15L 7s
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Step pattern
LLLsLLsLLsLLsLLsLLsLLs
sLLsLLsLLsLLsLLsLLsLLL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
19\22 to 13\15 (1036.4 ¢ to 1040.0 ¢)
Dark
2\15 to 3\22 (160.0 ¢ to 163.6 ¢)
Descends from
7L 1s (pine)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Parent
7L 8s
Sister
7L 15s
Daughters
22L 15s, 15L 22s
Neutralized
8L 14s
2-Flought
37L 7s, 15L 29s
Equalized (L:s = 1:1)
19\22 (1036.4 ¢)
Supersoft (L:s = 4:3)
70\81 (1037.0 ¢)
Soft (L:s = 3:2)
51\59 (1037.3 ¢)
Semisoft (L:s = 5:3)
83\96 (1037.5 ¢)
Basic (L:s = 2:1)
32\37 (1037.8 ¢)
Semihard (L:s = 5:2)
77\89 (1038.2 ¢)
Hard (L:s = 3:1)
45\52 (1038.5 ¢)
Superhard (L:s = 4:1)
58\67 (1038.8 ¢)
Collapsed (L:s = 1:0)
13\15 (1040.0 ¢)
| ↖ 14L 6s | ↑ 15L 6s | 16L 6s ↗ |
| ← 14L 7s | 15L 7s | 16L 7s → |
| ↙ 14L 8s | ↓ 15L 8s | 16L 8s ↘ |
┌╥╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬┐ │║║║│║║│║║│║║│║║│║║│║║││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLLsLLsLLsLLsLLsLLsLLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
15L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 7 small steps, repeating every octave. 15L 7s is a grandchild scale of 7L 1s, expanding it by 14 tones. Generators that produce this scale range from 1036.4 ¢ to 1040 ¢, or from 160 ¢ to 163.6 ¢.
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 80.0 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 80.0 ¢ to 109.1 ¢ |
| Major 2-mosstep | M2ms | 2L | 109.1 ¢ to 160.0 ¢ | |
| 3-mosstep | Perfect 3-mosstep | P3ms | 2L + s | 160.0 ¢ to 163.6 ¢ |
| Augmented 3-mosstep | A3ms | 3L | 163.6 ¢ to 240.0 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 160.0 ¢ to 218.2 ¢ |
| Major 4-mosstep | M4ms | 3L + s | 218.2 ¢ to 240.0 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 3L + 2s | 240.0 ¢ to 272.7 ¢ |
| Major 5-mosstep | M5ms | 4L + s | 272.7 ¢ to 320.0 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 4L + 2s | 320.0 ¢ to 327.3 ¢ |
| Major 6-mosstep | M6ms | 5L + s | 327.3 ¢ to 400.0 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 4L + 3s | 320.0 ¢ to 381.8 ¢ |
| Major 7-mosstep | M7ms | 5L + 2s | 381.8 ¢ to 400.0 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 5L + 3s | 400.0 ¢ to 436.4 ¢ |
| Major 8-mosstep | M8ms | 6L + 2s | 436.4 ¢ to 480.0 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 6L + 3s | 480.0 ¢ to 490.9 ¢ |
| Major 9-mosstep | M9ms | 7L + 2s | 490.9 ¢ to 560.0 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 6L + 4s | 480.0 ¢ to 545.5 ¢ |
| Major 10-mosstep | M10ms | 7L + 3s | 545.5 ¢ to 560.0 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 7L + 4s | 560.0 ¢ to 600.0 ¢ |
| Major 11-mosstep | M11ms | 8L + 3s | 600.0 ¢ to 640.0 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 8L + 4s | 640.0 ¢ to 654.5 ¢ |
| Major 12-mosstep | M12ms | 9L + 3s | 654.5 ¢ to 720.0 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 8L + 5s | 640.0 ¢ to 709.1 ¢ |
| Major 13-mosstep | M13ms | 9L + 4s | 709.1 ¢ to 720.0 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 9L + 5s | 720.0 ¢ to 763.6 ¢ |
| Major 14-mosstep | M14ms | 10L + 4s | 763.6 ¢ to 800.0 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 10L + 5s | 800.0 ¢ to 818.2 ¢ |
| Major 15-mosstep | M15ms | 11L + 4s | 818.2 ¢ to 880.0 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 10L + 6s | 800.0 ¢ to 872.7 ¢ |
| Major 16-mosstep | M16ms | 11L + 5s | 872.7 ¢ to 880.0 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 11L + 6s | 880.0 ¢ to 927.3 ¢ |
| Major 17-mosstep | M17ms | 12L + 5s | 927.3 ¢ to 960.0 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 12L + 6s | 960.0 ¢ to 981.8 ¢ |
| Major 18-mosstep | M18ms | 13L + 5s | 981.8 ¢ to 1040.0 ¢ | |
