12L 7s
Jump to navigation
Jump to search
Scale structure
Step pattern
LLsLLsLLsLsLLsLLsLs
sLsLLsLLsLsLLsLLsLL
Equave
2/1 (1200.0¢)
Period
1\19 (63.2¢)
Generator size
Bright
11\19 to 7\12 (694.7¢ to 700.0¢)
Dark
5\12 to 8\19 (500.0¢ to 505.3¢)
TAMNAMS information
Descends from
5L 2s (diatonic)
Ancestor's step ratio range
3:2 to 2:1 (hyposoft)
Related MOS scales
Parent
7L 5s
Sister
7L 12s
Daughters
19L 12s, 12L 19s
Neutralized
5L 14s
2-Flought
31L 7s, 12L 26s
Equal tunings
Equalized (L:s = 1:1)
11\19 (694.7¢)
Supersoft (L:s = 4:3)
40\69 (695.7¢)
Soft (L:s = 3:2)
29\50 (696.0¢)
Semisoft (L:s = 5:3)
47\81 (696.3¢)
Basic (L:s = 2:1)
18\31 (696.8¢)
Semihard (L:s = 5:2)
43\74 (697.3¢)
Hard (L:s = 3:1)
25\43 (697.7¢)
Superhard (L:s = 4:1)
32\55 (698.2¢)
Collapsed (L:s = 1:0)
7\12 (700.0¢)
| Todo: review Adopt scale tree, review entries |
| ↖ 11L 6s | ↑12L 6s | 13L 6s ↗ |
| ← 11L 7s | 12L 7s | 13L 7s → |
| ↙ 11L 8s | ↓12L 8s | 13L 8s ↘ |
┌╥╥┬╥╥┬╥╥┬╥┬╥╥┬╥╥┬╥┬┐ │║║│║║│║║│║│║║│║║│║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLLsLLsLsLLsLLsLL
12L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 7 small steps, repeating every octave. 12L 7s is a grandchild scale of 5L 2s, expanding it by 12 tones. Generators that produce this scale range from 694.7¢ to 700¢, or from 500¢ to 505.3¢. Temperaments associated with this scale include meantone, as the meantone enharmonic scale.
Modes
| UDP | Rotational order | Step pattern |
|---|---|---|
| 17|0 | 1 | LLsLLsLLsLsLLsLLsLs |
| 16|1 | 12 | LLsLLsLsLLsLLsLLsLs |
| 15|2 | 4 | LLsLLsLsLLsLLsLsLLs |
| 14|3 | 15 | LLsLsLLsLLsLLsLsLLs |
| 13|4 | 7 | LLsLsLLsLLsLsLLsLLs |
| 12|5 | 18 | LsLLsLLsLLsLsLLsLLs |
| 11|6 | 10 | LsLLsLLsLsLLsLLsLLs |
| 10|7 | 2 | LsLLsLLsLsLLsLLsLsL |
| 9|8 | 13 | LsLLsLsLLsLLsLLsLsL |
| 8|9 | 5 | LsLLsLsLLsLLsLsLLsL |
| 7|10 | 16 | LsLsLLsLLsLLsLsLLsL |
| 6|11 | 8 | LsLsLLsLLsLsLLsLLsL |
| 5|12 | 19 | sLLsLLsLLsLsLLsLLsL |
| 4|13 | 11 | sLLsLLsLsLLsLLsLLsL |
| 3|14 | 3 | sLLsLLsLsLLsLLsLsLL |
| 2|15 | 14 | sLLsLsLLsLLsLLsLsLL |
| 1|16 | 6 | sLLsLsLLsLLsLsLLsLL |
| 0|17 | 17 | sLsLLsLLsLLsLsLLsLL |
| -1|18 | 9 | sLsLLsLLsLsLLsLLsLL |
Scale tree
Generator ranges:
- Chroma-positive generator: 694.7368 cents (11\19) to 700 cents (7\12)
- Chroma-negative generator: 500 cents (5\12) to 505.2632 cents (8\19)
| Generator | Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 11\19 | 694.737 | 1 | 1 | 1.000 | ||||||
| 62\107 | 695.327 | 6 | 5 | 1.200 | ||||||
| 51\88 | 695.455 | 5 | 4 | 1.250 | ||||||
| 91\157 | 695.541 | 9 | 7 | 1.286 | ||||||
| 40\69 | 695.652 | 4 | 3 | 1.333 | ||||||
| 109\188 | 695.745 | 11 | 8 | 1.375 | ||||||
| 69\119 | 695.798 | 7 | 5 | 1.400 | ||||||
| 98\169 | 695.858 | 10 | 7 | 1.428 | ||||||
| 29\50 | 696.000 | 3 | 2 | 1.500 | Meantone / Meanpop | |||||
| 105\181 | 696.133 | 11 | 7 | 1.571 | ||||||
| 76\131 | 696.183 | 8 | 5 | 1.600 | ||||||
| 123\212 | 696.226 | 13 | 8 | 1.625 | Golden meantone (696.2145¢) | |||||
| 47\81 | 696.296 | 5 | 3 | 1.667 | Meantone / Meanpop | |||||
| 112\193 | 696.373 | 12 | 7 | 1.714 | ||||||
| 65\112 | 696.429 | 7 | 4 | 1.750 | ||||||
| 83\143 | 696.503 | 9 | 5 | 1.800 | ||||||
| 18\31 | 696.774 | 2 | 1 | 2.000 | Basic 12L 7s (Generators smaller than this are proper) | |||||
| 79\136 | 697.059 | 9 | 4 | 2.250 | ||||||
| 61\105 | 697.143 | 7 | 3 | 2.333 | Meantone / Huygens | |||||
| 104\179 | 697.207 | 12 | 5 | 2.400 | ||||||
| 43\74 | 697.297 | 5 | 2 | 2.500 | Meantone / Huygens / Grosstone | |||||
| 111\191 | 697.382 | 13 | 5 | 2.600 | Golden grosstone (697.3969¢) | |||||
| 68\117 | 697.436 | 8 | 3 | 2.667 | ||||||
| 93\160 | 697.500 | 11 | 4 | 2.750 | ||||||
| 25\43 | 697.674 | 3 | 1 | 3.000 | Meantone / Meridetone | |||||
| 82\141 | 697.872 | 10 | 3 | 3.333 | ||||||
| 57\98 | 697.959 | 7 | 2 | 3.500 | ||||||
| 89\153 | 698.039 | 11 | 3 | 3.667 | ||||||
| 32\55 | 698.182 | 4 | 1 | 4.000 | ||||||
| 71\122 | 698.361 | 9 | 2 | 4.500 | ||||||
| 39\67 | 698.507 | 5 | 1 | 5.000 | ||||||
| 46\79 | 698.734 | 6 | 1 | 6.000 | ||||||
| 7\12 | 700.000 | 1 | 0 | → inf | ||||||