19L 12s: Difference between revisions
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== Scale properties == | == Scale properties == | ||
{{TAMNAMS use}} | {{TAMNAMS use}} | ||
{{MOS | |||
=== Intervals === | |||
{{MOS intervals}} | |||
=== Generator chain === | |||
{{MOS genchain}} | |||
=== Modes === | |||
{{MOS mode degrees}} | |||
== Scale tree == | == Scale tree == | ||
Latest revision as of 14:18, 5 May 2025
| ↖ 18L 11s | ↑ 19L 11s | 20L 11s ↗ |
| ← 18L 12s | 19L 12s | 20L 12s → |
| ↙ 18L 13s | ↓ 19L 13s | 20L 13s ↘ |
Scale structure
sLsLLsLsLLsLsLLsLLsLsLLsLsLLsLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
19L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 19 large steps and 12 small steps, repeating every octave. 19L 12s is a great-grandchild scale of 5L 2s, expanding it by 24 tones. Generators that produce this scale range from 503.2 ¢ to 505.3 ¢, or from 694.7 ¢ to 696.8 ¢. It is associated with flatter meantone temperaments.
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 interval regions.
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 63.2 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 63.2 ¢ to 77.4 ¢ |
| Major 2-mosstep | M2ms | 2L | 77.4 ¢ to 126.3 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 63.2 ¢ to 116.1 ¢ |
| Major 3-mosstep | M3ms | 2L + s | 116.1 ¢ to 126.3 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 126.3 ¢ to 154.8 ¢ |
| Major 4-mosstep | M4ms | 3L + s | 154.8 ¢ to 189.5 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 3L + 2s | 189.5 ¢ to 193.5 ¢ |
| Major 5-mosstep | M5ms | 4L + s | 193.5 ¢ to 252.6 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 189.5 ¢ to 232.3 ¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 232.3 ¢ to 252.6 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 4L + 3s | 252.6 ¢ to 271.0 ¢ |
| Major 7-mosstep | M7ms | 5L + 2s | 271.0 ¢ to 315.8 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 4L + 4s | 252.6 ¢ to 309.7 ¢ |
| Major 8-mosstep | M8ms | 5L + 3s | 309.7 ¢ to 315.8 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 5L + 4s | 315.8 ¢ to 348.4 ¢ |
| Major 9-mosstep | M9ms | 6L + 3s | 348.4 ¢ to 378.9 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 6L + 4s | 378.9 ¢ to 387.1 ¢ |
| Major 10-mosstep | M10ms | 7L + 3s | 387.1 ¢ to 442.1 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 6L + 5s | 378.9 ¢ to 425.8 ¢ |
| Major 11-mosstep | M11ms | 7L + 4s | 425.8 ¢ to 442.1 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 7L + 5s | 442.1 ¢ to 464.5 ¢ |
| Major 12-mosstep | M12ms | 8L + 4s | 464.5 ¢ to 505.3 ¢ | |
| 13-mosstep | Diminished 13-mosstep | d13ms | 7L + 6s | 442.1 ¢ to 503.2 ¢ |
| Perfect 13-mosstep | P13ms | 8L + 5s | 503.2 ¢ to 505.3 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 8L + 6s | 505.3 ¢ to 541.9 ¢ |
| Major 14-mosstep | M14ms | 9L + 5s | 541.9 ¢ to 568.4 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 9L + 6s | 568.4 ¢ to 580.6 ¢ |
| Major 15-mosstep | M15ms | 10L + 5s | 580.6 ¢ to 631.6 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 9L + 7s | 568.4 ¢ to 619.4 ¢ |
| Major 16-mosstep | M16ms | 10L + 6s | 619.4 ¢ to 631.6 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 10L + 7s | 631.6 ¢ to 658.1 ¢ |
| Major 17-mosstep | M17ms | 11L + 6s | 658.1 ¢ to 694.7 ¢ | |
| 18-mosstep | Perfect 18-mosstep | P18ms | 11L + 7s | 694.7 ¢ to 696.8 ¢ |
| Augmented 18-mosstep | A18ms | 12L + 6s | 696.8 ¢ to 757.9 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 11L + 8s | 694.7 ¢ to 735.5 ¢ |
