4L 13s
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Scale structure
Step pattern
LsssLsssLsssLssss
ssssLsssLsssLsssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
4\17 to 1\4 (282.4¢ to 300.0¢)
Dark
3\4 to 13\17 (900.0¢ to 917.6¢)
TAMNAMS information
Descends from
4L 5s (gramitonic)
Ancestor's step ratio range
3:1 to 1:0 (hard)
Related MOS scales
Parent
4L 9s
Sister
13L 4s
Daughters
17L 4s, 4L 17s
Neutralized
8L 9s
2-Flought
21L 13s, 4L 30s
Equal tunings
Equalized (L:s = 1:1)
4\17 (282.4¢)
Supersoft (L:s = 4:3)
13\55 (283.6¢)
Soft (L:s = 3:2)
9\38 (284.2¢)
Semisoft (L:s = 5:3)
14\59 (284.7¢)
Basic (L:s = 2:1)
5\21 (285.7¢)
Semihard (L:s = 5:2)
11\46 (287.0¢)
Hard (L:s = 3:1)
6\25 (288.0¢)
Superhard (L:s = 4:1)
7\29 (289.7¢)
Collapsed (L:s = 1:0)
1\4 (300.0¢)
| ↖ 3L 12s | ↑ 4L 12s | 5L 12s ↗ |
| ← 3L 13s | 4L 13s | 5L 13s → |
| ↙ 3L 14s | ↓ 4L 14s | 5L 14s ↘ |
┌╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┬┐ │║│││║│││║│││║│││││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssLsssLsssLsssL
4L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 13 small steps, repeating every octave. 4L 13s is a grandchild scale of 4L 5s, expanding it by 8 tones. Generators that produce this scale range from 282.4¢ to 300¢, or from 900¢ to 917.6¢.
Modes
| UDP | Cyclic Order |
Step Pattern |
|---|---|---|
| 16|0 | 1 | LsssLsssLsssLssss |
| 15|1 | 5 | LsssLsssLssssLsss |
| 14|2 | 9 | LsssLssssLsssLsss |
| 13|3 | 13 | LssssLsssLsssLsss |
| 12|4 | 17 | sLsssLsssLsssLsss |
| 11|5 | 4 | sLsssLsssLssssLss |
| 10|6 | 8 | sLsssLssssLsssLss |
| 9|7 | 12 | sLssssLsssLsssLss |
| 8|8 | 16 | ssLsssLsssLsssLss |
| 7|9 | 3 | ssLsssLsssLssssLs |
| 6|10 | 7 | ssLsssLssssLsssLs |
| 5|11 | 11 | ssLssssLsssLsssLs |
| 4|12 | 15 | sssLsssLsssLsssLs |
| 3|13 | 2 | sssLsssLsssLssssL |
| 2|14 | 6 | sssLsssLssssLsssL |
| 1|15 | 10 | sssLssssLsssLsssL |
| 0|16 | 14 | ssssLsssLsssLsssL |
Scale tree
| Generator(edo) | Cents | Step Ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 4\17 | 282.353 | 917.647 | 1:1 | 1.000 | Equalized 4L 13s | |||||
| 21\89 | 283.146 | 916.854 | 6:5 | 1.200 | ||||||
| 17\72 | 283.333 | 916.667 | 5:4 | 1.250 | ||||||
| 30\127 | 283.465 | 916.535 | 9:7 | 1.286 | ||||||
| 13\55 | 283.636 | 916.364 | 4:3 | 1.333 | Supersoft 4L 13s | |||||
| 35\148 | 283.784 | 916.216 | 11:8 | 1.375 | ||||||
| 22\93 | 283.871 | 916.129 | 7:5 | 1.400 | ||||||
| 31\131 | 283.969 | 916.031 | 10:7 | 1.429 | ||||||
| 9\38 | 284.211 | 915.789 | 3:2 | 1.500 | Soft 4L 13s | |||||
| 32\135 | 284.444 | 915.556 | 11:7 | 1.571 | ||||||
| 23\97 | 284.536 | 915.464 | 8:5 | 1.600 | ||||||
| 37\156 | 284.615 | 915.385 | 13:8 | 1.625 | ||||||
| 14\59 | 284.746 | 915.254 | 5:3 | 1.667 | Semisoft 4L 13s | |||||
| 33\139 | 284.892 | 915.108 | 12:7 | 1.714 | ||||||
| 19\80 | 285.000 | 915.000 | 7:4 | 1.750 | ||||||
| 24\101 | 285.149 | 914.851 | 9:5 | 1.800 | ||||||
| 5\21 | 285.714 | 914.286 | 2:1 | 2.000 | Basic 4L 13s Scales with tunings softer than this are proper | |||||
| 21\88 | 286.364 | 913.636 | 9:4 | 2.250 | ||||||
| 16\67 | 286.567 | 913.433 | 7:3 | 2.333 | ||||||
| 27\113 | 286.726 | 913.274 | 12:5 | 2.400 | ||||||
| 11\46 | 286.957 | 913.043 | 5:2 | 2.500 | Semihard 4L 13s | |||||
| 28\117 | 287.179 | 912.821 | 13:5 | 2.600 | ||||||
| 17\71 | 287.324 | 912.676 | 8:3 | 2.667 | ||||||
| 23\96 | 287.500 | 912.500 | 11:4 | 2.750 | ||||||
| 6\25 | 288.000 | 912.000 | 3:1 | 3.000 | Hard 4L 13s | |||||
| 19\79 | 288.608 | 911.392 | 10:3 | 3.333 | ||||||
| 13\54 | 288.889 | 911.111 | 7:2 | 3.500 | ||||||
| 20\83 | 289.157 | 910.843 | 11:3 | 3.667 | ||||||
| 7\29 | 289.655 | 910.345 | 4:1 | 4.000 | Superhard 4L 13s | |||||
| 15\62 | 290.323 | 909.677 | 9:2 | 4.500 | ||||||
| 8\33 | 290.909 | 909.091 | 5:1 | 5.000 | ||||||
| 9\37 | 291.892 | 908.108 | 6:1 | 6.000 | ||||||
| 1\4 | 300.000 | 900.000 | 1:0 | → ∞ | Collapsed 4L 13s | |||||