5L 19s
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Step pattern
LsssLssssLssssLssssLssss
ssssLssssLssssLssssLsssL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
19\24 to 4\5 (950.0 ¢ to 960.0 ¢)
Dark
1\5 to 5\24 (240.0 ¢ to 250.0 ¢)
Related to
5L 4s (semiquartal)
With tunings
4:1 to 1:0 (ultrahard)
Parent
5L 14s
Sister
19L 5s
Daughters
24L 5s, 5L 24s
Neutralized
10L 14s
2-Flought
29L 19s, 5L 43s
Equalized (L:s = 1:1)
19\24 (950.0 ¢)
Supersoft (L:s = 4:3)
61\77 (950.6 ¢)
Soft (L:s = 3:2)
42\53 (950.9 ¢)
Semisoft (L:s = 5:3)
65\82 (951.2 ¢)
Basic (L:s = 2:1)
23\29 (951.7 ¢)
Semihard (L:s = 5:2)
50\63 (952.4 ¢)
Hard (L:s = 3:1)
27\34 (952.9 ¢)
Superhard (L:s = 4:1)
31\39 (953.8 ¢)
Collapsed (L:s = 1:0)
4\5 (960.0 ¢)
| ↖ 4L 18s | ↑ 5L 18s | 6L 18s ↗ |
| ← 4L 19s | 5L 19s | 6L 19s → |
| ↙ 4L 20s | ↓ 5L 20s | 6L 20s ↘ |
┌╥┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┐ │║│││║││││║││││║││││║│││││ ││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssssLssssLssssLssssLsssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
5L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 19 small steps, repeating every octave. 5L 19s is a great-grandchild scale of 5L 4s, expanding it by 15 tones. Generators that produce this scale range from 950 ¢ to 960 ¢, or from 240 ¢ to 250 ¢.
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 50.0 ¢ |
| Major 1-mosstep | M1ms | L | 50.0 ¢ to 240.0 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 100.0 ¢ |
| Major 2-mosstep | M2ms | L + s | 100.0 ¢ to 240.0 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0 ¢ to 150.0 ¢ |
| Major 3-mosstep | M3ms | L + 2s | 150.0 ¢ to 240.0 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 4s | 0.0 ¢ to 200.0 ¢ |
| Major 4-mosstep | M4ms | L + 3s | 200.0 ¢ to 240.0 ¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | L + 4s | 240.0 ¢ to 250.0 ¢ |
| Augmented 5-mosstep | A5ms | 2L + 3s | 250.0 ¢ to 480.0 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 240.0 ¢ to 300.0 ¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 300.0 ¢ to 480.0 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | L + 6s | 240.0 ¢ to 350.0 ¢ |
| Major 7-mosstep | M7ms | 2L + 5s | 350.0 ¢ to 480.0 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | L + 7s | 240.0 ¢ to 400.0 ¢ |
| Major 8-mosstep | M8ms | 2L + 6s | 400.0 ¢ to 480.0 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | L + 8s | 240.0 ¢ to 450.0 ¢ |
| Major 9-mosstep | M9ms | 2L + 7s | 450.0 ¢ to 480.0 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 2L + 8s | 480.0 ¢ to 500.0 ¢ |
| Major 10-mosstep | M10ms | 3L + 7s | 500.0 ¢ to 720.0 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 2L + 9s | 480.0 ¢ to 550.0 ¢ |
| Major 11-mosstep | M11ms | 3L + 8s | 550.0 ¢ to 720.0 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 2L + 10s | 480.0 ¢ to 600.0 ¢ |
| Major 12-mosstep | M12ms | 3L + 9s | 600.0 ¢ to 720.0 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 2L + 11s | 480.0 ¢ to 650.0 ¢ |
| Major 13-mosstep | M13ms | 3L + 10s | 650.0 ¢ to 720.0 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 2L + 12s | 480.0 ¢ to 700.0 ¢ |
| Major 14-mosstep | M14ms | 3L + 11s | 700.0 ¢ to 720.0 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 3L + 12s | 720.0 ¢ to 750.0 ¢ |
| Major 15-mosstep | M15ms | 4L + 11s | 750.0 ¢ to 960.0 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 3L + 13s | 720.0 ¢ to 800.0 ¢ |
| Major 16-mosstep | M16ms | 4L + 12s | 800.0 ¢ to 960.0 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 3L + 14s | 720.0 ¢ to 850.0 ¢ |
| Major 17-mosstep | M17ms | 4L + 13s | 850.0 ¢ to 960.0 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 3L + 15s | 720.0 ¢ to 900.0 ¢ |