| Major 19-mosstep | M19ms | 12L + 7s | 735.5 ¢ to 757.9 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 12L + 8s | 757.9 ¢ to 774.2 ¢ |
| Major 20-mosstep | M20ms | 13L + 7s | 774.2 ¢ to 821.1 ¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 12L + 9s | 757.9 ¢ to 812.9 ¢ |
| Major 21-mosstep | M21ms | 13L + 8s | 812.9 ¢ to 821.1 ¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 13L + 9s | 821.1 ¢ to 851.6 ¢ |
| Major 22-mosstep | M22ms | 14L + 8s | 851.6 ¢ to 884.2 ¢ | |
| 23-mosstep | Minor 23-mosstep | m23ms | 14L + 9s | 884.2 ¢ to 890.3 ¢ |
| Major 23-mosstep | M23ms | 15L + 8s | 890.3 ¢ to 947.4 ¢ | |
| 24-mosstep | Minor 24-mosstep | m24ms | 14L + 10s | 884.2 ¢ to 929.0 ¢ |
| Major 24-mosstep | M24ms | 15L + 9s | 929.0 ¢ to 947.4 ¢ | |
| 25-mosstep | Minor 25-mosstep | m25ms | 15L + 10s | 947.4 ¢ to 967.7 ¢ |
| Major 25-mosstep | M25ms | 16L + 9s | 967.7 ¢ to 1010.5 ¢ | |
| 26-mosstep | Minor 26-mosstep | m26ms | 15L + 11s | 947.4 ¢ to 1006.5 ¢ |
| Major 26-mosstep | M26ms | 16L + 10s | 1006.5 ¢ to 1010.5 ¢ | |
| 27-mosstep | Minor 27-mosstep | m27ms | 16L + 11s | 1010.5 ¢ to 1045.2 ¢ |
| Major 27-mosstep | M27ms | 17L + 10s | 1045.2 ¢ to 1073.7 ¢ | |
| 28-mosstep | Minor 28-mosstep | m28ms | 17L + 11s | 1073.7 ¢ to 1083.9 ¢ |
| Major 28-mosstep | M28ms | 18L + 10s | 1083.9 ¢ to 1136.8 ¢ | |
| 29-mosstep | Minor 29-mosstep | m29ms | 17L + 12s | 1073.7 ¢ to 1122.6 ¢ |
| Major 29-mosstep | M29ms | 18L + 11s | 1122.6 ¢ to 1136.8 ¢ | |
| 30-mosstep | Minor 30-mosstep | m30ms | 18L + 12s | 1136.8 ¢ to 1161.3 ¢ |
| Major 30-mosstep | M30ms | 19L + 11s | 1161.3 ¢ to 1200.0 ¢ | |
| 31-mosstep | Perfect 31-mosstep | P31ms | 19L + 12s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 49 | Augmented 17-mosdegree | A17md |
| 48 | Augmented 4-mosdegree | A4md |
| 47 | Augmented 22-mosdegree | A22md |
| 46 | Augmented 9-mosdegree | A9md |
| 45 | Augmented 27-mosdegree | A27md |
| 44 | Augmented 14-mosdegree | A14md |
| 43 | Augmented 1-mosdegree | A1md |
| 42 | Augmented 19-mosdegree | A19md |
| 41 | Augmented 6-mosdegree | A6md |
| 40 | Augmented 24-mosdegree | A24md |
| 39 | Augmented 11-mosdegree | A11md |
| 38 | Augmented 29-mosdegree | A29md |
| 37 | Augmented 16-mosdegree | A16md |
| 36 | Augmented 3-mosdegree | A3md |
| 35 | Augmented 21-mosdegree | A21md |
| 34 | Augmented 8-mosdegree | A8md |
| 33 | Augmented 26-mosdegree | A26md |
| 32 | Augmented 13-mosdegree | A13md |
| 31 | Augmented 0-mosdegree | A0md |
| 30 | Augmented 18-mosdegree | A18md |
| 29 | Major 5-mosdegree | M5md |
| 28 | Major 23-mosdegree | M23md |
| 27 | Major 10-mosdegree | M10md |
| 26 | Major 28-mosdegree | M28md |
| 25 | Major 15-mosdegree | M15md |
| 24 | Major 2-mosdegree | M2md |
| 23 | Major 20-mosdegree | M20md |
| 22 | Major 7-mosdegree | M7md |
| 21 | Major 25-mosdegree | M25md |
| 20 | Major 12-mosdegree | M12md |
| 19 | Major 30-mosdegree | M30md |
| 18 | Major 17-mosdegree | M17md |
| 17 | Major 4-mosdegree | M4md |
| 16 | Major 22-mosdegree | M22md |
| 15 | Major 9-mosdegree | M9md |
| 14 | Major 27-mosdegree | M27md |
| 13 | Major 14-mosdegree | M14md |
| 12 | Major 1-mosdegree | M1md |
| 11 | Major 19-mosdegree | M19md |
| 10 | Major 6-mosdegree | M6md |
| 9 | Major 24-mosdegree | M24md |
| 8 | Major 11-mosdegree | M11md |
| 7 | Major 29-mosdegree | M29md |
| 6 | Major 16-mosdegree | M16md |
| 5 | Major 3-mosdegree | M3md |
| 4 | Major 21-mosdegree | M21md |
| 3 | Major 8-mosdegree | M8md |
| 2 | Major 26-mosdegree | M26md |
| 1 | Perfect 13-mosdegree | P13md |
