7L 15s
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Step pattern
LssLssLssLssLssLssLsss
sssLssLssLssLssLssLssL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
3\22 to 1\7 (163.6 ¢ to 171.4 ¢)
Dark
6\7 to 19\22 (1028.6 ¢ to 1036.4 ¢)
Descends from
7L 1s (pine)
Ancestor's step ratio range
3:1 to 1:0 (hard)
Parent
7L 8s
Sister
15L 7s
Daughters
22L 7s, 7L 22s
Neutralized
14L 8s
2-Flought
29L 15s, 7L 37s
Equalized (L:s = 1:1)
3\22 (163.6 ¢)
Supersoft (L:s = 4:3)
10\73 (164.4 ¢)
Soft (L:s = 3:2)
7\51 (164.7 ¢)
Semisoft (L:s = 5:3)
11\80 (165.0 ¢)
Basic (L:s = 2:1)
4\29 (165.5 ¢)
Semihard (L:s = 5:2)
9\65 (166.2 ¢)
Hard (L:s = 3:1)
5\36 (166.7 ¢)
Superhard (L:s = 4:1)
6\43 (167.4 ¢)
Collapsed (L:s = 1:0)
1\7 (171.4 ¢)
↖ 6L 14s | ↑ 7L 14s | 8L 14s ↗ |
← 6L 15s | 7L 15s | 8L 15s → |
↙ 6L 16s | ↓ 7L 16s | 8L 16s ↘ |
┌╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┬┐ │║││║││║││║││║││║││║││││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sssLssLssLssLssLssLssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
7L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 15 small steps, repeating every octave. 7L 15s is a grandchild scale of 7L 1s, expanding it by 14 tones. Generators that produce this scale range from 163.6 ¢ to 171.4 ¢, or from 1028.6 ¢ to 1036.4 ¢. It is the enharmonic scale of Coendou temperament.
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 54.5 ¢ |
Major 1-mosstep | M1ms | L | 54.5 ¢ to 171.4 ¢ | |
2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 109.1 ¢ |
Major 2-mosstep | M2ms | L + s | 109.1 ¢ to 171.4 ¢ | |
3-mosstep | Diminished 3-mosstep | d3ms | 3s | 0.0 ¢ to 163.6 ¢ |
Perfect 3-mosstep | P3ms | L + 2s | 163.6 ¢ to 171.4 ¢ | |
4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 171.4 ¢ to 218.2 ¢ |
Major 4-mosstep | M4ms | 2L + 2s | 218.2 ¢ to 342.9 ¢ | |
5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 171.4 ¢ to 272.7 ¢ |
Major 5-mosstep | M5ms | 2L + 3s | 272.7 ¢ to 342.9 ¢ | |
6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 171.4 ¢ to 327.3 ¢ |
Major 6-mosstep | M6ms | 2L + 4s | 327.3 ¢ to 342.9 ¢ | |
7-mosstep | Minor 7-mosstep | m7ms | 2L + 5s | 342.9 ¢ to 381.8 ¢ |
Major 7-mosstep | M7ms | 3L + 4s | 381.8 ¢ to 514.3 ¢ | |
8-mosstep | Minor 8-mosstep | m8ms | 2L + 6s | 342.9 ¢ to 436.4 ¢ |
Major 8-mosstep | M8ms | 3L + 5s | 436.4 ¢ to 514.3 ¢ | |
9-mosstep | Minor 9-mosstep | m9ms | 2L + 7s | 342.9 ¢ to 490.9 ¢ |
Major 9-mosstep | M9ms | 3L + 6s | 490.9 ¢ to 514.3 ¢ | |
10-mosstep | Minor 10-mosstep | m10ms | 3L + 7s | 514.3 ¢ to 545.5 ¢ |
Major 10-mosstep | M10ms | 4L + 6s | 545.5 ¢ to 685.7 ¢ | |
11-mosstep | Minor 11-mosstep | m11ms | 3L + 8s | 514.3 ¢ to 600.0 ¢ |
Major 11-mosstep | M11ms | 4L + 7s | 600.0 ¢ to 685.7 ¢ | |
12-mosstep | Minor 12-mosstep | m12ms | 3L + 9s | 514.3 ¢ to 654.5 ¢ |
Major 12-mosstep | M12ms | 4L + 8s | 654.5 ¢ to 685.7 ¢ | |
13-mosstep | Minor 13-mosstep | m13ms | 4L + 9s | 685.7 ¢ to 709.1 ¢ |
Major 13-mosstep | M13ms | 5L + 8s | 709.1 ¢ to 857.1 ¢ | |
14-mosstep | Minor 14-mosstep | m14ms | 4L + 10s | 685.7 ¢ to 763.6 ¢ |
Major 14-mosstep | M14ms | 5L + 9s | 763.6 ¢ to 857.1 ¢ | |
15-mosstep | Minor 15-mosstep | m15ms | 4L + 11s | 685.7 ¢ to 818.2 ¢ |
Major 15-mosstep | M15ms | 5L + 10s | 818.2 ¢ to 857.1 ¢ | |
16-mosstep | Minor 16-mosstep | m16ms | 5L + 11s | 857.1 ¢ to 872.7 ¢ |
