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 |