10L 21s
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Step pattern
LssLssLssLssLssLssLssLssLssLsss
sssLssLssLssLssLssLssLssLssLssL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
3\31 to 1\10 (116.1 ¢ to 120.0 ¢)
Dark
9\10 to 28\31 (1080.0 ¢ to 1083.9 ¢)
Related to
1L 9s (antisinatonic)
With tunings
1:1 to 4:3 (ultrasoft)
Parent
10L 11s
Sister
21L 10s
Daughters
31L 10s, 10L 31s
Neutralized
20L 11s
2-Flought
41L 21s, 10L 52s
Equalized (L:s = 1:1)
3\31 (116.1 ¢)
Supersoft (L:s = 4:3)
10\103 (116.5 ¢)
Soft (L:s = 3:2)
7\72 (116.7 ¢)
Semisoft (L:s = 5:3)
11\113 (116.8 ¢)
Basic (L:s = 2:1)
4\41 (117.1 ¢)
Semihard (L:s = 5:2)
9\92 (117.4 ¢)
Hard (L:s = 3:1)
5\51 (117.6 ¢)
Superhard (L:s = 4:1)
6\61 (118.0 ¢)
Collapsed (L:s = 1:0)
1\10 (120.0 ¢)
| ↖ 9L 20s | ↑ 10L 20s | 11L 20s ↗ |
| ← 9L 21s | 10L 21s | 11L 21s → |
| ↙ 9L 22s | ↓ 10L 22s | 11L 22s ↘ |
┌╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┬┐ │║││║││║││║││║││║││║││║││║││║││││ │││││││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sssLssLssLssLssLssLssLssLssLssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
10L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 21 small steps, repeating every octave. 10L 21s is a great-grandchild scale of 1L 9s, expanding it by 21 tones. Generators that produce this scale range from 116.1 ¢ to 120 ¢, or from 1080 ¢ to 1083.9 ¢.
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 38.7 ¢ |
| Major 1-mosstep | M1ms | L | 38.7 ¢ to 120.0 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 77.4 ¢ |
| Major 2-mosstep | M2ms | L + s | 77.4 ¢ to 120.0 ¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | 3s | 0.0 ¢ to 116.1 ¢ |
| Perfect 3-mosstep | P3ms | L + 2s | 116.1 ¢ to 120.0 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 120.0 ¢ to 154.8 ¢ |
| Major 4-mosstep | M4ms | 2L + 2s | 154.8 ¢ to 240.0 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 120.0 ¢ to 193.5 ¢ |
| Major 5-mosstep | M5ms | 2L + 3s | 193.5 ¢ to 240.0 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 120.0 ¢ to 232.3 ¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 232.3 ¢ to 240.0 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 2L + 5s | 240.0 ¢ to 271.0 ¢ |
| Major 7-mosstep | M7ms | 3L + 4s | 271.0 ¢ to 360.0 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 2L + 6s | 240.0 ¢ to 309.7 ¢ |
| Major 8-mosstep | M8ms | 3L + 5s | 309.7 ¢ to 360.0 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 2L + 7s | 240.0 ¢ to 348.4 ¢ |
| Major 9-mosstep | M9ms | 3L + 6s | 348.4 ¢ to 360.0 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 3L + 7s | 360.0 ¢ to 387.1 ¢ |
| Major 10-mosstep | M10ms | 4L + 6s | 387.1 ¢ to 480.0 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 3L + 8s | 360.0 ¢ to 425.8 ¢ |
| Major 11-mosstep | M11ms | 4L + 7s | 425.8 ¢ to 480.0 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 3L + 9s | 360.0 ¢ to 464.5 ¢ |
| Major 12-mosstep | M12ms | 4L + 8s | 464.5 ¢ to 480.0 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 4L + 9s | 480.0 ¢ to 503.2 ¢ |
| Major 13-mosstep | M13ms | 5L + 8s | 503.2 ¢ to 600.0 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 4L + 10s | 480.0 ¢ to 541.9 ¢ |
| Major 14-mosstep | M14ms | 5L + 9s | 541.9 ¢ to 600.0 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 4L + 11s | 480.0 ¢ to 580.6 ¢ |
