8L 15s
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Step pattern
LsLssLssLssLssLssLssLss
ssLssLssLssLssLssLssLsL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
20\23 to 7\8 (1043.5 ¢ to 1050.0 ¢)
Dark
1\8 to 3\23 (150.0 ¢ to 156.5 ¢)
Descends from
7L 1s (pine)
Ancestor's step ratio range
1:1 to 3:2 (soft)
Parent
8L 7s
Sister
15L 8s
Daughters
23L 8s, 8L 23s
Neutralized
16L 7s
2-Flought
31L 15s, 8L 38s
Equalized (L:s = 1:1)
20\23 (1043.5 ¢)
Supersoft (L:s = 4:3)
67\77 (1044.2 ¢)
Soft (L:s = 3:2)
47\54 (1044.4 ¢)
Semisoft (L:s = 5:3)
74\85 (1044.7 ¢)
Basic (L:s = 2:1)
27\31 (1045.2 ¢)
Semihard (L:s = 5:2)
61\70 (1045.7 ¢)
Hard (L:s = 3:1)
34\39 (1046.2 ¢)
Superhard (L:s = 4:1)
41\47 (1046.8 ¢)
Collapsed (L:s = 1:0)
7\8 (1050.0 ¢)
| ↖ 7L 14s | ↑ 8L 14s | 9L 14s ↗ |
| ← 7L 15s | 8L 15s | 9L 15s → |
| ↙ 7L 16s | ↓ 8L 16s | 9L 16s ↘ |
┌╥┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┐ │║│║││║││║││║││║││║││║│││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssLssLssLssLssLssLssLsL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
8L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 15 small steps, repeating every octave. 8L 15s is a grandchild scale of 7L 1s, expanding it by 15 tones. Generators that produce this scale range from 1043.5 ¢ to 1050 ¢, or from 150 ¢ to 156.5 ¢.
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 52.2 ¢ |
| Major 1-mosstep | M1ms | L | 52.2 ¢ to 150.0 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 104.3 ¢ |
| Major 2-mosstep | M2ms | L + s | 104.3 ¢ to 150.0 ¢ | |
| 3-mosstep | Perfect 3-mosstep | P3ms | L + 2s | 150.0 ¢ to 156.5 ¢ |
| Augmented 3-mosstep | A3ms | 2L + s | 156.5 ¢ to 300.0 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 150.0 ¢ to 208.7 ¢ |
| Major 4-mosstep | M4ms | 2L + 2s | 208.7 ¢ to 300.0 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 150.0 ¢ to 260.9 ¢ |
| Major 5-mosstep | M5ms | 2L + 3s | 260.9 ¢ to 300.0 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 2L + 4s | 300.0 ¢ to 313.0 ¢ |
| Major 6-mosstep | M6ms | 3L + 3s | 313.0 ¢ to 450.0 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 2L + 5s | 300.0 ¢ to 365.2 ¢ |
| Major 7-mosstep | M7ms | 3L + 4s | 365.2 ¢ to 450.0 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 2L + 6s | 300.0 ¢ to 417.4 ¢ |
| Major 8-mosstep | M8ms | 3L + 5s | 417.4 ¢ to 450.0 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 3L + 6s | 450.0 ¢ to 469.6 ¢ |
| Major 9-mosstep | M9ms | 4L + 5s | 469.6 ¢ to 600.0 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 3L + 7s | 450.0 ¢ to 521.7 ¢ |
| Major 10-mosstep | M10ms | 4L + 6s | 521.7 ¢ to 600.0 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 3L + 8s | 450.0 ¢ to 573.9 ¢ |
| Major 11-mosstep | M11ms | 4L + 7s | 573.9 ¢ to 600.0 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 4L + 8s | 600.0 ¢ to 626.1 ¢ |
| Major 12-mosstep | M12ms | 5L + 7s | 626.1 ¢ to 750.0 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 4L + 9s | 600.0 ¢ to 678.3 ¢ |
| Major 13-mosstep | M13ms | 5L + 8s | 678.3 ¢ to 750.0 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 4L + 10s | 600.0 ¢ to 730.4 ¢ |
| Major 14-mosstep | M14ms | 5L + 9s | 730.4 ¢ to 750.0 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 5L + 10s | 750.0 ¢ to 782.6 ¢ |
| Major 15-mosstep | M15ms | 6L + 9s | 782.6 ¢ to 900.0 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 5L + 11s | 750.0 ¢ to 834.8 ¢ |
| Major 16-mosstep | M16ms | 6L + 10s | 834.8 ¢ to 900.0 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 5L + 12s | 750.0 ¢ to 887.0 ¢ |