| 0 | Perfect 0-mosdegree Perfect 31-mosdegree |
P0md P31md |
| −1 | Perfect 18-mosdegree | P18md |
| −2 | Minor 5-mosdegree | m5md |
| −3 | Minor 23-mosdegree | m23md |
| −4 | Minor 10-mosdegree | m10md |
| −5 | Minor 28-mosdegree | m28md |
| −6 | Minor 15-mosdegree | m15md |
| −7 | Minor 2-mosdegree | m2md |
| −8 | Minor 20-mosdegree | m20md |
| −9 | Minor 7-mosdegree | m7md |
| −10 | Minor 25-mosdegree | m25md |
| −11 | Minor 12-mosdegree | m12md |
| −12 | Minor 30-mosdegree | m30md |
| −13 | Minor 17-mosdegree | m17md |
| −14 | Minor 4-mosdegree | m4md |
| −15 | Minor 22-mosdegree | m22md |
| −16 | Minor 9-mosdegree | m9md |
| −17 | Minor 27-mosdegree | m27md |
| −18 | Minor 14-mosdegree | m14md |
| −19 | Minor 1-mosdegree | m1md |
| −20 | Minor 19-mosdegree | m19md |
| −21 | Minor 6-mosdegree | m6md |
| −22 | Minor 24-mosdegree | m24md |
| −23 | Minor 11-mosdegree | m11md |
| −24 | Minor 29-mosdegree | m29md |
| −25 | Minor 16-mosdegree | m16md |
| −26 | Minor 3-mosdegree | m3md |
| −27 | Minor 21-mosdegree | m21md |
| −28 | Minor 8-mosdegree | m8md |
| −29 | Minor 26-mosdegree | m26md |
| −30 | Diminished 13-mosdegree | d13md |
| −31 | Diminished 31-mosdegree | d31md |
| −32 | Diminished 18-mosdegree | d18md |
| −33 | Diminished 5-mosdegree | d5md |
| −34 | Diminished 23-mosdegree | d23md |
| −35 | Diminished 10-mosdegree | d10md |
| −36 | Diminished 28-mosdegree | d28md |
| −37 | Diminished 15-mosdegree | d15md |
| −38 | Diminished 2-mosdegree | d2md |
| −39 | Diminished 20-mosdegree | d20md |
| −40 | Diminished 7-mosdegree | d7md |
| −41 | Diminished 25-mosdegree | d25md |
| −42 | Diminished 12-mosdegree | d12md |
| −43 | Diminished 30-mosdegree | d30md |
| −44 | Diminished 17-mosdegree | d17md |
| −45 | Diminished 4-mosdegree | d4md |
| −46 | Diminished 22-mosdegree | d22md |
| −47 | Diminished 9-mosdegree | d9md |
| −48 | Diminished 27-mosdegree | d27md |
| −49 | Diminished 14-mosdegree | d14md |
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 | LLsLLsLsLLsLsLLsLLsLsLLsLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 29|1 | 14 | LLsLLsLsLLsLsLLsLsLLsLLsLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 28|2 | 27 | LLsLsLLsLLsLsLLsLsLLsLLsLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 27|3 | 9 | LLsLsLLsLLsLsLLsLsLLsLsLLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 26|4 | 22 | LLsLsLLsLsLLsLLsLsLLsLsLLsLLsLs | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 25|5 | 4 | LLsLsLLsLsLLsLLsLsLLsLsLLsLsLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 24|6 | 17 | LLsLsLLsLsLLsLsLLsLLsLsLLsLsLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 23|7 | 30 | LsLLsLLsLsLLsLsLLsLLsLsLLsLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 22|8 | 12 | LsLLsLLsLsLLsLsLLsLsLLsLLsLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 21|9 | 25 | LsLLsLsLLsLLsLsLLsLsLLsLLsLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 20|10 | 7 | LsLLsLsLLsLLsLsLLsLsLLsLsLLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 19|11 | 20 | LsLLsLsLLsLsLLsLLsLsLLsLsLLsLLs | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Maj. | Perf. |
| 18|12 | 2 | LsLLsLsLLsLsLLsLLsLsLLsLsLLsLsL | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. |
| 17|13 | 15 | LsLLsLsLLsLsLLsLsLLsLLsLsLLsLsL | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. |
| 16|14 | 28 | LsLsLLsLLsLsLLsLsLLsLLsLsLLsLsL | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. |
| 15|15 | 10 | LsLsLLsLLsLsLLsLsLLsLsLLsLLsLsL | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. |