| Major 15-mosstep | M15ms | 5L + 10s | 580.6 ¢ to 600.0 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 5L + 11s | 600.0 ¢ to 619.4 ¢ |
| Major 16-mosstep | M16ms | 6L + 10s | 619.4 ¢ to 720.0 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 5L + 12s | 600.0 ¢ to 658.1 ¢ |
| Major 17-mosstep | M17ms | 6L + 11s | 658.1 ¢ to 720.0 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 5L + 13s | 600.0 ¢ to 696.8 ¢ |
| Major 18-mosstep | M18ms | 6L + 12s | 696.8 ¢ to 720.0 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 6L + 13s | 720.0 ¢ to 735.5 ¢ |
| Major 19-mosstep | M19ms | 7L + 12s | 735.5 ¢ to 840.0 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 6L + 14s | 720.0 ¢ to 774.2 ¢ |
| Major 20-mosstep | M20ms | 7L + 13s | 774.2 ¢ to 840.0 ¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 6L + 15s | 720.0 ¢ to 812.9 ¢ |
| Major 21-mosstep | M21ms | 7L + 14s | 812.9 ¢ to 840.0 ¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 7L + 15s | 840.0 ¢ to 851.6 ¢ |
| Major 22-mosstep | M22ms | 8L + 14s | 851.6 ¢ to 960.0 ¢ | |
| 23-mosstep | Minor 23-mosstep | m23ms | 7L + 16s | 840.0 ¢ to 890.3 ¢ |
| Major 23-mosstep | M23ms | 8L + 15s | 890.3 ¢ to 960.0 ¢ | |
| 24-mosstep | Minor 24-mosstep | m24ms | 7L + 17s | 840.0 ¢ to 929.0 ¢ |
| Major 24-mosstep | M24ms | 8L + 16s | 929.0 ¢ to 960.0 ¢ | |
| 25-mosstep | Minor 25-mosstep | m25ms | 8L + 17s | 960.0 ¢ to 967.7 ¢ |
| Major 25-mosstep | M25ms | 9L + 16s | 967.7 ¢ to 1080.0 ¢ | |
| 26-mosstep | Minor 26-mosstep | m26ms | 8L + 18s | 960.0 ¢ to 1006.5 ¢ |
| Major 26-mosstep | M26ms | 9L + 17s | 1006.5 ¢ to 1080.0 ¢ | |
| 27-mosstep | Minor 27-mosstep | m27ms | 8L + 19s | 960.0 ¢ to 1045.2 ¢ |
| Major 27-mosstep | M27ms | 9L + 18s | 1045.2 ¢ to 1080.0 ¢ | |
| 28-mosstep | Perfect 28-mosstep | P28ms | 9L + 19s | 1080.0 ¢ to 1083.9 ¢ |
| Augmented 28-mosstep | A28ms | 10L + 18s | 1083.9 ¢ to 1200.0 ¢ | |
| 29-mosstep | Minor 29-mosstep | m29ms | 9L + 20s | 1080.0 ¢ to 1122.6 ¢ |
| Major 29-mosstep | M29ms | 10L + 19s | 1122.6 ¢ to 1200.0 ¢ | |
| 30-mosstep | Minor 30-mosstep | m30ms | 9L + 21s | 1080.0 ¢ to 1161.3 ¢ |
| Major 30-mosstep | M30ms | 10L + 20s | 1161.3 ¢ to 1200.0 ¢ | |
| 31-mosstep | Perfect 31-mosstep | P31ms | 10L + 21s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 40 | Augmented 27-mosdegree | A27md |
| 39 | Augmented 24-mosdegree | A24md |
| 38 | Augmented 21-mosdegree | A21md |
| 37 | Augmented 18-mosdegree | A18md |
| 36 | Augmented 15-mosdegree | A15md |
| 35 | Augmented 12-mosdegree | A12md |
| 34 | Augmented 9-mosdegree | A9md |
| 33 | Augmented 6-mosdegree | A6md |
| 32 | Augmented 3-mosdegree | A3md |
| 31 | Augmented 0-mosdegree | A0md |
| 30 | Augmented 28-mosdegree | A28md |
| 29 | Major 25-mosdegree | M25md |
| 28 | Major 22-mosdegree | M22md |
| 27 | Major 19-mosdegree | M19md |
| 26 | Major 16-mosdegree | M16md |
| 25 | Major 13-mosdegree | M13md |
| 24 | Major 10-mosdegree | M10md |
| 23 | Major 7-mosdegree | M7md |
| 22 | Major 4-mosdegree | M4md |
| 21 | Major 1-mosdegree | M1md |
| 20 | Major 29-mosdegree | M29md |
| 19 | Major 26-mosdegree | M26md |
| 18 | Major 23-mosdegree | M23md |
| 17 | Major 20-mosdegree | M20md |
| 16 | Major 17-mosdegree | M17md |
| 15 | Major 14-mosdegree | M14md |
| 14 | Major 11-mosdegree | M11md |
| 13 | Major 8-mosdegree | M8md |
| 12 | Major 5-mosdegree | M5md |
| 11 | Major 2-mosdegree | M2md |
