||||
| 40\43 | 1116.279 | 83.721 | 7:3 | 2.333 | ||||||
| 67\72 | 1116.667 | 83.333 | 12:5 | 2.400 | ||||||
| 27\29 | 1117.241 | 82.759 | 5:2 | 2.500 | Semihard 1L 12s | |||||
| 68\73 | 1117.808 | 82.192 | 13:5 | 2.600 | ||||||
| 41\44 | 1118.182 | 81.818 | 8:3 | 2.667 | ||||||
| 55\59 | 1118.644 | 81.356 | 11:4 | 2.750 | ||||||
| 14\15 | 1120.000 | 80.000 | 3:1 | 3.000 | Hard 1L 12s | |||||
| 43\46 | 1121.739 | 78.261 | 10:3 | 3.333 | ||||||
| 29\31 | 1122.581 | 77.419 | 7:2 | 3.500 | ||||||
| 44\47 | 1123.404 | 76.596 | 11:3 | 3.667 | ||||||
| 15\16 | 1125.000 | 75.000 | 4:1 | 4.000 | Superhard 1L 12s | |||||
| 31\33 | 1127.273 | 72.727 | 9:2 | 4.500 | ||||||
| 16\17 | 1129.412 | 70.588 | 5:1 | 5.000 | ||||||
| 17\18 | 1133.333 | 66.667 | 6:1 | 6.000 | ||||||
| 1\1 | 1200.000 | 0.000 | 1:0 | → ∞ | Collapsed 1L 12s | |||||