3L 14s
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Scale structure
Step pattern
LssssLsssssLsssss
sssssLsssssLssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
11\17 to 2\3 (776.5¢ to 800.0¢)
Dark
1\3 to 6\17 (400.0¢ to 423.5¢)
TAMNAMS information
Descends from
3L 5s (checkertonic)
Required step ratio range
4:1 to 1:0 (ultrahard)
Related MOS scales
Parent
3L 11s
Sister
14L 3s
Daughters
17L 3s
3L 17s
Neutralized
6L 11s
Equal tunings
Equalized (L:s = 1:1)
11\17 (776.5¢)
Supersoft (L:s = 4:3)
35\54 (777.8¢)
Soft (L:s = 3:2)
24\37 (778.4¢)
Semisoft (L:s = 5:3)
37\57 (778.9¢)
Basic (L:s = 2:1)
13\20 (780.0¢)
Semihard (L:s = 5:2)
28\43 (781.4¢)
Hard (L:s = 3:1)
15\23 (782.6¢)
Superhard (L:s = 4:1)
17\26 (784.6¢)
Collapsed (L:s = 1:0)
2\3 (800.0¢)
Todo: review
Adopt scale tree template, review entries
| ↖2L 13s | ↑3L 13s | 4L 13s↗ |
| ←2L 14s | 3L 14s | 4L 14s→ |
| ↙2L 15s | ↓3L 15s | 4L 15s↘ |
┌╥┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┐ │║││││║│││││║││││││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssssLsssssLssssL
3L 17s
3L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 14 small steps, repeating every octave. 3L 14s is a great-grandchild scale of 3L 5s, expanding it by 9 tones. Generators that produce this scale range from 776.5¢ to 800¢, or from 400¢ to 423.5¢.
Modes
| UDP | Rotational order | Step pattern |
|---|---|---|
| 16|0 | 1 | LssssLsssssLsssss |
| 15|1 | 12 | LsssssLssssLsssss |
| 14|2 | 6 | LsssssLsssssLssss |
| 13|3 | 17 | sLssssLsssssLssss |
| 12|4 | 11 | sLsssssLssssLssss |
| 11|5 | 5 | sLsssssLsssssLsss |
| 10|6 | 16 | ssLssssLsssssLsss |
| 9|7 | 10 | ssLsssssLssssLsss |
| 8|8 | 4 | ssLsssssLsssssLss |
| 7|9 | 15 | sssLssssLsssssLss |
| 6|10 | 9 | sssLsssssLssssLss |
| 5|11 | 3 | sssLsssssLsssssLs |
| 4|12 | 14 | ssssLssssLsssssLs |
| 3|13 | 8 | ssssLsssssLssssLs |
| 2|14 | 2 | ssssLsssssLsssssL |
| 1|15 | 13 | sssssLssssLsssssL |
| 0|16 | 7 | sssssLsssssLssssL |
Tuning spectrum
| generator | L | s | L/s | gen (cents) | comment | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1\3 | 1 | 0 | 400.000 | |||||||||||
| 15\44 | 10 | 1 | 10.000 | 409.091 | ||||||||||
| 14\41 | 9 | 1 | 9.000 | 409.756 | Hocus | |||||||||
| 27\79 | 17 | 2 | 8.500 | 410.127 | ||||||||||
| 13\38 | 8 | 1 | 8.000 | 410.526 | ||||||||||
| 12\35 | 7 | 1 | 7.000 | 411.429 | ||||||||||
| 23\67 | 13 | 2 | 6.500 | 411.940 | ||||||||||
| 11\32 | 6 | 1 | 6.000 | 412.500 | ||||||||||
| 32\93 | 17 | 3 | 5.667 | 412.903 | ||||||||||
| 21\61 | 11 | 2 | 5.500 | 413.115 | ||||||||||
| 31\90 | 16 | 3 | 5.333 | 413.333 | ||||||||||
| 10\29 | 5 | 1 | 5.000 | 413.793 | ||||||||||
| 39\113 | 19 | 4 | 4.750 | 414.159 | ||||||||||
| 29\84 | 14 | 3 | 4.667 | 414.286 | ||||||||||
| 19\55 | 9 | 2 | 4.500 | 414.545 | Roman | |||||||||
| 28\81 | 13 | 3 | 4.333 | 414.815 | ||||||||||
| 37\107 | 17 | 4 | 4.250 | 414.953 | ||||||||||
| 9\26 | 4 | 1 | 4.000 | 415.385 | ||||||||||
| 35\101 | 15 | 4 | 3.750 | 415.842 | ||||||||||
| 26\75 | 11 | 3 | 3.667 | 416.000 | ||||||||||
| 17\49 | 7 | 2 | 3.500 | 416.327 | ||||||||||
| 25\72 | 10 | 3 | 3.333 | 416.667 | Sqrtphi | |||||||||
| 33\95 | 13 | 4 | 3.250 | 416.842 | ||||||||||
| 41\118 | 16 | 5 | 3.200 | 416.949 | ||||||||||
| 8\23 | 3 | 1 | 3.000 | 417.391 | ||||||||||
| 39\112 | 14 | 5 | 2.800 | 417.857 | ||||||||||
| 31\89 | 11 | 4 | 2.750 | 417.978 | ||||||||||
| 23\66 | 8 | 3 | 2.667 | 418.182 | ||||||||||
| 38\109 | 13 | 5 | 2.600 | 418.349 | ||||||||||
| 15\43 | 5 | 2 | 2.500 | 418.605 | ||||||||||
| 37\106 | 12 | 5 | 2.400 | 418.868 | ||||||||||
| 22\63 | 7 | 3 | 2.333 | 419.048 | ||||||||||
| 29\83 | 9 | 4 | 2.250 | 419.277 | ||||||||||
| 36\103 | 11 | 5 | 2.200 | 419.417 | ||||||||||
| 7\20 | 2 | 1 | 2.000 | 420.000 | ||||||||||
| 41\117 | 11 | 6 | 1.833 | 420.513 | ||||||||||
| 34\97 | 9 | 5 | 1.800 | 420.619 | ||||||||||
| 27\77 | 7 | 4 | 1.750 | 420.779 | ||||||||||
| 20\57 | 5 | 3 | 1.667 | 421.053 | ||||||||||
| 33\94 | 8 | 5 | 1.600 | 421.277 | Bossier | |||||||||
| 13\37 | 3 | 2 | 1.500 | 421.622 | ||||||||||
| 32\91 | 7 | 5 | 1.400 | 421.978 | ||||||||||
| 19\54 | 4 | 3 | 1.333 | 422.222 | ||||||||||
| 25\71 | 5 | 4 | 1.250 | 422.535 | ||||||||||
| 31\88 | 6 | 5 | 1.200 | 422.727 | ||||||||||
| 37\105 | 7 | 6 | 1.167 | 422.857 | ||||||||||
| 43\122 | 8 | 7 | 1.143 | 422.951 | ||||||||||
| 49\139 | 9 | 8 | 1.125 | 423.022 | ||||||||||
| 55\156 | 10 | 9 | 1.111 | 423.077 | ||||||||||
| 6\17 | 1 | 1 | 1.000 | 423.529 | ||||||||||