17L 14s
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Scale structure
Step pattern
LLsLsLsLsLLsLsLsLsLsLLsLsLsLsLs
sLsLsLsLsLLsLsLsLsLsLLsLsLsLsLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
20\31 to 11\17 (774.2¢ to 776.5¢)
Dark
6\17 to 11\31 (423.5¢ to 425.8¢)
TAMNAMS information
Descends from
3L 5s (checkertonic)
Required step ratio range
7:2 to 4:1
Related MOS scales
Parent
14L 3s
Sister
14L 17s
Daughters
31L 17s
17L 31s
Neutralized
3L 28s
Equal tunings
Equalized (L:s = 1:1)
20\31 (774.2¢)
Supersoft (L:s = 4:3)
71\110 (774.5¢)
Soft (L:s = 3:2)
51\79 (774.7¢)
Semisoft (L:s = 5:3)
82\127 (774.8¢)
Basic (L:s = 2:1)
31\48 (775.0¢)
Semihard (L:s = 5:2)
73\113 (775.2¢)
Hard (L:s = 3:1)
42\65 (775.4¢)
Superhard (L:s = 4:1)
53\82 (775.6¢)
Collapsed (L:s = 1:0)
11\17 (776.5¢)
| ↖16L 13s | ↑17L 13s | 18L 13s↗ |
| ←16L 14s | 17L 14s | 18L 14s→ |
| ↙16L 15s | ↓17L 15s | 18L 15s↘ |
┌╥╥┬╥┬╥┬╥┬╥╥┬╥┬╥┬╥┬╥┬╥╥┬╥┬╥┬╥┬╥┬┐ │║║│║│║│║│║║│║│║│║│║│║║│║│║│║│║││ │││││││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLsLsLsLLsLsLsLsLsLLsLsLsLsLL
17L 31s
17L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 14 small steps, repeating every octave. 17L 14s is related to 3L 5s, expanding it by 23 tones. Generators that produce this scale range from 774.2¢ to 776.5¢, or from 423.5¢ to 425.8¢.
Modes
| UDP | Rotational order | Step pattern |
|---|---|---|
| 30|0 | 1 | LLsLsLsLsLLsLsLsLsLsLLsLsLsLsLs |
| 29|1 | 21 | LLsLsLsLsLsLLsLsLsLsLLsLsLsLsLs |
| 28|2 | 10 | LLsLsLsLsLsLLsLsLsLsLsLLsLsLsLs |
| 27|3 | 30 | LsLLsLsLsLsLLsLsLsLsLsLLsLsLsLs |
| 26|4 | 19 | LsLLsLsLsLsLsLLsLsLsLsLLsLsLsLs |
| 25|5 | 8 | LsLLsLsLsLsLsLLsLsLsLsLsLLsLsLs |
| 24|6 | 28 | LsLsLLsLsLsLsLLsLsLsLsLsLLsLsLs |
| 23|7 | 17 | LsLsLLsLsLsLsLsLLsLsLsLsLLsLsLs |
| 22|8 | 6 | LsLsLLsLsLsLsLsLLsLsLsLsLsLLsLs |
| 21|9 | 26 | LsLsLsLLsLsLsLsLLsLsLsLsLsLLsLs |
| 20|10 | 15 | LsLsLsLLsLsLsLsLsLLsLsLsLsLLsLs |
| 19|11 | 4 | LsLsLsLLsLsLsLsLsLLsLsLsLsLsLLs |
| 18|12 | 24 | LsLsLsLsLLsLsLsLsLLsLsLsLsLsLLs |
| 17|13 | 13 | LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLs |
| 16|14 | 2 | LsLsLsLsLLsLsLsLsLsLLsLsLsLsLsL |
| 15|15 | 22 | LsLsLsLsLsLLsLsLsLsLLsLsLsLsLsL |
| 14|16 | 11 | LsLsLsLsLsLLsLsLsLsLsLLsLsLsLsL |
| 13|17 | 31 | sLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL |
| 12|18 | 20 | sLLsLsLsLsLsLLsLsLsLsLLsLsLsLsL |
| 11|19 | 9 | sLLsLsLsLsLsLLsLsLsLsLsLLsLsLsL |
| 10|20 | 29 | sLsLLsLsLsLsLLsLsLsLsLsLLsLsLsL |
| 9|21 | 18 | sLsLLsLsLsLsLsLLsLsLsLsLLsLsLsL |