| Major 18-mosstep | M18ms | 4L + 14s | 900.0 ¢ to 960.0 ¢ | |
| 19-mosstep | Diminished 19-mosstep | d19ms | 3L + 16s | 720.0 ¢ to 950.0 ¢ |
| Perfect 19-mosstep | P19ms | 4L + 15s | 950.0 ¢ to 960.0 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 4L + 16s | 960.0 ¢ to 1000.0 ¢ |
| Major 20-mosstep | M20ms | 5L + 15s | 1000.0 ¢ to 1200.0 ¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 4L + 17s | 960.0 ¢ to 1050.0 ¢ |
| Major 21-mosstep | M21ms | 5L + 16s | 1050.0 ¢ to 1200.0 ¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 4L + 18s | 960.0 ¢ to 1100.0 ¢ |
| Major 22-mosstep | M22ms | 5L + 17s | 1100.0 ¢ to 1200.0 ¢ | |
| 23-mosstep | Minor 23-mosstep | m23ms | 4L + 19s | 960.0 ¢ to 1150.0 ¢ |
| Major 23-mosstep | M23ms | 5L + 18s | 1150.0 ¢ to 1200.0 ¢ | |
| 24-mosstep | Perfect 24-mosstep | P24ms | 5L + 19s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 28 | Augmented 4-mosdegree | A4md |
| 27 | Augmented 9-mosdegree | A9md |
| 26 | Augmented 14-mosdegree | A14md |
| 25 | Augmented 19-mosdegree | A19md |
| 24 | Augmented 0-mosdegree | A0md |
| 23 | Augmented 5-mosdegree | A5md |
| 22 | Major 10-mosdegree | M10md |
| 21 | Major 15-mosdegree | M15md |
| 20 | Major 20-mosdegree | M20md |
| 19 | Major 1-mosdegree | M1md |
| 18 | Major 6-mosdegree | M6md |
| 17 | Major 11-mosdegree | M11md |
| 16 | Major 16-mosdegree | M16md |
| 15 | Major 21-mosdegree | M21md |
| 14 | Major 2-mosdegree | M2md |
| 13 | Major 7-mosdegree | M7md |
| 12 | Major 12-mosdegree | M12md |
| 11 | Major 17-mosdegree | M17md |
| 10 | Major 22-mosdegree | M22md |
| 9 | Major 3-mosdegree | M3md |
| 8 | Major 8-mosdegree | M8md |
| 7 | Major 13-mosdegree | M13md |
| 6 | Major 18-mosdegree | M18md |
| 5 | Major 23-mosdegree | M23md |
| 4 | Major 4-mosdegree | M4md |
| 3 | Major 9-mosdegree | M9md |
| 2 | Major 14-mosdegree | M14md |
| 1 | Perfect 19-mosdegree | P19md |
| 0 | Perfect 0-mosdegree Perfect 24-mosdegree |
P0md P24md |
| −1 | Perfect 5-mosdegree | P5md |
| −2 | Minor 10-mosdegree | m10md |
| −3 | Minor 15-mosdegree | m15md |
| −4 | Minor 20-mosdegree | m20md |
| −5 | Minor 1-mosdegree | m1md |
| −6 | Minor 6-mosdegree | m6md |
| −7 | Minor 11-mosdegree | m11md |
| −8 | Minor 16-mosdegree | m16md |
| −9 | Minor 21-mosdegree | m21md |
| −10 | Minor 2-mosdegree | m2md |
| −11 | Minor 7-mosdegree | m7md |
| −12 | Minor 12-mosdegree | m12md |
| −13 | Minor 17-mosdegree | m17md |
| −14 | Minor 22-mosdegree | m22md |
| −15 | Minor 3-mosdegree | m3md |
| −16 | Minor 8-mosdegree | m8md |
| −17 | Minor 13-mosdegree | m13md |
| −18 | Minor 18-mosdegree | m18md |
| −19 | Minor 23-mosdegree | m23md |
| −20 | Minor 4-mosdegree | m4md |
| −21 | Minor 9-mosdegree | m9md |
| −22 | Minor 14-mosdegree | m14md |
| −23 | Diminished 19-mosdegree | d19md |
| −24 | Diminished 24-mosdegree | d24md |
| −25 | Diminished 5-mosdegree | d5md |
| −26 | Diminished 10-mosdegree | d10md |
| −27 | Diminished 15-mosdegree | d15md |
| −28 | 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 | 23 | 24 | |||
| 23|0 | 1 | LsssLssssLssssLssssLssss | Perf. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 22|1 | 20 | LssssLsssLssssLssssLssss | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 21|2 | 15 | LssssLssssLsssLssssLssss | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 20|3 | 10 | LssssLssssLssssLsssLssss | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 19|4 | 5 | LssssLssssLssssLssssLsss | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. |
| 18|5 | 24 | sLsssLssssLssssLssssLsss | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. |