| 19-mosstep | Diminished 19-mosstep | d19ms | 12L + 7s | 960.0 ¢ to 1036.4 ¢ |
| Perfect 19-mosstep | P19ms | 13L + 6s | 1036.4 ¢ to 1040.0 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 13L + 7s | 1040.0 ¢ to 1090.9 ¢ |
| Major 20-mosstep | M20ms | 14L + 6s | 1090.9 ¢ to 1120.0 ¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 14L + 7s | 1120.0 ¢ to 1145.5 ¢ |
| Major 21-mosstep | M21ms | 15L + 6s | 1145.5 ¢ to 1200.0 ¢ | |
| 22-mosstep | Perfect 22-mosstep | P22ms | 15L + 7s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 36 | Augmented 2-mosdegree | A2md |
| 35 | Augmented 5-mosdegree | A5md |
| 34 | Augmented 8-mosdegree | A8md |
| 33 | Augmented 11-mosdegree | A11md |
| 32 | Augmented 14-mosdegree | A14md |
| 31 | Augmented 17-mosdegree | A17md |
| 30 | Augmented 20-mosdegree | A20md |
| 29 | Augmented 1-mosdegree | A1md |
| 28 | Augmented 4-mosdegree | A4md |
| 27 | Augmented 7-mosdegree | A7md |
| 26 | Augmented 10-mosdegree | A10md |
| 25 | Augmented 13-mosdegree | A13md |
| 24 | Augmented 16-mosdegree | A16md |
| 23 | Augmented 19-mosdegree | A19md |
| 22 | Augmented 0-mosdegree | A0md |
| 21 | Augmented 3-mosdegree | A3md |
| 20 | Major 6-mosdegree | M6md |
| 19 | Major 9-mosdegree | M9md |
| 18 | Major 12-mosdegree | M12md |
| 17 | Major 15-mosdegree | M15md |
| 16 | Major 18-mosdegree | M18md |
| 15 | Major 21-mosdegree | M21md |
| 14 | Major 2-mosdegree | M2md |
| 13 | Major 5-mosdegree | M5md |
| 12 | Major 8-mosdegree | M8md |
| 11 | Major 11-mosdegree | M11md |
| 10 | Major 14-mosdegree | M14md |
| 9 | Major 17-mosdegree | M17md |
| 8 | Major 20-mosdegree | M20md |
| 7 | Major 1-mosdegree | M1md |
| 6 | Major 4-mosdegree | M4md |
| 5 | Major 7-mosdegree | M7md |
| 4 | Major 10-mosdegree | M10md |
| 3 | Major 13-mosdegree | M13md |
| 2 | Major 16-mosdegree | M16md |
| 1 | Perfect 19-mosdegree | P19md |
| 0 | Perfect 0-mosdegree Perfect 22-mosdegree |
P0md P22md |
| −1 | Perfect 3-mosdegree | P3md |
| −2 | Minor 6-mosdegree | m6md |
| −3 | Minor 9-mosdegree | m9md |
| −4 | Minor 12-mosdegree | m12md |
| −5 | Minor 15-mosdegree | m15md |
| −6 | Minor 18-mosdegree | m18md |
| −7 | Minor 21-mosdegree | m21md |
| −8 | Minor 2-mosdegree | m2md |
| −9 | Minor 5-mosdegree | m5md |
| −10 | Minor 8-mosdegree | m8md |
| −11 | Minor 11-mosdegree | m11md |
| −12 | Minor 14-mosdegree | m14md |
| −13 | Minor 17-mosdegree | m17md |
| −14 | Minor 20-mosdegree | m20md |
| −15 | Minor 1-mosdegree | m1md |
| −16 | Minor 4-mosdegree | m4md |
| −17 | Minor 7-mosdegree | m7md |
| −18 | Minor 10-mosdegree | m10md |
| −19 | Minor 13-mosdegree | m13md |
| −20 | Minor 16-mosdegree | m16md |
| −21 | Diminished 19-mosdegree | d19md |
| −22 | Diminished 22-mosdegree | d22md |
| −23 | Diminished 3-mosdegree | d3md |
| −24 | Diminished 6-mosdegree | d6md |
| −25 | Diminished 9-mosdegree | d9md |
| −26 | Diminished 12-mosdegree | d12md |
| −27 | Diminished 15-mosdegree | d15md |
| −28 | Diminished 18-mosdegree | d18md |
| −29 | Diminished 21-mosdegree | d21md |
| −30 | Diminished 2-mosdegree | d2md |
| −31 | Diminished 5-mosdegree | d5md |
| −32 | Diminished 8-mosdegree | d8md |
| −33 | Diminished 11-mosdegree | d11md |
| −34 | Diminished 14-mosdegree | d14md |
| −35 | Diminished 17-mosdegree | d17md |
| −36 | Diminished 20-mosdegree | d20md |
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 | LLLsLLsLLsLLsLLsLLsLLs | Perf. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 20|1 | 20 | LLsLLLsLLsLLsLLsLLsLLs | 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 | 17 | LLsLLsLLLsLLsLLsLLsLLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 18|3 | 14 | LLsLLsLLsLLLsLLsLLsLLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 17|4 | 11 | LLsLLsLLsLLsLLLsLLsLLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 16|5 | 8 | LLsLLsLLsLLsLLsLLLsLLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 15|6 | 5 | LLsLLsLLsLLsLLsLLsLLLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Perf. |
