7L 17s
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Step pattern
LssLssLsssLssLsssLssLsss
sssLssLsssLssLsssLssLssL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
17\24 to 5\7 (850.0 ¢ to 857.1 ¢)
Dark
2\7 to 7\24 (342.9 ¢ to 350.0 ¢)
Descends from
7L 3s (dicoid)
Ancestor's step ratio range
3:1 to 1:0 (hard)
Parent
7L 10s
Sister
17L 7s
Daughters
24L 7s, 7L 24s
Neutralized
14L 10s
2-Flought
31L 17s, 7L 41s
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 ↘ |
┌╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐ │║││║││║│││║││║│││║││║││││ ││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sssLssLsssLssLsssLssLssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
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.
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.
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 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 30 | Augmented 6-mosdegree | A6md |
| 29 | Augmented 13-mosdegree | A13md |
| 28 | Augmented 20-mosdegree | A20md |
| 27 | Augmented 3-mosdegree | A3md |
| 26 | Augmented 10-mosdegree | A10md |
| 25 | Augmented 17-mosdegree | A17md |
| 24 | Augmented 0-mosdegree | A0md |
| 23 | Augmented 7-mosdegree | A7md |
| 22 | Major 14-mosdegree | M14md |
| 21 | Major 21-mosdegree | M21md |
| 20 | Major 4-mosdegree | M4md |
| 19 | Major 11-mosdegree | M11md |
| 18 | Major 18-mosdegree | M18md |
| 17 | Major 1-mosdegree | M1md |
| 16 | Major 8-mosdegree | M8md |
| 15 | Major 15-mosdegree | M15md |
| 14 | Major 22-mosdegree | M22md |
| 13 | Major 5-mosdegree | M5md |
| 12 | Major 12-mosdegree | M12md |
| 11 | Major 19-mosdegree | M19md |
| 10 | Major 2-mosdegree | M2md |
| 9 | Major 9-mosdegree | M9md |
| 8 | Major 16-mosdegree | M16md |
| 7 | Major 23-mosdegree | M23md |
| 6 | Major 6-mosdegree | M6md |
| 5 | Major 13-mosdegree | M13md |
| 4 | Major 20-mosdegree | M20md |
| 3 | Major 3-mosdegree | M3md |
| 2 | Major 10-mosdegree | M10md |
| 1 | Perfect 17-mosdegree | P17md |
| 0 | Perfect 0-mosdegree Perfect 24-mosdegree |
P0md P24md |
| −1 | Perfect 7-mosdegree | P7md |
| −2 | Minor 14-mosdegree | m14md |
| −3 | Minor 21-mosdegree | m21md |
| −4 | Minor 4-mosdegree | m4md |
| −5 | Minor 11-mosdegree | m11md |
| −6 | Minor 18-mosdegree | m18md |
| −7 | Minor 1-mosdegree | m1md |
| −8 | Minor 8-mosdegree | m8md |
| −9 | Minor 15-mosdegree | m15md |
| −10 | Minor 22-mosdegree | m22md |
| −11 | Minor 5-mosdegree | m5md |
| −12 | Minor 12-mosdegree | m12md |
| −13 | Minor 19-mosdegree | m19md |
| −14 | Minor 2-mosdegree | m2md |
| −15 | Minor 9-mosdegree | m9md |
| −16 | Minor 16-mosdegree | m16md |
| −17 | Minor 23-mosdegree | m23md |
| −18 | Minor 6-mosdegree | m6md |
| −19 | Minor 13-mosdegree | m13md |
| −20 | Minor 20-mosdegree | m20md |
| −21 | Minor 3-mosdegree | m3md |
| −22 | Minor 10-mosdegree | m10md |
| −23 | Diminished 17-mosdegree | d17md |
| −24 | Diminished 24-mosdegree | d24md |
| −25 | Diminished 7-mosdegree | d7md |
| −26 | Diminished 14-mosdegree | d14md |
| −27 | Diminished 21-mosdegree | d21md |
| −28 | Diminished 4-mosdegree | d4md |
| −29 | Diminished 11-mosdegree | d11md |
| −30 | Diminished 18-mosdegree | d18md |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |||
| 23|0 | 1 | LssLssLsssLssLsssLssLsss | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 22|1 | 18 | LssLsssLssLssLsssLssLsss | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 21|2 | 11 | LssLsssLssLsssLssLssLsss | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 20|3 | 4 | LssLsssLssLsssLssLsssLss | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 19|4 | 21 | LsssLssLssLsssLssLsssLss | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 18|5 | 14 | LsssLssLsssLssLssLsssLss | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 17|6 | 7 | LsssLssLsssLssLsssLssLss | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 16|7 | 24 | sLssLssLsssLssLsssLssLss | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 15|8 | 17 | sLssLsssLssLssLsssLssLss | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 14|9 | 10 | sLssLsssLssLsssLssLssLss | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 13|10 | 3 | sLssLsssLssLsssLssLsssLs | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. |
| 12|11 | 20 | sLsssLssLssLsssLssLsssLs | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. |
| 11|12 | 13 | sLsssLssLsssLssLssLsssLs | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. |
| 10|13 | 6 | sLsssLssLsssLssLsssLssLs | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. |
| 9|14 | 23 | ssLssLssLsssLssLsssLssLs | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. |
| 8|15 | 16 | ssLssLsssLssLssLsssLssLs | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. |
| 7|16 | 9 | ssLssLsssLssLsssLssLssLs | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. |
| 6|17 | 2 | ssLssLsssLssLsssLssLsssL | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. |
| 5|18 | 19 | ssLsssLssLssLsssLssLsssL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. |
| 4|19 | 12 | ssLsssLssLsssLssLssLsssL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. |
| 3|20 | 5 | ssLsssLssLsssLssLsssLssL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 2|21 | 22 | sssLssLssLsssLssLsssLssL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 1|22 | 15 | sssLssLsssLssLssLsssLssL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 0|23 | 8 | sssLssLsssLssLsssLssLssL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
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 | |||||