7L 17s
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Scale structure
Step pattern
LssLssLsssLssLsssLssLsss
sssLssLsssLssLsssLssLssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
17\24 to 5\7 (850.0¢ to 857.1¢)
Dark
2\7 to 7\24 (342.9¢ to 350.0¢)
TAMNAMS information
Descends from
7L 3s (dicoid)
Ancestor's step ratio range
3:1 to 1:0 (hard)
Related MOS scales
Parent
7L 10s
Sister
17L 7s
Daughters
24L 7s, 7L 24s
Neutralized
14L 10s
2-Flought
31L 17s, 7L 41s
Equal tunings
Equalized (L:s = 1:1)
17\24 (850.0¢)
Supersoft (L:s = 4:3)
56\79 (850.6¢)
Soft (L:s = 3:2)
39\55 (850.9¢)
Semisoft (L:s = 5:3)
61\86 (851.2¢)
Basic (L:s = 2:1)
22\31 (851.6¢)
Semihard (L:s = 5:2)
49\69 (852.2¢)
Hard (L:s = 3:1)
27\38 (852.6¢)
Superhard (L:s = 4:1)
32\45 (853.3¢)
Collapsed (L:s = 1:0)
5\7 (857.1¢)
| ↖ 6L 16s | ↑ 7L 16s | 8L 16s ↗ |
| ← 6L 17s | 7L 17s | 8L 17s → |
| ↙ 6L 18s | ↓ 7L 18s | 8L 18s ↘ |
┌╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐ │║││║││║│││║││║│││║││║││││ ││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssLssLsssLssLsssLssLssL
7L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 17 small steps, repeating every octave. 7L 17s is a grandchild scale of 7L 3s, expanding it by 14 tones. Generators that produce this scale range from 850¢ to 857.1¢, or from 342.9¢ to 350¢. The dark generator serves as an approximate 11/9 (347¢), with 11\38 – the low estimate for the boundary of "practicality" – giving this ratio almost exactly.
Notable harmonic entropy minima are mohajira and migration, two alternative extensions of the 2.3.5.11 temperament mohaha to the full 11-limit, merging in 31edo.
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 17\24 | 850.000 | 350.000 | 1:1 | 1.000 | Equalized 7L 17s | |||||
| 90\127 | 850.394 | 349.606 | 6:5 | 1.200 | ||||||
| 73\103 | 850.485 | 349.515 | 5:4 | 1.250 | ||||||
| 129\182 | 850.549 | 349.451 | 9:7 | 1.286 | ||||||
| 56\79 | 850.633 | 349.367 | 4:3 | 1.333 | Supersoft 7L 17s | |||||
| 151\213 | 850.704 | 349.296 | 11:8 | 1.375 | ||||||
| 95\134 | 850.746 | 349.254 | 7:5 | 1.400 | ||||||
| 134\189 | 850.794 | 349.206 | 10:7 | 1.429 | ||||||
| 39\55 | 850.909 | 349.091 | 3:2 | 1.500 | Soft 7L 17s | |||||
| 139\196 | 851.020 | 348.980 | 11:7 | 1.571 | ||||||
| 100\141 | 851.064 | 348.936 | 8:5 | 1.600 | ||||||
| 161\227 | 851.101 | 348.899 | 13:8 | 1.625 | ||||||
| 61\86 | 851.163 | 348.837 | 5:3 | 1.667 | Semisoft 7L 17s | |||||
| 144\203 | 851.232 | 348.768 | 12:7 | 1.714 | ||||||
| 83\117 | 851.282 | 348.718 | 7:4 | 1.750 | ||||||
| 105\148 | 851.351 | 348.649 | 9:5 | 1.800 | ||||||
| 22\31 | 851.613 | 348.387 | 2:1 | 2.000 | Basic 7L 17s Scales with tunings softer than this are proper | |||||
| 93\131 | 851.908 | 348.092 | 9:4 | 2.250 | ||||||
| 71\100 | 852.000 | 348.000 | 7:3 | 2.333 | ||||||
| 120\169 | 852.071 | 347.929 | 12:5 | 2.400 | ||||||
| 49\69 | 852.174 | 347.826 | 5:2 | 2.500 | Semihard 7L 17s | |||||
| 125\176 | 852.273 | 347.727 | 13:5 | 2.600 | ||||||
| 76\107 | 852.336 | 347.664 | 8:3 | 2.667 | ||||||
| 103\145 | 852.414 | 347.586 | 11:4 | 2.750 | ||||||
| 27\38 | 852.632 | 347.368 | 3:1 | 3.000 | Hard 7L 17s | |||||
| 86\121 | 852.893 | 347.107 | 10:3 | 3.333 | ||||||
| 59\83 | 853.012 | 346.988 | 7:2 | 3.500 | ||||||
| 91\128 | 853.125 | 346.875 | 11:3 | 3.667 | ||||||
| 32\45 | 853.333 | 346.667 | 4:1 | 4.000 | Superhard 7L 17s | |||||
| 69\97 | 853.608 | 346.392 | 9:2 | 4.500 | ||||||
| 37\52 | 853.846 | 346.154 | 5:1 | 5.000 | ||||||
| 42\59 | 854.237 | 345.763 | 6:1 | 6.000 | ||||||
| 5\7 | 857.143 | 342.857 | 1:0 | → ∞ | Collapsed 7L 17s | |||||