Major 16-mosstep | M16ms | 6L + 10s | 872.7 ¢ to 1028.6 ¢ | |
17-mosstep | Minor 17-mosstep | m17ms | 5L + 12s | 857.1 ¢ to 927.3 ¢ |
Major 17-mosstep | M17ms | 6L + 11s | 927.3 ¢ to 1028.6 ¢ | |
18-mosstep | Minor 18-mosstep | m18ms | 5L + 13s | 857.1 ¢ to 981.8 ¢ |
Major 18-mosstep | M18ms | 6L + 12s | 981.8 ¢ to 1028.6 ¢ | |
19-mosstep | Perfect 19-mosstep | P19ms | 6L + 13s | 1028.6 ¢ to 1036.4 ¢ |
Augmented 19-mosstep | A19ms | 7L + 12s | 1036.4 ¢ to 1200.0 ¢ | |
20-mosstep | Minor 20-mosstep | m20ms | 6L + 14s | 1028.6 ¢ to 1090.9 ¢ |
Major 20-mosstep | M20ms | 7L + 13s | 1090.9 ¢ to 1200.0 ¢ | |
21-mosstep | Minor 21-mosstep | m21ms | 6L + 15s | 1028.6 ¢ to 1145.5 ¢ |
Major 21-mosstep | M21ms | 7L + 14s | 1145.5 ¢ to 1200.0 ¢ | |
22-mosstep | Perfect 22-mosstep | P22ms | 7L + 15s | 1200.0 ¢ |
Generator chain
Bright gens | Scale degree | Abbrev. |
---|---|---|
28 | Augmented 18-mosdegree | A18md |
27 | Augmented 15-mosdegree | A15md |
26 | Augmented 12-mosdegree | A12md |
25 | Augmented 9-mosdegree | A9md |
24 | Augmented 6-mosdegree | A6md |
23 | Augmented 3-mosdegree | A3md |
22 | Augmented 0-mosdegree | A0md |
21 | Augmented 19-mosdegree | A19md |
20 | Major 16-mosdegree | M16md |
19 | Major 13-mosdegree | M13md |
18 | Major 10-mosdegree | M10md |
17 | Major 7-mosdegree | M7md |
16 | Major 4-mosdegree | M4md |
15 | Major 1-mosdegree | M1md |
14 | Major 20-mosdegree | M20md |
13 | Major 17-mosdegree | M17md |
12 | Major 14-mosdegree | M14md |
11 | Major 11-mosdegree | M11md |
10 | Major 8-mosdegree | M8md |
9 | Major 5-mosdegree | M5md |
8 | Major 2-mosdegree | M2md |
7 | Major 21-mosdegree | M21md |
6 | Major 18-mosdegree | M18md |
5 | Major 15-mosdegree | M15md |
4 | Major 12-mosdegree | M12md |
3 | Major 9-mosdegree | M9md |
2 | Major 6-mosdegree | M6md |
1 | Perfect 3-mosdegree | P3md |
0 | Perfect 0-mosdegree Perfect 22-mosdegree |
P0md P22md |
−1 | Perfect 19-mosdegree | P19md |
−2 | Minor 16-mosdegree | m16md |
−3 | Minor 13-mosdegree | m13md |
−4 | Minor 10-mosdegree | m10md |
−5 | Minor 7-mosdegree | m7md |
−6 | Minor 4-mosdegree | m4md |
−7 | Minor 1-mosdegree | m1md |
−8 | Minor 20-mosdegree | m20md |
−9 | Minor 17-mosdegree | m17md |
−10 | Minor 14-mosdegree | m14md |
−11 | Minor 11-mosdegree | m11md |
−12 | Minor 8-mosdegree | m8md |
−13 | Minor 5-mosdegree | m5md |
−14 | Minor 2-mosdegree | m2md |
−15 | Minor 21-mosdegree | m21md |
−16 | Minor 18-mosdegree | m18md |
−17 | Minor 15-mosdegree | m15md |
−18 | Minor 12-mosdegree | m12md |
−19 | Minor 9-mosdegree | m9md |
−20 | Minor 6-mosdegree | m6md |
−21 | Diminished 3-mosdegree | d3md |
−22 | Diminished 22-mosdegree | d22md |
−23 | Diminished 19-mosdegree | d19md |
−24 | Diminished 16-mosdegree | d16md |
−25 | Diminished 13-mosdegree | d13md |
−26 | Diminished 10-mosdegree | d10md |
−27 | Diminished 7-mosdegree | d7md |
−28 | Diminished 4-mosdegree | d4md |
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 | |||
21|0 | 1 | LssLssLssLssLssLssLsss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Perf. |
20|1 | 4 | LssLssLssLssLssLsssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
19|2 | 7 | LssLssLssLssLsssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
18|3 | 10 | LssLssLssLsssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
17|4 | 13 | LssLssLsssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
16|5 | 16 | LssLsssLssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
