13L 7s
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Scale structure
Step pattern
LLsLLsLLsLLsLLsLLsLs
sLsLLsLLsLLsLLsLLsLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
3\20 to 2\13 (180.0¢ to 184.6¢)
Dark
11\13 to 17\20 (1015.4¢ to 1020.0¢)
TAMNAMS information
Descends from
6L 1s (archaeotonic)
Required step ratio range
3:2 to 2:1 (hyposoft)
Related MOS scales
Parent
7L 6s
Sister
7L 13s
Daughters
20L 13s, 13L 20s
Neutralized
6L 14s
Equal tunings
Equalized (L:s = 1:1)
3\20 (180.0¢)
Supersoft (L:s = 4:3)
11\73 (180.8¢)
Soft (L:s = 3:2)
8\53 (181.1¢)
Semisoft (L:s = 5:3)
13\86 (181.4¢)
Basic (L:s = 2:1)
5\33 (181.8¢)
Semihard (L:s = 5:2)
12\79 (182.3¢)
Hard (L:s = 3:1)
7\46 (182.6¢)
Superhard (L:s = 4:1)
9\59 (183.1¢)
Collapsed (L:s = 1:0)
2\13 (184.6¢)
| ↖12L 6s | ↑13L 6s | 14L 6s↗ |
| ←12L 7s | 13L 7s | 14L 7s→ |
| ↙12L 8s | ↓13L 8s | 14L 8s↘ |
┌╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥┬┐ │║║│║║│║║│║║│║║│║║│║││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLLsLLsLLsLLsLLsLL
13L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 7 small steps, repeating every octave. 13L 7s is a grandchild scale of 6L 1s, expanding it by 13 tones. Generators that produce this scale range from 180¢ to 184.6¢, or from 1015.4¢ to 1020¢.
Modes
| UDP | Rotational order | Step pattern |
|---|---|---|
| 19|0 | 1 | LLsLLsLLsLLsLLsLLsLs |
| 18|1 | 4 | LLsLLsLLsLLsLLsLsLLs |
| 17|2 | 7 | LLsLLsLLsLLsLsLLsLLs |
| 16|3 | 10 | LLsLLsLLsLsLLsLLsLLs |
| 15|4 | 13 | LLsLLsLsLLsLLsLLsLLs |
| 14|5 | 16 | LLsLsLLsLLsLLsLLsLLs |
| 13|6 | 19 | LsLLsLLsLLsLLsLLsLLs |
| 12|7 | 2 | LsLLsLLsLLsLLsLLsLsL |
| 11|8 | 5 | LsLLsLLsLLsLLsLsLLsL |
| 10|9 | 8 | LsLLsLLsLLsLsLLsLLsL |
| 9|10 | 11 | LsLLsLLsLsLLsLLsLLsL |
| 8|11 | 14 | LsLLsLsLLsLLsLLsLLsL |
| 7|12 | 17 | LsLsLLsLLsLLsLLsLLsL |
| 6|13 | 20 | sLLsLLsLLsLLsLLsLLsL |
| 5|14 | 3 | sLLsLLsLLsLLsLLsLsLL |
| 4|15 | 6 | sLLsLLsLLsLLsLsLLsLL |
| 3|16 | 9 | sLLsLLsLLsLsLLsLLsLL |
| 2|17 | 12 | sLLsLLsLsLLsLLsLLsLL |
| 1|18 | 15 | sLLsLsLLsLLsLLsLLsLL |
| 0|19 | 18 | sLsLLsLLsLLsLLsLLsLL |
Scale tree
| Generator(edo) | Cents | Step Ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\20 | 180.000 | 1020.000 | 1:1 | 1.000 | Equalized 13L 7s | |||||
| 17\113 | 180.531 | 1019.469 | 6:5 | 1.200 | ||||||
| 14\93 | 180.645 | 1019.355 | 5:4 | 1.250 | ||||||
| 25\166 | 180.723 | 1019.277 | 9:7 | 1.286 | ||||||
| 11\73 | 180.822 | 1019.178 | 4:3 | 1.333 | Supersoft 13L 7s | |||||
| 30\199 | 180.905 | 1019.095 | 11:8 | 1.375 | ||||||
| 19\126 | 180.952 | 1019.048 | 7:5 | 1.400 | ||||||
| 27\179 | 181.006 | 1018.994 | 10:7 | 1.429 | ||||||
| 8\53 | 181.132 | 1018.868 | 3:2 | 1.500 | Soft 13L 7s | |||||
| 29\192 | 181.250 | 1018.750 | 11:7 | 1.571 | ||||||
| 21\139 | 181.295 | 1018.705 | 8:5 | 1.600 | ||||||
| 34\225 | 181.333 | 1018.667 | 13:8 | 1.625 | ||||||
| 13\86 | 181.395 | 1018.605 | 5:3 | 1.667 | Semisoft 13L 7s | |||||
| 31\205 | 181.463 | 1018.537 | 12:7 | 1.714 | ||||||
| 18\119 | 181.513 | 1018.487 | 7:4 | 1.750 | ||||||
| 23\152 | 181.579 | 1018.421 | 9:5 | 1.800 | ||||||
| 5\33 | 181.818 | 1018.182 | 2:1 | 2.000 | Basic 13L 7s Scales with tunings softer than this are proper | |||||
| 22\145 | 182.069 | 1017.931 | 9:4 | 2.250 | ||||||
| 17\112 | 182.143 | 1017.857 | 7:3 | 2.333 | ||||||
| 29\191 | 182.199 | 1017.801 | 12:5 | 2.400 | ||||||
| 12\79 | 182.278 | 1017.722 | 5:2 | 2.500 | Semihard 13L 7s | |||||
| 31\204 | 182.353 | 1017.647 | 13:5 | 2.600 | ||||||
| 19\125 | 182.400 | 1017.600 | 8:3 | 2.667 | ||||||
| 26\171 | 182.456 | 1017.544 | 11:4 | 2.750 | ||||||
| 7\46 | 182.609 | 1017.391 | 3:1 | 3.000 | Hard 13L 7s Mitonic / Minortone | |||||
| 23\151 | 182.781 | 1017.219 | 10:3 | 3.333 | ||||||
| 16\105 | 182.857 | 1017.143 | 7:2 | 3.500 | ||||||
| 25\164 | 182.927 | 1017.073 | 11:3 | 3.667 | ||||||
| 9\59 | 183.051 | 1016.949 | 4:1 | 4.000 | Superhard 13L 7s | |||||
| 20\131 | 183.206 | 1016.794 | 9:2 | 4.500 | ||||||
| 11\72 | 183.333 | 1016.667 | 5:1 | 5.000 | ||||||
| 13\85 | 183.529 | 1016.471 | 6:1 | 6.000 | ||||||
| 2\13 | 184.615 | 1015.385 | 1:0 | → ∞ | Collapsed 13L 7s | |||||