3L 17s
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Scale structure
Step pattern
LsssssLssssssLssssss
ssssssLssssssLsssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
13\20 to 2\3 (780.0¢ to 800.0¢)
Dark
1\3 to 7\20 (400.0¢ to 420.0¢)
TAMNAMS information
Descends from
3L 5s (checkertonic)
Required step ratio range
5:1 to 1:0
Related MOS scales
Parent
3L 14s
Sister
17L 3s
Daughters
20L 3s
3L 20s
Neutralized
6L 14s
Equal tunings
Equalized (L:s = 1:1)
13\20 (780.0¢)
Supersoft (L:s = 4:3)
41\63 (781.0¢)
Soft (L:s = 3:2)
28\43 (781.4¢)
Semisoft (L:s = 5:3)
43\66 (781.8¢)
Basic (L:s = 2:1)
15\23 (782.6¢)
Semihard (L:s = 5:2)
32\49 (783.7¢)
Hard (L:s = 3:1)
17\26 (784.6¢)
Superhard (L:s = 4:1)
19\29 (786.2¢)
Collapsed (L:s = 1:0)
2\3 (800.0¢)
| ↖2L 16s | ↑3L 16s | 4L 16s↗ |
| ←2L 17s | 3L 17s | 4L 17s→ |
| ↙2L 18s | ↓3L 18s | 4L 18s↘ |
┌╥┬┬┬┬┬╥┬┬┬┬┬┬╥┬┬┬┬┬┬┐ │║│││││║││││││║│││││││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssssLssssssLsssssL
3L 20s
3L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 17 small steps, repeating every octave. 3L 17s is related to 3L 5s, expanding it by 12 tones. Generators that produce this scale range from 780¢ to 800¢, or from 400¢ to 420¢.
This is the MOS which splits its small steps 6-6-5 between its large steps. Its most consonant generator is a 14/11 supermajor third, and its generator in general is a supermajor third of no more than 7/20edo (420 cents).
| Generator(edo) | Cents | Step Ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 13\20 | 780.000 | 420.000 | 1:1 | 1.000 | Equalized 3L 17s | |||||
| 67\103 | 780.583 | 419.417 | 6:5 | 1.200 | ||||||
| 54\83 | 780.723 | 419.277 | 5:4 | 1.250 | ||||||
| 95\146 | 780.822 | 419.178 | 9:7 | 1.286 | ||||||
| 41\63 | 780.952 | 419.048 | 4:3 | 1.333 | Supersoft 3L 17s | |||||
| 110\169 | 781.065 | 418.935 | 11:8 | 1.375 | ||||||
| 69\106 | 781.132 | 418.868 | 7:5 | 1.400 | ||||||
| 97\149 | 781.208 | 418.792 | 10:7 | 1.429 | ||||||
| 28\43 | 781.395 | 418.605 | 3:2 | 1.500 | Soft 3L 17s | |||||
| 99\152 | 781.579 | 418.421 | 11:7 | 1.571 | ||||||
| 71\109 | 781.651 | 418.349 | 8:5 | 1.600 | ||||||
| 114\175 | 781.714 | 418.286 | 13:8 | 1.625 | ||||||
| 43\66 | 781.818 | 418.182 | 5:3 | 1.667 | Semisoft 3L 17s | |||||
| 101\155 | 781.935 | 418.065 | 12:7 | 1.714 | ||||||
| 58\89 | 782.022 | 417.978 | 7:4 | 1.750 | ||||||
| 73\112 | 782.143 | 417.857 | 9:5 | 1.800 | ||||||
| 15\23 | 782.609 | 417.391 | 2:1 | 2.000 | Basic 3L 17s Scales with tunings softer than this are proper | |||||
| 62\95 | 783.158 | 416.842 | 9:4 | 2.250 | ||||||
| 47\72 | 783.333 | 416.667 | 7:3 | 2.333 | ||||||
| 79\121 | 783.471 | 416.529 | 12:5 | 2.400 | ||||||
| 32\49 | 783.673 | 416.327 | 5:2 | 2.500 | Semihard 3L 17s | |||||
| 81\124 | 783.871 | 416.129 | 13:5 | 2.600 | ||||||
| 49\75 | 784.000 | 416.000 | 8:3 | 2.667 | ||||||
| 66\101 | 784.158 | 415.842 | 11:4 | 2.750 | ||||||
| 17\26 | 784.615 | 415.385 | 3:1 | 3.000 | Hard 3L 17s | |||||
| 53\81 | 785.185 | 414.815 | 10:3 | 3.333 | ||||||
| 36\55 | 785.455 | 414.545 | 7:2 | 3.500 | ||||||
| 55\84 | 785.714 | 414.286 | 11:3 | 3.667 | ||||||
| 19\29 | 786.207 | 413.793 | 4:1 | 4.000 | Superhard 3L 17s | |||||
| 40\61 | 786.885 | 413.115 | 9:2 | 4.500 | ||||||
| 21\32 | 787.500 | 412.500 | 5:1 | 5.000 | ||||||
| 23\35 | 788.571 | 411.429 | 6:1 | 6.000 | ||||||
| 2\3 | 800.000 | 400.000 | 1:0 | → ∞ | Collapsed 3L 17s | |||||