4L 21s
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Scale structure
Step pattern
LsssssLsssssLsssssLssssss
ssssssLsssssLsssssLsssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
6\25 to 1\4 (288.0¢ to 300.0¢)
Dark
3\4 to 19\25 (900.0¢ to 912.0¢)
TAMNAMS information
Descends from
4L 5s (gramitonic)
Ancestor's step ratio range
5:1 to 1:0
Related MOS scales
Parent
4L 17s
Sister
21L 4s
Daughters
25L 4s, 4L 25s
Neutralized
8L 17s
2-Flought
29L 21s, 4L 46s
Equal tunings
Equalized (L:s = 1:1)
6\25 (288.0¢)
Supersoft (L:s = 4:3)
19\79 (288.6¢)
Soft (L:s = 3:2)
13\54 (288.9¢)
Semisoft (L:s = 5:3)
20\83 (289.2¢)
Basic (L:s = 2:1)
7\29 (289.7¢)
Semihard (L:s = 5:2)
15\62 (290.3¢)
Hard (L:s = 3:1)
8\33 (290.9¢)
Superhard (L:s = 4:1)
9\37 (291.9¢)
Collapsed (L:s = 1:0)
1\4 (300.0¢)
| ↖ 3L 20s | ↑ 4L 20s | 5L 20s ↗ |
| ← 3L 21s | 4L 21s | 5L 21s → |
| ↙ 3L 22s | ↓ 4L 22s | 5L 22s ↘ |
┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┬┐ │║│││││║│││││║│││││║│││││││ │││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssssLsssssLsssssLsssssL
4L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 21 small steps, repeating every octave. 4L 21s is related to 4L 5s, expanding it by 16 tones. Generators that produce this scale range from 288¢ to 300¢, or from 900¢ to 912¢.
This scale is associated with moulin temperament, which includes a very precise 8:11:13 triad. Eliora proposes the name moulinoid for this pattern.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 24|0 | 1 | LsssssLsssssLsssssLssssss |
| 23|1 | 7 | LsssssLsssssLssssssLsssss |
| 22|2 | 13 | LsssssLssssssLsssssLsssss |
| 21|3 | 19 | LssssssLsssssLsssssLsssss |
| 20|4 | 25 | sLsssssLsssssLsssssLsssss |
| 19|5 | 6 | sLsssssLsssssLssssssLssss |
| 18|6 | 12 | sLsssssLssssssLsssssLssss |
| 17|7 | 18 | sLssssssLsssssLsssssLssss |
| 16|8 | 24 | ssLsssssLsssssLsssssLssss |
| 15|9 | 5 | ssLsssssLsssssLssssssLsss |
| 14|10 | 11 | ssLsssssLssssssLsssssLsss |
| 13|11 | 17 | ssLssssssLsssssLsssssLsss |
| 12|12 | 23 | sssLsssssLsssssLsssssLsss |
| 11|13 | 4 | sssLsssssLsssssLssssssLss |
| 10|14 | 10 | sssLsssssLssssssLsssssLss |
| 9|15 | 16 | sssLssssssLsssssLsssssLss |
| 8|16 | 22 | ssssLsssssLsssssLsssssLss |
| 7|17 | 3 | ssssLsssssLsssssLssssssLs |
| 6|18 | 9 | ssssLsssssLssssssLsssssLs |
| 5|19 | 15 | ssssLssssssLsssssLsssssLs |
| 4|20 | 21 | sssssLsssssLsssssLsssssLs |
| 3|21 | 2 | sssssLsssssLsssssLssssssL |
| 2|22 | 8 | sssssLsssssLssssssLsssssL |
| 1|23 | 14 | sssssLssssssLsssssLsssssL |
| 0|24 | 20 | ssssssLsssssLsssssLsssssL |
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 48.0¢ |
| Major 1-mosstep | M1ms | L | 48.0¢ to 300.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 96.0¢ |
| Major 2-mosstep | M2ms | L + s | 96.0¢ to 300.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 144.0¢ |
| Major 3-mosstep | M3ms | L + 2s | 144.0¢ to 300.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 4s | 0.0¢ to 192.0¢ |
| Major 4-mosstep | M4ms | L + 3s | 192.0¢ to 300.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 5s | 0.0¢ to 240.0¢ |
| Major 5-mosstep | M5ms | L + 4s | 240.0¢ to 300.0¢ | |
| 6-mosstep | Diminished 6-mosstep | d6ms | 6s | 0.0¢ to 288.0¢ |
| Perfect 6-mosstep | P6ms | L + 5s | 288.0¢ to 300.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | L + 6s | 300.0¢ to 336.0¢ |
| Major 7-mosstep | M7ms | 2L + 5s | 336.0¢ to 600.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | L + 7s | 300.0¢ to 384.0¢ |
| Major 8-mosstep | M8ms | 2L + 6s | 384.0¢ to 600.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | L + 8s | 300.0¢ to 432.0¢ |
| Major 9-mosstep | M9ms | 2L + 7s | 432.0¢ to 600.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | L + 9s | 300.0¢ to 480.0¢ |
| Major 10-mosstep | M10ms | 2L + 8s | 480.0¢ to 600.0¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | L + 10s | 300.0¢ to 528.0¢ |