| 14|7 | 2 | LLsLLsLLsLLsLLsLLsLLsL | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 13|8 | 21 | LsLLLsLLsLLsLLsLLsLLsL | Perf. | Maj. | Min. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 12|9 | 18 | LsLLsLLLsLLsLLsLLsLLsL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 11|10 | 15 | LsLLsLLsLLLsLLsLLsLLsL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 10|11 | 12 | LsLLsLLsLLsLLLsLLsLLsL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 9|12 | 9 | LsLLsLLsLLsLLsLLLsLLsL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Perf. | Maj. | Min. | Perf. |
| 8|13 | 6 | LsLLsLLsLLsLLsLLsLLLsL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Maj. | Min. | Perf. |
| 7|14 | 3 | LsLLsLLsLLsLLsLLsLLsLL | Perf. | Maj. | Min. | Perf. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 6|15 | 22 | sLLLsLLsLLsLLsLLsLLsLL | Perf. | Min. | Min. | Perf. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 5|16 | 19 | sLLsLLLsLLsLLsLLsLLsLL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 4|17 | 16 | sLLsLLsLLLsLLsLLsLLsLL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 3|18 | 13 | sLLsLLsLLsLLLsLLsLLsLL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 2|19 | 10 | sLLsLLsLLsLLsLLLsLLsLL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 1|20 | 7 | sLLsLLsLLsLLsLLsLLLsLL | 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 | 4 | sLLsLLsLLsLLsLLsLLsLLL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Dim. | Min. | Min. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 19\22 | 1036.364 | 163.636 | 1:1 | 1.000 | Equalized 15L 7s | |||||
| 108\125 | 1036.800 | 163.200 | 6:5 | 1.200 | ||||||
| 89\103 | 1036.893 | 163.107 | 5:4 | 1.250 | ||||||
| 159\184 | 1036.957 | 163.043 | 9:7 | 1.286 | ||||||
| 70\81 | 1037.037 | 162.963 | 4:3 | 1.333 | Supersoft 15L 7s | |||||
| 191\221 | 1037.104 | 162.896 | 11:8 | 1.375 | ||||||
| 121\140 | 1037.143 | 162.857 | 7:5 | 1.400 | ||||||
| 172\199 | 1037.186 | 162.814 | 10:7 | 1.429 | ||||||
| 51\59 | 1037.288 | 162.712 | 3:2 | 1.500 | Soft 15L 7s | |||||
| 185\214 | 1037.383 | 162.617 | 11:7 | 1.571 | ||||||
| 134\155 | 1037.419 | 162.581 | 8:5 | 1.600 | ||||||
| 217\251 | 1037.450 | 162.550 | 13:8 | 1.625 | ||||||
| 83\96 | 1037.500 | 162.500 | 5:3 | 1.667 | Semisoft 15L 7s | |||||
| 198\229 | 1037.555 | 162.445 | 12:7 | 1.714 | ||||||
| 115\133 | 1037.594 | 162.406 | 7:4 | 1.750 | ||||||
| 147\170 | 1037.647 | 162.353 | 9:5 | 1.800 | ||||||
| 32\37 | 1037.838 | 162.162 | 2:1 | 2.000 | Basic 15L 7s Scales with tunings softer than this are proper | |||||
| 141\163 | 1038.037 | 161.963 | 9:4 | 2.250 | ||||||
| 109\126 | 1038.095 | 161.905 | 7:3 | 2.333 | ||||||
| 186\215 | 1038.140 | 161.860 | 12:5 | 2.400 | ||||||
| 77\89 | 1038.202 | 161.798 | 5:2 | 2.500 | Semihard 15L 7s | |||||
| 199\230 | 1038.261 | 161.739 | 13:5 | 2.600 | ||||||
| 122\141 | 1038.298 | 161.702 | 8:3 | 2.667 | ||||||
| 167\193 | 1038.342 | 161.658 | 11:4 | 2.750 | ||||||
| 45\52 | 1038.462 | 161.538 | 3:1 | 3.000 | Hard 15L 7s | |||||
| 148\171 | 1038.596 | 161.404 | 10:3 | 3.333 | ||||||
| 103\119 | 1038.655 | 161.345 | 7:2 | 3.500 | ||||||
| 161\186 | 1038.710 | 161.290 | 11:3 | 3.667 | ||||||
| 58\67 | 1038.806 | 161.194 | 4:1 | 4.000 | Superhard 15L 7s | |||||
| 129\149 | 1038.926 | 161.074 | 9:2 | 4.500 | ||||||
| 71\82 | 1039.024 | 160.976 | 5:1 | 5.000 | ||||||
| 84\97 | 1039.175 | 160.825 | 6:1 | 6.000 | ||||||
| 13\15 | 1040.000 | 160.000 | 1:0 | → ∞ | Collapsed 15L 7s | |||||
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