15|6 | 19 | LsssLssLssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
14|7 | 22 | sLssLssLssLssLssLssLss | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
13|8 | 3 | sLssLssLssLssLssLsssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Perf. |
12|9 | 6 | sLssLssLssLssLsssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
11|10 | 9 | sLssLssLssLsssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
10|11 | 12 | sLssLssLsssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
9|12 | 15 | sLssLsssLssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
8|13 | 18 | sLsssLssLssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
7|14 | 21 | ssLssLssLssLssLssLssLs | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
6|15 | 2 | ssLssLssLssLssLssLsssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Min. | Perf. |
5|16 | 5 | ssLssLssLssLssLsssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
4|17 | 8 | ssLssLssLssLsssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
3|18 | 11 | ssLssLssLsssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
2|19 | 14 | ssLssLsssLssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
1|20 | 17 | ssLsssLssLssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
0|21 | 20 | sssLssLssLssLssLssLssL | Perf. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
Scale tree
Generator(edo) | Cents | Step ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
3\22 | 163.636 | 1036.364 | 1:1 | 1.000 | Equalized 7L 15s | |||||
16\117 | 164.103 | 1035.897 | 6:5 | 1.200 | ||||||
13\95 | 164.211 | 1035.789 | 5:4 | 1.250 | ||||||
23\168 | 164.286 | 1035.714 | 9:7 | 1.286 | ||||||
10\73 | 164.384 | 1035.616 | 4:3 | 1.333 | Supersoft 7L 15s | |||||
27\197 | 164.467 | 1035.533 | 11:8 | 1.375 | ||||||
17\124 | 164.516 | 1035.484 | 7:5 | 1.400 | ||||||
24\175 | 164.571 | 1035.429 | 10:7 | 1.429 | ||||||
7\51 | 164.706 | 1035.294 | 3:2 | 1.500 | Soft 7L 15s | |||||
25\182 | 164.835 | 1035.165 | 11:7 | 1.571 | ||||||
18\131 | 164.885 | 1035.115 | 8:5 | 1.600 | ||||||
29\211 | 164.929 | 1035.071 | 13:8 | 1.625 | ||||||
11\80 | 165.000 | 1035.000 | 5:3 | 1.667 | Semisoft 7L 15s | |||||
26\189 | 165.079 | 1034.921 | 12:7 | 1.714 | ||||||
15\109 | 165.138 | 1034.862 | 7:4 | 1.750 | ||||||
19\138 | 165.217 | 1034.783 | 9:5 | 1.800 | ||||||
4\29 | 165.517 | 1034.483 | 2:1 | 2.000 | Basic 7L 15s Scales with tunings softer than this are proper | |||||
17\123 | 165.854 | 1034.146 | 9:4 | 2.250 | ||||||
13\94 | 165.957 | 1034.043 | 7:3 | 2.333 | Coendou | |||||
22\159 | 166.038 | 1033.962 | 12:5 | 2.400 | ||||||
9\65 | 166.154 | 1033.846 | 5:2 | 2.500 | Semihard 7L 15s | |||||
23\166 | 166.265 | 1033.735 | 13:5 | 2.600 | ||||||
14\101 | 166.337 | 1033.663 | 8:3 | 2.667 | ||||||
19\137 | 166.423 | 1033.577 | 11:4 | 2.750 | ||||||
5\36 | 166.667 | 1033.333 | 3:1 | 3.000 | Hard 7L 15s | |||||
16\115 | 166.957 | 1033.043 | 10:3 | 3.333 | ||||||
11\79 | 167.089 | 1032.911 | 7:2 | 3.500 | ||||||
17\122 | 167.213 | 1032.787 | 11:3 | 3.667 | ||||||
6\43 | 167.442 | 1032.558 | 4:1 | 4.000 | Superhard 7L 15s | |||||
13\93 | 167.742 | 1032.258 | 9:2 | 4.500 | ||||||
7\50 | 168.000 | 1032.000 | 5:1 | 5.000 | ||||||
8\57 | 168.421 | 1031.579 | 6:1 | 6.000 | ||||||
1\7 | 171.429 | 1028.571 | 1:0 | → ∞ | Collapsed 7L 15s |
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