| Major 11-mosstep | M11ms | 2L + 9s | 528.0¢ to 600.0¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | L + 11s | 300.0¢ to 576.0¢ |
| Major 12-mosstep | M12ms | 2L + 10s | 576.0¢ to 600.0¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 2L + 11s | 600.0¢ to 624.0¢ |
| Major 13-mosstep | M13ms | 3L + 10s | 624.0¢ to 900.0¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 2L + 12s | 600.0¢ to 672.0¢ |
| Major 14-mosstep | M14ms | 3L + 11s | 672.0¢ to 900.0¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 2L + 13s | 600.0¢ to 720.0¢ |
| Major 15-mosstep | M15ms | 3L + 12s | 720.0¢ to 900.0¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 2L + 14s | 600.0¢ to 768.0¢ |
| Major 16-mosstep | M16ms | 3L + 13s | 768.0¢ to 900.0¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 2L + 15s | 600.0¢ to 816.0¢ |
| Major 17-mosstep | M17ms | 3L + 14s | 816.0¢ to 900.0¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 2L + 16s | 600.0¢ to 864.0¢ |
| Major 18-mosstep | M18ms | 3L + 15s | 864.0¢ to 900.0¢ | |
| 19-mosstep | Perfect 19-mosstep | P19ms | 3L + 16s | 900.0¢ to 912.0¢ |
| Augmented 19-mosstep | A19ms | 4L + 15s | 912.0¢ to 1200.0¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 3L + 17s | 900.0¢ to 960.0¢ |
| Major 20-mosstep | M20ms | 4L + 16s | 960.0¢ to 1200.0¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 3L + 18s | 900.0¢ to 1008.0¢ |
| Major 21-mosstep | M21ms | 4L + 17s | 1008.0¢ to 1200.0¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 3L + 19s | 900.0¢ to 1056.0¢ |
| Major 22-mosstep | M22ms | 4L + 18s | 1056.0¢ to 1200.0¢ | |
| 23-mosstep | Minor 23-mosstep | m23ms | 3L + 20s | 900.0¢ to 1104.0¢ |
| Major 23-mosstep | M23ms | 4L + 19s | 1104.0¢ to 1200.0¢ | |
| 24-mosstep | Minor 24-mosstep | m24ms | 3L + 21s | 900.0¢ to 1152.0¢ |
| Major 24-mosstep | M24ms | 4L + 20s | 1152.0¢ to 1200.0¢ | |
| 25-mosstep | Perfect 25-mosstep | P25ms | 4L + 21s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 6\25 | 288.000 | 912.000 | 1:1 | 1.000 | Equalized 4L 21s | |||||
| 31\129 | 288.372 | 911.628 | 6:5 | 1.200 | ||||||
| 25\104 | 288.462 | 911.538 | 5:4 | 1.250 | ||||||
| 44\183 | 288.525 | 911.475 | 9:7 | 1.286 | ||||||
| 19\79 | 288.608 | 911.392 | 4:3 | 1.333 | Supersoft 4L 21s | |||||
| 51\212 | 288.679 | 911.321 | 11:8 | 1.375 | ||||||
| 32\133 | 288.722 | 911.278 | 7:5 | 1.400 | ||||||
| 45\187 | 288.770 | 911.230 | 10:7 | 1.429 | ||||||
| 13\54 | 288.889 | 911.111 | 3:2 | 1.500 | Soft 4L 21s | |||||
| 46\191 | 289.005 | 910.995 | 11:7 | 1.571 | ||||||
| 33\137 | 289.051 | 910.949 | 8:5 | 1.600 | ||||||
| 53\220 | 289.091 | 910.909 | 13:8 | 1.625 | ||||||
| 20\83 | 289.157 | 910.843 | 5:3 | 1.667 | Semisoft 4L 21s | |||||
| 47\195 | 289.231 | 910.769 | 12:7 | 1.714 | ||||||
| 27\112 | 289.286 | 910.714 | 7:4 | 1.750 | ||||||
| 34\141 | 289.362 | 910.638 | 9:5 | 1.800 | ||||||
| 7\29 | 289.655 | 910.345 | 2:1 | 2.000 | Basic 4L 21s Scales with tunings softer than this are proper | |||||
| 29\120 | 290.000 | 910.000 | 9:4 | 2.250 | ||||||
| 22\91 | 290.110 | 909.890 | 7:3 | 2.333 | ||||||
| 37\153 | 290.196 | 909.804 | 12:5 | 2.400 | ||||||
| 15\62 | 290.323 | 909.677 | 5:2 | 2.500 | Semihard 4L 21s | |||||
| 38\157 | 290.446 | 909.554 | 13:5 | 2.600 | ||||||
| 23\95 | 290.526 | 909.474 | 8:3 | 2.667 | ||||||
| 31\128 | 290.625 | 909.375 | 11:4 | 2.750 | ||||||
| 8\33 | 290.909 | 909.091 | 3:1 | 3.000 | Hard 4L 21s | |||||
| 25\103 | 291.262 | 908.738 | 10:3 | 3.333 | ||||||
| 17\70 | 291.429 | 908.571 | 7:2 | 3.500 | ||||||
| 26\107 | 291.589 | 908.411 | 11:3 | 3.667 | ||||||
| 9\37 | 291.892 | 908.108 | 4:1 | 4.000 | Superhard 4L 21s | |||||
| 19\78 | 292.308 | 907.692 | 9:2 | 4.500 | ||||||
| 10\41 | 292.683 | 907.317 | 5:1 | 5.000 | ||||||
| 11\45 | 293.333 | 906.667 | 6:1 | 6.000 | ||||||
| 1\4 | 300.000 | 900.000 | 1:0 | → ∞ | Collapsed 4L 21s | |||||
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