| 8|22 | 7 | sLsLLsLsLsLsLsLLsLsLsLsLsLLsLsL |
| 7|23 | 27 | sLsLsLLsLsLsLsLLsLsLsLsLsLLsLsL |
| 6|24 | 16 | sLsLsLLsLsLsLsLsLLsLsLsLsLLsLsL |
| 5|25 | 5 | sLsLsLLsLsLsLsLsLLsLsLsLsLsLLsL |
| 4|26 | 25 | sLsLsLsLLsLsLsLsLLsLsLsLsLsLLsL |
| 3|27 | 14 | sLsLsLsLLsLsLsLsLsLLsLsLsLsLLsL |
| 2|28 | 3 | sLsLsLsLLsLsLsLsLsLLsLsLsLsLsLL |
| 1|29 | 23 | sLsLsLsLsLLsLsLsLsLLsLsLsLsLsLL |
| 0|30 | 12 | sLsLsLsLsLLsLsLsLsLsLLsLsLsLsLL |
Scale tree
| Generator(edo) | Cents | Step Ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 20\31 | 774.194 | 425.806 | 1:1 | 1.000 | Equalized 17L 14s | |||||
| 111\172 | 774.419 | 425.581 | 6:5 | 1.200 | ||||||
| 91\141 | 774.468 | 425.532 | 5:4 | 1.250 | ||||||
| 162\251 | 774.502 | 425.498 | 9:7 | 1.286 | ||||||
| 71\110 | 774.545 | 425.455 | 4:3 | 1.333 | Supersoft 17L 14s | |||||
| 193\299 | 774.582 | 425.418 | 11:8 | 1.375 | ||||||
| 122\189 | 774.603 | 425.397 | 7:5 | 1.400 | ||||||
| 173\268 | 774.627 | 425.373 | 10:7 | 1.429 | ||||||
| 51\79 | 774.684 | 425.316 | 3:2 | 1.500 | Soft 17L 14s | |||||
| 184\285 | 774.737 | 425.263 | 11:7 | 1.571 | ||||||
| 133\206 | 774.757 | 425.243 | 8:5 | 1.600 | ||||||
| 215\333 | 774.775 | 425.225 | 13:8 | 1.625 | ||||||
| 82\127 | 774.803 | 425.197 | 5:3 | 1.667 | Semisoft 17L 14s | |||||
| 195\302 | 774.834 | 425.166 | 12:7 | 1.714 | ||||||
| 113\175 | 774.857 | 425.143 | 7:4 | 1.750 | ||||||
| 144\223 | 774.888 | 425.112 | 9:5 | 1.800 | ||||||
| 31\48 | 775.000 | 425.000 | 2:1 | 2.000 | Basic 17L 14s Scales with tunings softer than this are proper | |||||
| 135\209 | 775.120 | 424.880 | 9:4 | 2.250 | ||||||
| 104\161 | 775.155 | 424.845 | 7:3 | 2.333 | ||||||
| 177\274 | 775.182 | 424.818 | 12:5 | 2.400 | ||||||
| 73\113 | 775.221 | 424.779 | 5:2 | 2.500 | Semihard 17L 14s | |||||
| 188\291 | 775.258 | 424.742 | 13:5 | 2.600 | ||||||
| 115\178 | 775.281 | 424.719 | 8:3 | 2.667 | ||||||
| 157\243 | 775.309 | 424.691 | 11:4 | 2.750 | ||||||
| 42\65 | 775.385 | 424.615 | 3:1 | 3.000 | Hard 17L 14s | |||||
| 137\212 | 775.472 | 424.528 | 10:3 | 3.333 | ||||||
| 95\147 | 775.510 | 424.490 | 7:2 | 3.500 | ||||||
| 148\229 | 775.546 | 424.454 | 11:3 | 3.667 | ||||||
| 53\82 | 775.610 | 424.390 | 4:1 | 4.000 | Superhard 17L 14s | |||||
| 117\181 | 775.691 | 424.309 | 9:2 | 4.500 | ||||||
| 64\99 | 775.758 | 424.242 | 5:1 | 5.000 | ||||||
| 75\116 | 775.862 | 424.138 | 6:1 | 6.000 | ||||||
| 11\17 | 776.471 | 423.529 | 1:0 | → ∞ | Collapsed 17L 14s | |||||
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