7L 17s
↖ 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.
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
The intervals of 7L 17s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 24-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.
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
A chain of bright generators, each a perfect 17-mosstep, produces the following scale degrees. A chain of 24 bright generators contains the scale degrees of one of the modes of 7L 17s. Expanding the chain to 31 scale degrees produces the modes of either 24L 7s (for soft-of-basic tunings) or 7L 24s (for hard-of-basic tunings).
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 |