| 10 | Major 30-mosdegree | M30md |
| 9 | Major 27-mosdegree | M27md |
| 8 | Major 24-mosdegree | M24md |
| 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 31-mosdegree |
P0md P31md |
| −1 | Perfect 28-mosdegree | P28md |
| −2 | Minor 25-mosdegree | m25md |
| −3 | Minor 22-mosdegree | m22md |
| −4 | Minor 19-mosdegree | m19md |
| −5 | Minor 16-mosdegree | m16md |
| −6 | Minor 13-mosdegree | m13md |
| −7 | Minor 10-mosdegree | m10md |
| −8 | Minor 7-mosdegree | m7md |
| −9 | Minor 4-mosdegree | m4md |
| −10 | Minor 1-mosdegree | m1md |
| −11 | Minor 29-mosdegree | m29md |
| −12 | Minor 26-mosdegree | m26md |
| −13 | Minor 23-mosdegree | m23md |
| −14 | Minor 20-mosdegree | m20md |
| −15 | Minor 17-mosdegree | m17md |
| −16 | Minor 14-mosdegree | m14md |
| −17 | Minor 11-mosdegree | m11md |
| −18 | Minor 8-mosdegree | m8md |
| −19 | Minor 5-mosdegree | m5md |
| −20 | Minor 2-mosdegree | m2md |
| −21 | Minor 30-mosdegree | m30md |
| −22 | Minor 27-mosdegree | m27md |
| −23 | Minor 24-mosdegree | m24md |
| −24 | Minor 21-mosdegree | m21md |
| −25 | Minor 18-mosdegree | m18md |
| −26 | Minor 15-mosdegree | m15md |
| −27 | Minor 12-mosdegree | m12md |
| −28 | Minor 9-mosdegree | m9md |
| −29 | Minor 6-mosdegree | m6md |
| −30 | Diminished 3-mosdegree | d3md |
| −31 | Diminished 31-mosdegree | d31md |
| −32 | Diminished 28-mosdegree | d28md |
| −33 | Diminished 25-mosdegree | d25md |
| −34 | Diminished 22-mosdegree | d22md |
| −35 | Diminished 19-mosdegree | d19md |
| −36 | Diminished 16-mosdegree | d16md |
| −37 | Diminished 13-mosdegree | d13md |
| −38 | Diminished 10-mosdegree | d10md |
| −39 | Diminished 7-mosdegree | d7md |
| −40 | 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 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | |||
| 30|0 | 1 | LssLssLssLssLssLssLssLssLssLsss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Perf. |
| 29|1 | 4 | LssLssLssLssLssLssLssLssLsssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 28|2 | 7 | LssLssLssLssLssLssLssLsssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 27|3 | 10 | LssLssLssLssLssLssLsssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 26|4 | 13 | LssLssLssLssLssLsssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 25|5 | 16 | LssLssLssLssLsssLssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 24|6 | 19 | LssLssLssLsssLssLssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 23|7 | 22 | LssLssLsssLssLssLssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 22|8 | 25 | LssLsssLssLssLssLssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 21|9 | 28 | LsssLssLssLssLssLssLssLssLssLss | Perf. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 20|10 | 31 | sLssLssLssLssLssLssLssLssLssLss | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
| 19|11 | 3 | sLssLssLssLssLssLssLssLssLsssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Perf. |
| 18|12 | 6 | sLssLssLssLssLssLssLssLsssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 17|13 | 9 | sLssLssLssLssLssLssLsssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 16|14 | 12 | sLssLssLssLssLssLsssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 15|15 | 15 | sLssLssLssLssLsssLssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 14|16 | 18 | sLssLssLssLsssLssLssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 13|17 | 21 | sLssLssLsssLssLssLssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 12|18 | 24 | sLssLsssLssLssLssLssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 11|19 | 27 | sLsssLssLssLssLssLssLssLssLssLs | Perf. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 10|20 | 30 | ssLssLssLssLssLssLssLssLssLssLs | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