| 14|16 | 23 | LsLsLLsLsLLsLLsLsLLsLsLLsLLsLsL | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Maj. | Min. | Maj. | Min. | Perf. |
| 13|17 | 5 | LsLsLLsLsLLsLLsLsLLsLsLLsLsLLsL | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 12|18 | 18 | LsLsLLsLsLLsLsLLsLLsLsLLsLsLLsL | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 11|19 | 31 | sLLsLLsLsLLsLsLLsLLsLsLLsLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 10|20 | 13 | sLLsLLsLsLLsLsLLsLsLLsLLsLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 9|21 | 26 | sLLsLsLLsLLsLsLLsLsLLsLLsLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 8|22 | 8 | sLLsLsLLsLLsLsLLsLsLLsLsLLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 7|23 | 21 | sLLsLsLLsLsLLsLLsLsLLsLsLLsLLsL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Maj. | Min. | Perf. |
| 6|24 | 3 | sLLsLsLLsLsLLsLLsLsLLsLsLLsLsLL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. |
| 5|25 | 16 | sLLsLsLLsLsLLsLsLLsLLsLsLLsLsLL | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. |
| 4|26 | 29 | sLsLLsLLsLsLLsLsLLsLLsLsLLsLsLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. |
| 3|27 | 11 | sLsLLsLLsLsLLsLsLLsLsLLsLLsLsLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. |
| 2|28 | 24 | sLsLLsLsLLsLLsLsLLsLsLLsLLsLsLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. |
| 1|29 | 6 | sLsLLsLsLLsLLsLsLLsLsLLsLsLLsLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 0|30 | 19 | sLsLLsLsLLsLsLLsLLsLsLLsLsLLsLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 13\31 | 503.226 | 696.774 | 1:1 | 1.000 | Equalized 19L 12s | |||||
| 73\174 | 503.448 | 696.552 | 6:5 | 1.200 | ||||||
| 60\143 | 503.497 | 696.503 | 5:4 | 1.250 | ||||||
| 107\255 | 503.529 | 696.471 | 9:7 | 1.286 | ||||||
| 47\112 | 503.571 | 696.429 | 4:3 | 1.333 | Supersoft 19L 12s | |||||
| 128\305 | 503.607 | 696.393 | 11:8 | 1.375 | ||||||
| 81\193 | 503.627 | 696.373 | 7:5 | 1.400 | ||||||
| 115\274 | 503.650 | 696.350 | 10:7 | 1.429 | ||||||
| 34\81 | 503.704 | 696.296 | 3:2 | 1.500 | Soft 19L 12s | |||||
| 123\293 | 503.754 | 696.246 | 11:7 | 1.571 | ||||||
| 89\212 | 503.774 | 696.226 | 8:5 | 1.600 | ||||||
| 144\343 | 503.790 | 696.210 | 13:8 | 1.625 | ||||||
| 55\131 | 503.817 | 696.183 | 5:3 | 1.667 | Semisoft 19L 12s | |||||
| 131\312 | 503.846 | 696.154 | 12:7 | 1.714 | ||||||
| 76\181 | 503.867 | 696.133 | 7:4 | 1.750 | ||||||
| 97\231 | 503.896 | 696.104 | 9:5 | 1.800 | ||||||
| 21\50 | 504.000 | 696.000 | 2:1 | 2.000 | Basic 19L 12s Scales with tunings softer than this are proper | |||||
| 92\219 | 504.110 | 695.890 | 9:4 | 2.250 | ||||||
| 71\169 | 504.142 | 695.858 | 7:3 | 2.333 | ||||||
| 121\288 | 504.167 | 695.833 | 12:5 | 2.400 | ||||||
| 50\119 | 504.202 | 695.798 | 5:2 | 2.500 | Semihard 19L 12s | |||||
| 129\307 | 504.235 | 695.765 | 13:5 | 2.600 | ||||||
| 79\188 | 504.255 | 695.745 | 8:3 | 2.667 | ||||||
| 108\257 | 504.280 | 695.720 | 11:4 | 2.750 | ||||||
| 29\69 | 504.348 | 695.652 | 3:1 | 3.000 | Hard 19L 12s | |||||
| 95\226 | 504.425 | 695.575 | 10:3 | 3.333 | ||||||
| 66\157 | 504.459 | 695.541 | 7:2 | 3.500 | ||||||
| 103\245 | 504.490 | 695.510 | 11:3 | 3.667 | ||||||
| 37\88 | 504.545 | 695.455 | 4:1 | 4.000 | Superhard 19L 12s | |||||
| 82\195 | 504.615 | 695.385 | 9:2 | 4.500 | ||||||
| 45\107 | 504.673 | 695.327 | 5:1 | 5.000 | ||||||
| 53\126 | 504.762 | 695.238 | 6:1 | 6.000 | ||||||
| 8\19 | 505.263 | 694.737 | 1:0 | → ∞ | Collapsed 19L 12s | |||||
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