| Major 17-mosstep | M17ms | 6L + 11s | 887.0 ¢ to 900.0 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 6L + 12s | 900.0 ¢ to 939.1 ¢ |
| Major 18-mosstep | M18ms | 7L + 11s | 939.1 ¢ to 1050.0 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 6L + 13s | 900.0 ¢ to 991.3 ¢ |
| Major 19-mosstep | M19ms | 7L + 12s | 991.3 ¢ to 1050.0 ¢ | |
| 20-mosstep | Diminished 20-mosstep | d20ms | 6L + 14s | 900.0 ¢ to 1043.5 ¢ |
| Perfect 20-mosstep | P20ms | 7L + 13s | 1043.5 ¢ to 1050.0 ¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 7L + 14s | 1050.0 ¢ to 1095.7 ¢ |
| Major 21-mosstep | M21ms | 8L + 13s | 1095.7 ¢ to 1200.0 ¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 7L + 15s | 1050.0 ¢ to 1147.8 ¢ |
| Major 22-mosstep | M22ms | 8L + 14s | 1147.8 ¢ to 1200.0 ¢ | |
| 23-mosstep | Perfect 23-mosstep | P23ms | 8L + 15s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 30 | Augmented 2-mosdegree | A2md |
| 29 | Augmented 5-mosdegree | A5md |
| 28 | Augmented 8-mosdegree | A8md |
| 27 | Augmented 11-mosdegree | A11md |
| 26 | Augmented 14-mosdegree | A14md |
| 25 | Augmented 17-mosdegree | A17md |
| 24 | Augmented 20-mosdegree | A20md |
| 23 | Augmented 0-mosdegree | A0md |
| 22 | Augmented 3-mosdegree | A3md |
| 21 | Major 6-mosdegree | M6md |
| 20 | Major 9-mosdegree | M9md |
| 19 | Major 12-mosdegree | M12md |
| 18 | Major 15-mosdegree | M15md |
| 17 | Major 18-mosdegree | M18md |
| 16 | Major 21-mosdegree | M21md |
| 15 | Major 1-mosdegree | M1md |
| 14 | Major 4-mosdegree | M4md |
| 13 | Major 7-mosdegree | M7md |
| 12 | Major 10-mosdegree | M10md |
| 11 | Major 13-mosdegree | M13md |
| 10 | Major 16-mosdegree | M16md |
| 9 | Major 19-mosdegree | M19md |
| 8 | Major 22-mosdegree | M22md |
| 7 | Major 2-mosdegree | M2md |
| 6 | Major 5-mosdegree | M5md |
| 5 | Major 8-mosdegree | M8md |
| 4 | Major 11-mosdegree | M11md |
| 3 | Major 14-mosdegree | M14md |
| 2 | Major 17-mosdegree | M17md |
| 1 | Perfect 20-mosdegree | P20md |
| 0 | Perfect 0-mosdegree Perfect 23-mosdegree |
P0md P23md |
| −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 1-mosdegree | m1md |
| −9 | Minor 4-mosdegree | m4md |
| −10 | Minor 7-mosdegree | m7md |
| −11 | Minor 10-mosdegree | m10md |
| −12 | Minor 13-mosdegree | m13md |
| −13 | Minor 16-mosdegree | m16md |
| −14 | Minor 19-mosdegree | m19md |
| −15 | Minor 22-mosdegree | m22md |
| −16 | Minor 2-mosdegree | m2md |
| −17 | Minor 5-mosdegree | m5md |
| −18 | Minor 8-mosdegree | m8md |
| −19 | Minor 11-mosdegree | m11md |
| −20 | Minor 14-mosdegree | m14md |
| −21 | Minor 17-mosdegree | m17md |
| −22 | Diminished 20-mosdegree | d20md |
| −23 | Diminished 23-mosdegree | d23md |
| −24 | Diminished 3-mosdegree | d3md |
| −25 | Diminished 6-mosdegree | d6md |
| −26 | Diminished 9-mosdegree | d9md |
| −27 | Diminished 12-mosdegree | d12md |
| −28 | Diminished 15-mosdegree | d15md |
| −29 | Diminished 18-mosdegree | d18md |
| −30 | Diminished 21-mosdegree | d21md |
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 | |||