| 9|21 | 2 | ssLssLssLssLssLssLssLssLssLsssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Perf. | Min. | Min. | Perf. |
| 8|22 | 5 | ssLssLssLssLssLssLssLssLsssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 7|23 | 8 | ssLssLssLssLssLssLssLsssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 6|24 | 11 | ssLssLssLssLssLssLsssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 5|25 | 14 | ssLssLssLssLssLsssLssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 4|26 | 17 | ssLssLssLssLsssLssLssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 3|27 | 20 | ssLssLssLsssLssLssLssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 2|28 | 23 | ssLssLsssLssLssLssLssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 1|29 | 26 | ssLsssLssLssLssLssLssLssLssLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
| 0|30 | 29 | sssLssLssLssLssLssLssLssLssLssL | Perf. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | 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\31 | 116.129 | 1083.871 | 1:1 | 1.000 | Equalized 10L 21s | |||||
| 16\165 | 116.364 | 1083.636 | 6:5 | 1.200 | ||||||
| 13\134 | 116.418 | 1083.582 | 5:4 | 1.250 | ||||||
| 23\237 | 116.456 | 1083.544 | 9:7 | 1.286 | ||||||
| 10\103 | 116.505 | 1083.495 | 4:3 | 1.333 | Supersoft 10L 21s | |||||
| 27\278 | 116.547 | 1083.453 | 11:8 | 1.375 | ||||||
| 17\175 | 116.571 | 1083.429 | 7:5 | 1.400 | ||||||
| 24\247 | 116.599 | 1083.401 | 10:7 | 1.429 | ||||||
| 7\72 | 116.667 | 1083.333 | 3:2 | 1.500 | Soft 10L 21s | |||||
| 25\257 | 116.732 | 1083.268 | 11:7 | 1.571 | ||||||
| 18\185 | 116.757 | 1083.243 | 8:5 | 1.600 | ||||||
| 29\298 | 116.779 | 1083.221 | 13:8 | 1.625 | ||||||
| 11\113 | 116.814 | 1083.186 | 5:3 | 1.667 | Semisoft 10L 21s | |||||
| 26\267 | 116.854 | 1083.146 | 12:7 | 1.714 | ||||||
| 15\154 | 116.883 | 1083.117 | 7:4 | 1.750 | ||||||
| 19\195 | 116.923 | 1083.077 | 9:5 | 1.800 | ||||||
| 4\41 | 117.073 | 1082.927 | 2:1 | 2.000 | Basic 10L 21s Scales with tunings softer than this are proper | |||||
| 17\174 | 117.241 | 1082.759 | 9:4 | 2.250 | ||||||
| 13\133 | 117.293 | 1082.707 | 7:3 | 2.333 | ||||||
| 22\225 | 117.333 | 1082.667 | 12:5 | 2.400 | ||||||
| 9\92 | 117.391 | 1082.609 | 5:2 | 2.500 | Semihard 10L 21s | |||||
| 23\235 | 117.447 | 1082.553 | 13:5 | 2.600 | ||||||
| 14\143 | 117.483 | 1082.517 | 8:3 | 2.667 | ||||||
| 19\194 | 117.526 | 1082.474 | 11:4 | 2.750 | ||||||
| 5\51 | 117.647 | 1082.353 | 3:1 | 3.000 | Hard 10L 21s | |||||
| 16\163 | 117.791 | 1082.209 | 10:3 | 3.333 | ||||||
| 11\112 | 117.857 | 1082.143 | 7:2 | 3.500 | ||||||
| 17\173 | 117.919 | 1082.081 | 11:3 | 3.667 | ||||||
| 6\61 | 118.033 | 1081.967 | 4:1 | 4.000 | Superhard 10L 21s | |||||
| 13\132 | 118.182 | 1081.818 | 9:2 | 4.500 | ||||||
| 7\71 | 118.310 | 1081.690 | 5:1 | 5.000 | ||||||
| 8\81 | 118.519 | 1081.481 | 6:1 | 6.000 | ||||||
| 1\10 | 120.000 | 1080.000 | 1:0 | → ∞ | Collapsed 10L 21s | |||||
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