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.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 23|0 | 1 | LssLssLsssLssLsssLssLsss |
| 22|1 | 18 | LssLsssLssLssLsssLssLsss |
| 21|2 | 11 | LssLsssLssLsssLssLssLsss |
| 20|3 | 4 | LssLsssLssLsssLssLsssLss |
| 19|4 | 21 | LsssLssLssLsssLssLsssLss |
| 18|5 | 14 | LsssLssLsssLssLssLsssLss |
| 17|6 | 7 | LsssLssLsssLssLsssLssLss |
| 16|7 | 24 | sLssLssLsssLssLsssLssLss |
| 15|8 | 17 | sLssLsssLssLssLsssLssLss |
| 14|9 | 10 | sLssLsssLssLsssLssLssLss |
| 13|10 | 3 | sLssLsssLssLsssLssLsssLs |
| 12|11 | 20 | sLsssLssLssLsssLssLsssLs |
| 11|12 | 13 | sLsssLssLsssLssLssLsssLs |
| 10|13 | 6 | sLsssLssLsssLssLsssLssLs |
| 9|14 | 23 | ssLssLssLsssLssLsssLssLs |
| 8|15 | 16 | ssLssLsssLssLssLsssLssLs |
| 7|16 | 9 | ssLssLsssLssLsssLssLssLs |
| 6|17 | 2 | ssLssLsssLssLsssLssLsssL |
| 5|18 | 19 | ssLsssLssLssLsssLssLsssL |
| 4|19 | 12 | ssLsssLssLsssLssLssLsssL |
| 3|20 | 5 | ssLsssLssLsssLssLsssLssL |
| 2|21 | 22 | sssLssLssLsssLssLsssLssL |
| 1|22 | 15 | sssLssLsssLssLssLsssLssL |
| 0|23 | 8 | sssLssLsssLssLsssLssLssL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Minor 1-mosstep | m1ms | s | 0.0¢ to 50.0¢ |
| Major 1-mosstep | M1ms | L | 50.0¢ to 171.4¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 100.0¢ |
| Major 2-mosstep | M2ms | L + s | 100.0¢ to 171.4¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 150.0¢ |
| Major 3-mosstep | M3ms | L + 2s | 150.0¢ to 171.4¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 171.4¢ to 200.0¢ |
| Major 4-mosstep | M4ms | 2L + 2s | 200.0¢ to 342.9¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 171.4¢ to 250.0¢ |
| Major 5-mosstep | M5ms | 2L + 3s | 250.0¢ to 342.9¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 171.4¢ to 300.0¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 300.0¢ to 342.9¢ | |
| 7-mosstep | Perfect 7-mosstep | P7ms | 2L + 5s | 342.9¢ to 350.0¢ |
| Augmented 7-mosstep | A7ms | 3L + 4s | 350.0¢ to 514.3¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 2L + 6s | 342.9¢ to 400.0¢ |
| Major 8-mosstep | M8ms | 3L + 5s | 400.0¢ to 514.3¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 2L + 7s | 342.9¢ to 450.0¢ |
| Major 9-mosstep | M9ms | 3L + 6s | 450.0¢ to 514.3¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 2L + 8s | 342.9¢ to 500.0¢ |
| Major 10-mosstep | M10ms | 3L + 7s | 500.0¢ to 514.3¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 3L + 8s | 514.3¢ to 550.0¢ |
| Major 11-mosstep | M11ms | 4L + 7s | 550.0¢ to 685.7¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 3L + 9s | 514.3¢ to 600.0¢ |
| Major 12-mosstep | M12ms | 4L + 8s | 600.0¢ to 685.7¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 3L + 10s | 514.3¢ to 650.0¢ |
| Major 13-mosstep | M13ms | 4L + 9s | 650.0¢ to 685.7¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 4L + 10s | 685.7¢ to 700.0¢ |
| Major 14-mosstep | M14ms | 5L + 9s | 700.0¢ to 857.1¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 4L + 11s | 685.7¢ to 750.0¢ |
| Major 15-mosstep | M15ms | 5L + 10s | 750.0¢ to 857.1¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 4L + 12s | 685.7¢ to 800.0¢ |
| Major 16-mosstep | M16ms | 5L + 11s | 800.0¢ to 857.1¢ | |
| 17-mosstep | Diminished 17-mosstep | d17ms | 4L + 13s | 685.7¢ to 850.0¢ |
| Perfect 17-mosstep | P17ms | 5L + 12s | 850.0¢ to 857.1¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 5L + 13s | 857.1¢ to 900.0¢ |
| Major 18-mosstep | M18ms | 6L + 12s | 900.0¢ to 1028.6¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 5L + 14s | 857.1¢ to 950.0¢ |
| Major 19-mosstep | M19ms | 6L + 13s | 950.0¢ to 1028.6¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 5L + 15s | 857.1¢ to 1000.0¢ |
| Major 20-mosstep | M20ms | 6L + 14s | 1000.0¢ to 1028.6¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 6L + 15s | 1028.6¢ to 1050.0¢ |
| Major 21-mosstep | M21ms | 7L + 14s | 1050.0¢ to 1200.0¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 6L + 16s | 1028.6¢ to 1100.0¢ |
| Major 22-mosstep | M22ms | 7L + 15s | 1100.0¢ to 1200.0¢ | |
| 23-mosstep | Minor 23-mosstep | m23ms | 6L + 17s | 1028.6¢ to 1150.0¢ |
| Major 23-mosstep | M23ms | 7L + 16s | 1150.0¢ to 1200.0¢ | |
| 24-mosstep | Perfect 24-mosstep | P24ms | 7L + 17s | 1200.0¢ |
Scale tree
| 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 | |||||