| 17|6 | 19 | sLssssLsssLssssLssssLsss | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. |
| 16|7 | 14 | sLssssLssssLsssLssssLsss | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. |
| 15|8 | 9 | sLssssLssssLssssLsssLsss | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. |
| 14|9 | 4 | sLssssLssssLssssLssssLss | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. |
| 13|10 | 23 | ssLsssLssssLssssLssssLss | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. |
| 12|11 | 18 | ssLssssLsssLssssLssssLss | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. |
| 11|12 | 13 | ssLssssLssssLsssLssssLss | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. |
| 10|13 | 8 | ssLssssLssssLssssLsssLss | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Perf. |
| 9|14 | 3 | ssLssssLssssLssssLssssLs | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Perf. |
| 8|15 | 22 | sssLsssLssssLssssLssssLs | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Perf. |
| 7|16 | 17 | sssLssssLsssLssssLssssLs | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Perf. |
| 6|17 | 12 | sssLssssLssssLsssLssssLs | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Perf. |
| 5|18 | 7 | sssLssssLssssLssssLsssLs | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Perf. |
| 4|19 | 2 | sssLssssLssssLssssLssssL | Perf. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
| 3|20 | 21 | ssssLsssLssssLssssLssssL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
| 2|21 | 16 | ssssLssssLsssLssssLssssL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
| 1|22 | 11 | ssssLssssLssssLsssLssssL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. |
| 0|23 | 6 | ssssLssssLssssLssssLsssL | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 19\24 | 950.000 | 250.000 | 1:1 | 1.000 | Equalized 5L 19s | |||||
| 99\125 | 950.400 | 249.600 | 6:5 | 1.200 | ||||||
| 80\101 | 950.495 | 249.505 | 5:4 | 1.250 | ||||||
| 141\178 | 950.562 | 249.438 | 9:7 | 1.286 | ||||||
| 61\77 | 950.649 | 249.351 | 4:3 | 1.333 | Supersoft 5L 19s | |||||
| 164\207 | 950.725 | 249.275 | 11:8 | 1.375 | ||||||
| 103\130 | 950.769 | 249.231 | 7:5 | 1.400 | ||||||
| 145\183 | 950.820 | 249.180 | 10:7 | 1.429 | ||||||
| 42\53 | 950.943 | 249.057 | 3:2 | 1.500 | Soft 5L 19s | |||||
| 149\188 | 951.064 | 248.936 | 11:7 | 1.571 | ||||||
| 107\135 | 951.111 | 248.889 | 8:5 | 1.600 | ||||||
| 172\217 | 951.152 | 248.848 | 13:8 | 1.625 | ||||||
| 65\82 | 951.220 | 248.780 | 5:3 | 1.667 | Semisoft 5L 19s | |||||
| 153\193 | 951.295 | 248.705 | 12:7 | 1.714 | ||||||
| 88\111 | 951.351 | 248.649 | 7:4 | 1.750 | ||||||
| 111\140 | 951.429 | 248.571 | 9:5 | 1.800 | ||||||
| 23\29 | 951.724 | 248.276 | 2:1 | 2.000 | Basic 5L 19s Scales with tunings softer than this are proper | |||||
| 96\121 | 952.066 | 247.934 | 9:4 | 2.250 | ||||||
| 73\92 | 952.174 | 247.826 | 7:3 | 2.333 | ||||||
| 123\155 | 952.258 | 247.742 | 12:5 | 2.400 | ||||||
| 50\63 | 952.381 | 247.619 | 5:2 | 2.500 | Semihard 5L 19s | |||||
| 127\160 | 952.500 | 247.500 | 13:5 | 2.600 | ||||||
| 77\97 | 952.577 | 247.423 | 8:3 | 2.667 | ||||||
| 104\131 | 952.672 | 247.328 | 11:4 | 2.750 | ||||||
| 27\34 | 952.941 | 247.059 | 3:1 | 3.000 | Hard 5L 19s | |||||
| 85\107 | 953.271 | 246.729 | 10:3 | 3.333 | ||||||
| 58\73 | 953.425 | 246.575 | 7:2 | 3.500 | ||||||
| 89\112 | 953.571 | 246.429 | 11:3 | 3.667 | ||||||
| 31\39 | 953.846 | 246.154 | 4:1 | 4.000 | Superhard 5L 19s | |||||
| 66\83 | 954.217 | 245.783 | 9:2 | 4.500 | ||||||
| 35\44 | 954.545 | 245.455 | 5:1 | 5.000 | ||||||
| 39\49 | 955.102 | 244.898 | 6:1 | 6.000 | ||||||
| 4\5 | 960.000 | 240.000 | 1:0 | → ∞ | Collapsed 5L 19s | |||||
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