| 22|0 | 1 | LsLssLssLssLssLssLssLss | Perf. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 21|1 | 21 | LssLsLssLssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 20|2 | 18 | LssLssLsLssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 19|3 | 15 | LssLssLssLsLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 18|4 | 12 | LssLssLssLssLsLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 17|5 | 9 | LssLssLssLssLssLsLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 16|6 | 6 | LssLssLssLssLssLssLsLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 15|7 | 3 | LssLssLssLssLssLssLssLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 14|8 | 23 | sLsLssLssLssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 13|9 | 20 | sLssLsLssLssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 12|10 | 17 | sLssLssLsLssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 11|11 | 14 | sLssLssLssLsLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 10|12 | 11 | sLssLssLssLssLsLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 9|13 | 8 | sLssLssLssLssLssLsLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 8|14 | 5 | sLssLssLssLssLssLssLsLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Maj. | Perf. |
| 7|15 | 2 | sLssLssLssLssLssLssLssL | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 6|16 | 22 | ssLsLssLssLssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 5|17 | 19 | ssLssLsLssLssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 4|18 | 16 | ssLssLssLsLssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 3|19 | 13 | ssLssLssLssLsLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 2|20 | 10 | ssLssLssLssLssLsLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 1|21 | 7 | ssLssLssLssLssLssLsLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 0|22 | 4 | ssLssLssLssLssLssLssLsL | Perf. | Min. | Min. | Perf. | Min. | 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 | |||||||
| 20\23 | 1043.478 | 156.522 | 1:1 | 1.000 | Equalized 8L 15s | |||||
| 107\123 | 1043.902 | 156.098 | 6:5 | 1.200 | ||||||
| 87\100 | 1044.000 | 156.000 | 5:4 | 1.250 | ||||||
| 154\177 | 1044.068 | 155.932 | 9:7 | 1.286 | ||||||
| 67\77 | 1044.156 | 155.844 | 4:3 | 1.333 | Supersoft 8L 15s | |||||
| 181\208 | 1044.231 | 155.769 | 11:8 | 1.375 | ||||||
| 114\131 | 1044.275 | 155.725 | 7:5 | 1.400 | ||||||
| 161\185 | 1044.324 | 155.676 | 10:7 | 1.429 | ||||||
| 47\54 | 1044.444 | 155.556 | 3:2 | 1.500 | Soft 8L 15s | |||||
| 168\193 | 1044.560 | 155.440 | 11:7 | 1.571 | ||||||
| 121\139 | 1044.604 | 155.396 | 8:5 | 1.600 | ||||||
| 195\224 | 1044.643 | 155.357 | 13:8 | 1.625 | ||||||
| 74\85 | 1044.706 | 155.294 | 5:3 | 1.667 | Semisoft 8L 15s | |||||
| 175\201 | 1044.776 | 155.224 | 12:7 | 1.714 | ||||||
| 101\116 | 1044.828 | 155.172 | 7:4 | 1.750 | ||||||
| 128\147 | 1044.898 | 155.102 | 9:5 | 1.800 | ||||||
| 27\31 | 1045.161 | 154.839 | 2:1 | 2.000 | Basic 8L 15s Scales with tunings softer than this are proper | |||||
| 115\132 | 1045.455 | 154.545 | 9:4 | 2.250 | ||||||
| 88\101 | 1045.545 | 154.455 | 7:3 | 2.333 | ||||||
| 149\171 | 1045.614 | 154.386 | 12:5 | 2.400 | ||||||
| 61\70 | 1045.714 | 154.286 | 5:2 | 2.500 | Semihard 8L 15s | |||||
| 156\179 | 1045.810 | 154.190 | 13:5 | 2.600 | ||||||
| 95\109 | 1045.872 | 154.128 | 8:3 | 2.667 | ||||||
| 129\148 | 1045.946 | 154.054 | 11:4 | 2.750 | ||||||
| 34\39 | 1046.154 | 153.846 | 3:1 | 3.000 | Hard 8L 15s | |||||
| 109\125 | 1046.400 | 153.600 | 10:3 | 3.333 | ||||||
| 75\86 | 1046.512 | 153.488 | 7:2 | 3.500 | ||||||
| 116\133 | 1046.617 | 153.383 | 11:3 | 3.667 | ||||||
| 41\47 | 1046.809 | 153.191 | 4:1 | 4.000 | Superhard 8L 15s | |||||
| 89\102 | 1047.059 | 152.941 | 9:2 | 4.500 | ||||||
| 48\55 | 1047.273 | 152.727 | 5:1 | 5.000 | ||||||
| 55\63 | 1047.619 | 152.381 | 6:1 | 6.000 | ||||||
| 7\8 | 1050.000 | 150.000 | 1:0 | → ∞ | Collapsed 8L 15s | |||||
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