17L 3s
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Scale structure
Step pattern
LLLLLLsLLLLLLsLLLLLs
sLLLLLsLLLLLLsLLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
7\20 to 6\17 (420.0¢ to 423.5¢)
Dark
11\17 to 13\20 (776.5¢ to 780.0¢)
TAMNAMS information
Descends from
3L 5s (checkertonic)
Ancestor's step ratio range
4:1 to 5:1
Related MOS scales
Parent
3L 14s
Sister
3L 17s
Daughters
20L 17s, 17L 20s
Neutralized
14L 6s
2-Flought
37L 3s, 17L 23s
Equal tunings
Equalized (L:s = 1:1)
7\20 (420.0¢)
Supersoft (L:s = 4:3)
27\77 (420.8¢)
Soft (L:s = 3:2)
20\57 (421.1¢)
Semisoft (L:s = 5:3)
33\94 (421.3¢)
Basic (L:s = 2:1)
13\37 (421.6¢)
Semihard (L:s = 5:2)
32\91 (422.0¢)
Hard (L:s = 3:1)
19\54 (422.2¢)
Superhard (L:s = 4:1)
25\71 (422.5¢)
Collapsed (L:s = 1:0)
6\17 (423.5¢)
| ↖ 16L 2s | ↑ 17L 2s | 18L 2s ↗ |
| ← 16L 3s | 17L 3s | 18L 3s → |
| ↙ 16L 4s | ↓ 17L 4s | 18L 4s ↘ |
┌╥╥╥╥╥╥┬╥╥╥╥╥╥┬╥╥╥╥╥┬┐ │║║║║║║│║║║║║║│║║║║║││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLsLLLLLLsLLLLLL
17L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 3 small steps, repeating every octave. 17L 3s is related to 3L 5s, expanding it by 12 tones. Generators that produce this scale range from 420¢ to 423.5¢, or from 776.5¢ to 780¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 19|0 | 1 | LLLLLLsLLLLLLsLLLLLs |
| 18|1 | 8 | LLLLLLsLLLLLsLLLLLLs |
| 17|2 | 15 | LLLLLsLLLLLLsLLLLLLs |
| 16|3 | 2 | LLLLLsLLLLLLsLLLLLsL |
| 15|4 | 9 | LLLLLsLLLLLsLLLLLLsL |
| 14|5 | 16 | LLLLsLLLLLLsLLLLLLsL |
| 13|6 | 3 | LLLLsLLLLLLsLLLLLsLL |
| 12|7 | 10 | LLLLsLLLLLsLLLLLLsLL |
| 11|8 | 17 | LLLsLLLLLLsLLLLLLsLL |
| 10|9 | 4 | LLLsLLLLLLsLLLLLsLLL |
| 9|10 | 11 | LLLsLLLLLsLLLLLLsLLL |
| 8|11 | 18 | LLsLLLLLLsLLLLLLsLLL |
| 7|12 | 5 | LLsLLLLLLsLLLLLsLLLL |
| 6|13 | 12 | LLsLLLLLsLLLLLLsLLLL |
| 5|14 | 19 | LsLLLLLLsLLLLLLsLLLL |
| 4|15 | 6 | LsLLLLLLsLLLLLsLLLLL |
| 3|16 | 13 | LsLLLLLsLLLLLLsLLLLL |
| 2|17 | 20 | sLLLLLLsLLLLLLsLLLLL |
| 1|18 | 7 | sLLLLLLsLLLLLsLLLLLL |
| 0|19 | 14 | sLLLLLsLLLLLLsLLLLLL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 7\20 | 420.000 | 780.000 | 1:1 | 1.000 | Equalized 17L 3s | |||||
| 41\117 | 420.513 | 779.487 | 6:5 | 1.200 | ||||||
| 34\97 | 420.619 | 779.381 | 5:4 | 1.250 | ||||||
| 61\174 | 420.690 | 779.310 | 9:7 | 1.286 | ||||||
| 27\77 | 420.779 | 779.221 | 4:3 | 1.333 | Supersoft 17L 3s | |||||
| 74\211 | 420.853 | 779.147 | 11:8 | 1.375 | ||||||
| 47\134 | 420.896 | 779.104 | 7:5 | 1.400 | ||||||
| 67\191 | 420.942 | 779.058 | 10:7 | 1.429 | ||||||
| 20\57 | 421.053 | 778.947 | 3:2 | 1.500 | Soft 17L 3s | |||||
| 73\208 | 421.154 | 778.846 | 11:7 | 1.571 | ||||||
| 53\151 | 421.192 | 778.808 | 8:5 | 1.600 | ||||||
| 86\245 | 421.224 | 778.776 | 13:8 | 1.625 | ||||||
| 33\94 | 421.277 | 778.723 | 5:3 | 1.667 | Semisoft 17L 3s | |||||
| 79\225 | 421.333 | 778.667 | 12:7 | 1.714 | ||||||
| 46\131 | 421.374 | 778.626 | 7:4 | 1.750 | ||||||
| 59\168 | 421.429 | 778.571 | 9:5 | 1.800 | ||||||
| 13\37 | 421.622 | 778.378 | 2:1 | 2.000 | Basic 17L 3s Scales with tunings softer than this are proper | |||||
| 58\165 | 421.818 | 778.182 | 9:4 | 2.250 | ||||||
| 45\128 | 421.875 | 778.125 | 7:3 | 2.333 | ||||||
| 77\219 | 421.918 | 778.082 | 12:5 | 2.400 | ||||||
| 32\91 | 421.978 | 778.022 | 5:2 | 2.500 | Semihard 17L 3s | |||||
| 83\236 | 422.034 | 777.966 | 13:5 | 2.600 | ||||||
| 51\145 | 422.069 | 777.931 | 8:3 | 2.667 | ||||||
| 70\199 | 422.111 | 777.889 | 11:4 | 2.750 | ||||||
| 19\54 | 422.222 | 777.778 | 3:1 | 3.000 | Hard 17L 3s | |||||
| 63\179 | 422.346 | 777.654 | 10:3 | 3.333 | ||||||
| 44\125 | 422.400 | 777.600 | 7:2 | 3.500 | ||||||
| 69\196 | 422.449 | 777.551 | 11:3 | 3.667 | ||||||
| 25\71 | 422.535 | 777.465 | 4:1 | 4.000 | Superhard 17L 3s | |||||
| 56\159 | 422.642 | 777.358 | 9:2 | 4.500 | ||||||
| 31\88 | 422.727 | 777.273 | 5:1 | 5.000 | ||||||
| 37\105 | 422.857 | 777.143 | 6:1 | 6.000 | ||||||
| 6\17 | 423.529 | 776.471 | 1:0 | → ∞ | Collapsed 17L 3s | |||||
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