13L 4s
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Scale structure
Step pattern
LLLLsLLLsLLLsLLLs
sLLLsLLLsLLLsLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
13\17 to 10\13 (917.6¢ to 923.1¢)
Dark
3\13 to 4\17 (276.9¢ to 282.4¢)
TAMNAMS information
Descends from
4L 5s (gramitonic)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Related MOS scales
Parent
4L 9s
Sister
4L 13s
Daughters
17L 13s, 13L 17s
Neutralized
9L 8s
2-Flought
30L 4s, 13L 21s
Equal tunings
Equalized (L:s = 1:1)
13\17 (917.6¢)
Supersoft (L:s = 4:3)
49\64 (918.8¢)
Soft (L:s = 3:2)
36\47 (919.1¢)
Semisoft (L:s = 5:3)
59\77 (919.5¢)
Basic (L:s = 2:1)
23\30 (920.0¢)
Semihard (L:s = 5:2)
56\73 (920.5¢)
Hard (L:s = 3:1)
33\43 (920.9¢)
Superhard (L:s = 4:1)
43\56 (921.4¢)
Collapsed (L:s = 1:0)
10\13 (923.1¢)
| ↖ 12L 3s | ↑ 13L 3s | 14L 3s ↗ |
| ← 12L 4s | 13L 4s | 14L 4s → |
| ↙ 12L 5s | ↓ 13L 5s | 14L 5s ↘ |
┌╥╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║║│║║║│║║║│║║║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLsLLLsLLLsLLLL
13L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 4 small steps, repeating every octave. 13L 4s is a grandchild scale of 4L 5s, expanding it by 8 tones. Generators that produce this scale range from 917.6¢ to 923.1¢, or from 276.9¢ to 282.4¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 16|0 | 1 | LLLLsLLLsLLLsLLLs |
| 15|1 | 14 | LLLsLLLLsLLLsLLLs |
| 14|2 | 10 | LLLsLLLsLLLLsLLLs |
| 13|3 | 6 | LLLsLLLsLLLsLLLLs |
| 12|4 | 2 | LLLsLLLsLLLsLLLsL |
| 11|5 | 15 | LLsLLLLsLLLsLLLsL |
| 10|6 | 11 | LLsLLLsLLLLsLLLsL |
| 9|7 | 7 | LLsLLLsLLLsLLLLsL |
| 8|8 | 3 | LLsLLLsLLLsLLLsLL |
| 7|9 | 16 | LsLLLLsLLLsLLLsLL |
| 6|10 | 12 | LsLLLsLLLLsLLLsLL |
| 5|11 | 8 | LsLLLsLLLsLLLLsLL |
| 4|12 | 4 | LsLLLsLLLsLLLsLLL |
| 3|13 | 17 | sLLLLsLLLsLLLsLLL |
| 2|14 | 13 | sLLLsLLLLsLLLsLLL |
| 1|15 | 9 | sLLLsLLLsLLLLsLLL |
| 0|16 | 5 | sLLLsLLLsLLLsLLLL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 13\17 | 917.647 | 282.353 | 1:1 | 1.000 | Equalized 13L 4s | |||||
| 75\98 | 918.367 | 281.633 | 6:5 | 1.200 | ||||||
| 62\81 | 918.519 | 281.481 | 5:4 | 1.250 | ||||||
| 111\145 | 918.621 | 281.379 | 9:7 | 1.286 | ||||||
| 49\64 | 918.750 | 281.250 | 4:3 | 1.333 | Supersoft 13L 4s | |||||
| 134\175 | 918.857 | 281.143 | 11:8 | 1.375 | ||||||
| 85\111 | 918.919 | 281.081 | 7:5 | 1.400 | ||||||
| 121\158 | 918.987 | 281.013 | 10:7 | 1.429 | ||||||
| 36\47 | 919.149 | 280.851 | 3:2 | 1.500 | Soft 13L 4s | |||||
| 131\171 | 919.298 | 280.702 | 11:7 | 1.571 | ||||||
| 95\124 | 919.355 | 280.645 | 8:5 | 1.600 | ||||||
| 154\201 | 919.403 | 280.597 | 13:8 | 1.625 | ||||||
| 59\77 | 919.481 | 280.519 | 5:3 | 1.667 | Semisoft 13L 4s | |||||
| 141\184 | 919.565 | 280.435 | 12:7 | 1.714 | ||||||
| 82\107 | 919.626 | 280.374 | 7:4 | 1.750 | ||||||
| 105\137 | 919.708 | 280.292 | 9:5 | 1.800 | ||||||
| 23\30 | 920.000 | 280.000 | 2:1 | 2.000 | Basic 13L 4s Scales with tunings softer than this are proper | |||||
| 102\133 | 920.301 | 279.699 | 9:4 | 2.250 | ||||||
| 79\103 | 920.388 | 279.612 | 7:3 | 2.333 | ||||||
| 135\176 | 920.455 | 279.545 | 12:5 | 2.400 | ||||||
| 56\73 | 920.548 | 279.452 | 5:2 | 2.500 | Semihard 13L 4s | |||||
| 145\189 | 920.635 | 279.365 | 13:5 | 2.600 | ||||||
| 89\116 | 920.690 | 279.310 | 8:3 | 2.667 | ||||||
| 122\159 | 920.755 | 279.245 | 11:4 | 2.750 | ||||||
| 33\43 | 920.930 | 279.070 | 3:1 | 3.000 | Hard 13L 4s | |||||
| 109\142 | 921.127 | 278.873 | 10:3 | 3.333 | ||||||
| 76\99 | 921.212 | 278.788 | 7:2 | 3.500 | ||||||
| 119\155 | 921.290 | 278.710 | 11:3 | 3.667 | ||||||
| 43\56 | 921.429 | 278.571 | 4:1 | 4.000 | Superhard 13L 4s | |||||
| 96\125 | 921.600 | 278.400 | 9:2 | 4.500 | ||||||
| 53\69 | 921.739 | 278.261 | 5:1 | 5.000 | ||||||
| 63\82 | 921.951 | 278.049 | 6:1 | 6.000 | ||||||
| 10\13 | 923.077 | 276.923 | 1:0 | → ∞ | Collapsed 13L 4s | |||||