4L 17s
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Scale structure
Step pattern
LssssLssssLssssLsssss
sssssLssssLssssLssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
5\21 to 1\4 (285.7¢ to 300.0¢)
Dark
3\4 to 16\21 (900.0¢ to 914.3¢)
TAMNAMS information
Descends from
4L 5s (gramitonic)
Ancestor's step ratio range
4:1 to 1:0 (ultrahard)
Related MOS scales
Parent
4L 13s
Sister
17L 4s
Daughters
21L 4s, 4L 21s
Neutralized
8L 13s
2-Flought
25L 17s, 4L 38s
Equal tunings
Equalized (L:s = 1:1)
5\21 (285.7¢)
Supersoft (L:s = 4:3)
16\67 (286.6¢)
Soft (L:s = 3:2)
11\46 (287.0¢)
Semisoft (L:s = 5:3)
17\71 (287.3¢)
Basic (L:s = 2:1)
6\25 (288.0¢)
Semihard (L:s = 5:2)
13\54 (288.9¢)
Hard (L:s = 3:1)
7\29 (289.7¢)
Superhard (L:s = 4:1)
8\33 (290.9¢)
Collapsed (L:s = 1:0)
1\4 (300.0¢)
| ↖ 3L 16s | ↑ 4L 16s | 5L 16s ↗ |
| ← 3L 17s | 4L 17s | 5L 17s → |
| ↙ 3L 18s | ↓ 4L 18s | 5L 18s ↘ |
┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║││││║││││║││││││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssssLssssLssssLssssL
4L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 17 small steps, repeating every octave. 4L 17s is a great-grandchild scale of 4L 5s, expanding it by 12 tones. Generators that produce this scale range from 285.7¢ to 300¢, or from 900¢ to 914.3¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 20|0 | 1 | LssssLssssLssssLsssss |
| 19|1 | 6 | LssssLssssLsssssLssss |
| 18|2 | 11 | LssssLsssssLssssLssss |
| 17|3 | 16 | LsssssLssssLssssLssss |
| 16|4 | 21 | sLssssLssssLssssLssss |
| 15|5 | 5 | sLssssLssssLsssssLsss |
| 14|6 | 10 | sLssssLsssssLssssLsss |
| 13|7 | 15 | sLsssssLssssLssssLsss |
| 12|8 | 20 | ssLssssLssssLssssLsss |
| 11|9 | 4 | ssLssssLssssLsssssLss |
| 10|10 | 9 | ssLssssLsssssLssssLss |
| 9|11 | 14 | ssLsssssLssssLssssLss |
| 8|12 | 19 | sssLssssLssssLssssLss |
| 7|13 | 3 | sssLssssLssssLsssssLs |
| 6|14 | 8 | sssLssssLsssssLssssLs |
| 5|15 | 13 | sssLsssssLssssLssssLs |
| 4|16 | 18 | ssssLssssLssssLssssLs |
| 3|17 | 2 | ssssLssssLssssLsssssL |
| 2|18 | 7 | ssssLssssLsssssLssssL |
| 1|19 | 12 | ssssLsssssLssssLssssL |
| 0|20 | 17 | sssssLssssLssssLssssL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 5\21 | 285.714 | 914.286 | 1:1 | 1.000 | Equalized 4L 17s | |||||
| 26\109 | 286.239 | 913.761 | 6:5 | 1.200 | ||||||
| 21\88 | 286.364 | 913.636 | 5:4 | 1.250 | ||||||
| 37\155 | 286.452 | 913.548 | 9:7 | 1.286 | ||||||
| 16\67 | 286.567 | 913.433 | 4:3 | 1.333 | Supersoft 4L 17s | |||||
| 43\180 | 286.667 | 913.333 | 11:8 | 1.375 | ||||||
| 27\113 | 286.726 | 913.274 | 7:5 | 1.400 | ||||||
| 38\159 | 286.792 | 913.208 | 10:7 | 1.429 | ||||||
| 11\46 | 286.957 | 913.043 | 3:2 | 1.500 | Soft 4L 17s | |||||
| 39\163 | 287.117 | 912.883 | 11:7 | 1.571 | ||||||
| 28\117 | 287.179 | 912.821 | 8:5 | 1.600 | ||||||
| 45\188 | 287.234 | 912.766 | 13:8 | 1.625 | ||||||
| 17\71 | 287.324 | 912.676 | 5:3 | 1.667 | Semisoft 4L 17s | |||||
| 40\167 | 287.425 | 912.575 | 12:7 | 1.714 | ||||||
| 23\96 | 287.500 | 912.500 | 7:4 | 1.750 | ||||||
| 29\121 | 287.603 | 912.397 | 9:5 | 1.800 | ||||||
| 6\25 | 288.000 | 912.000 | 2:1 | 2.000 | Basic 4L 17s Scales with tunings softer than this are proper | |||||
| 25\104 | 288.462 | 911.538 | 9:4 | 2.250 | ||||||
| 19\79 | 288.608 | 911.392 | 7:3 | 2.333 | ||||||
| 32\133 | 288.722 | 911.278 | 12:5 | 2.400 | ||||||
| 13\54 | 288.889 | 911.111 | 5:2 | 2.500 | Semihard 4L 17s | |||||
| 33\137 | 289.051 | 910.949 | 13:5 | 2.600 | ||||||
| 20\83 | 289.157 | 910.843 | 8:3 | 2.667 | ||||||
| 27\112 | 289.286 | 910.714 | 11:4 | 2.750 | ||||||
| 7\29 | 289.655 | 910.345 | 3:1 | 3.000 | Hard 4L 17s | |||||
| 22\91 | 290.110 | 909.890 | 10:3 | 3.333 | ||||||
| 15\62 | 290.323 | 909.677 | 7:2 | 3.500 | ||||||
| 23\95 | 290.526 | 909.474 | 11:3 | 3.667 | ||||||
| 8\33 | 290.909 | 909.091 | 4:1 | 4.000 | Superhard 4L 17s | |||||
| 17\70 | 291.429 | 908.571 | 9:2 | 4.500 | ||||||
| 9\37 | 291.892 | 908.108 | 5:1 | 5.000 | ||||||
| 10\41 | 292.683 | 907.317 | 6:1 | 6.000 | ||||||
| 1\4 | 300.000 | 900.000 | 1:0 | → ∞ | Collapsed 4L 17s | |||||