3L 22s
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Scale structure
Step pattern
LsssssssLsssssssLssssssss
ssssssssLsssssssLsssssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
8\25 to 1\3 (384.0¢ to 400.0¢)
Dark
2\3 to 17\25 (800.0¢ to 816.0¢)
TAMNAMS information
Descends from
3L 7s (sephiroid)
Ancestor's step ratio range
6:1 to 1:0
Related MOS scales
Parent
3L 19s
Sister
22L 3s
Daughters
25L 3s, 3L 25s
Neutralized
6L 19s
2-Flought
28L 22s, 3L 47s
Equal tunings
Equalized (L:s = 1:1)
8\25 (384.0¢)
Supersoft (L:s = 4:3)
25\78 (384.6¢)
Soft (L:s = 3:2)
17\53 (384.9¢)
Semisoft (L:s = 5:3)
26\81 (385.2¢)
Basic (L:s = 2:1)
9\28 (385.7¢)
Semihard (L:s = 5:2)
19\59 (386.4¢)
Hard (L:s = 3:1)
10\31 (387.1¢)
Superhard (L:s = 4:1)
11\34 (388.2¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
| ↖ 2L 21s | ↑ 3L 21s | 4L 21s ↗ |
| ← 2L 22s | 3L 22s | 4L 22s → |
| ↙ 2L 23s | ↓ 3L 23s | 4L 23s ↘ |
┌╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┐ │║│││││││║│││││││║│││││││││ │││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssssssLsssssssLsssssssL
3L 22s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 22 small steps, repeating every octave. 3L 22s is related to 3L 7s, expanding it by 15 tones. Generators that produce this scale range from 384¢ to 400¢, or from 800¢ to 816¢. This generator range is most closely associated with würschmidt (where 8 gens is 6/1), magus (where 11 gens is 12/1) and supermagus (where 14 gens is 24/1), where an increasing amount of gens corresponds to a sharper-tempered ~5/4 and therefore a smaller ~128/125 remnant to the octave.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 24|0 | 1 | LsssssssLsssssssLssssssss |
| 23|1 | 9 | LsssssssLssssssssLsssssss |
| 22|2 | 17 | LssssssssLsssssssLsssssss |
| 21|3 | 25 | sLsssssssLsssssssLsssssss |
| 20|4 | 8 | sLsssssssLssssssssLssssss |
| 19|5 | 16 | sLssssssssLsssssssLssssss |
| 18|6 | 24 | ssLsssssssLsssssssLssssss |
| 17|7 | 7 | ssLsssssssLssssssssLsssss |
| 16|8 | 15 | ssLssssssssLsssssssLsssss |
| 15|9 | 23 | sssLsssssssLsssssssLsssss |
| 14|10 | 6 | sssLsssssssLssssssssLssss |
| 13|11 | 14 | sssLssssssssLsssssssLssss |
| 12|12 | 22 | ssssLsssssssLsssssssLssss |
| 11|13 | 5 | ssssLsssssssLssssssssLsss |
| 10|14 | 13 | ssssLssssssssLsssssssLsss |
| 9|15 | 21 | sssssLsssssssLsssssssLsss |
| 8|16 | 4 | sssssLsssssssLssssssssLss |
| 7|17 | 12 | sssssLssssssssLsssssssLss |
| 6|18 | 20 | ssssssLsssssssLsssssssLss |
| 5|19 | 3 | ssssssLsssssssLssssssssLs |
| 4|20 | 11 | ssssssLssssssssLsssssssLs |
| 3|21 | 19 | sssssssLsssssssLsssssssLs |
| 2|22 | 2 | sssssssLsssssssLssssssssL |
| 1|23 | 10 | sssssssLssssssssLsssssssL |
| 0|24 | 18 | ssssssssLsssssssLsssssssL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 8\25 | 384.000 | 816.000 | 1:1 | 1.000 | Equalized 3L 22s | |||||
| 41\128 | 384.375 | 815.625 | 6:5 | 1.200 | ||||||
| 33\103 | 384.466 | 815.534 | 5:4 | 1.250 | ||||||
| 58\181 | 384.530 | 815.470 | 9:7 | 1.286 | ||||||
| 25\78 | 384.615 | 815.385 | 4:3 | 1.333 | Supersoft 3L 22s | |||||
| 67\209 | 384.689 | 815.311 | 11:8 | 1.375 | ||||||
| 42\131 | 384.733 | 815.267 | 7:5 | 1.400 | ||||||
| 59\184 | 384.783 | 815.217 | 10:7 | 1.429 | ||||||
| 17\53 | 384.906 | 815.094 | 3:2 | 1.500 | Soft 3L 22s | |||||
| 60\187 | 385.027 | 814.973 | 11:7 | 1.571 | ||||||
| 43\134 | 385.075 | 814.925 | 8:5 | 1.600 | ||||||
| 69\215 | 385.116 | 814.884 | 13:8 | 1.625 | ||||||
| 26\81 | 385.185 | 814.815 | 5:3 | 1.667 | Semisoft 3L 22s | |||||
| 61\190 | 385.263 | 814.737 | 12:7 | 1.714 | ||||||
| 35\109 | 385.321 | 814.679 | 7:4 | 1.750 | ||||||
| 44\137 | 385.401 | 814.599 | 9:5 | 1.800 | ||||||
| 9\28 | 385.714 | 814.286 | 2:1 | 2.000 | Basic 3L 22s Scales with tunings softer than this are proper | |||||
| 37\115 | 386.087 | 813.913 | 9:4 | 2.250 | ||||||
| 28\87 | 386.207 | 813.793 | 7:3 | 2.333 | ||||||
| 47\146 | 386.301 | 813.699 | 12:5 | 2.400 | ||||||
| 19\59 | 386.441 | 813.559 | 5:2 | 2.500 | Semihard 3L 22s | |||||
| 48\149 | 386.577 | 813.423 | 13:5 | 2.600 | ||||||
| 29\90 | 386.667 | 813.333 | 8:3 | 2.667 | ||||||
| 39\121 | 386.777 | 813.223 | 11:4 | 2.750 | ||||||
| 10\31 | 387.097 | 812.903 | 3:1 | 3.000 | Hard 3L 22s | |||||
| 31\96 | 387.500 | 812.500 | 10:3 | 3.333 | ||||||
| 21\65 | 387.692 | 812.308 | 7:2 | 3.500 | ||||||
| 32\99 | 387.879 | 812.121 | 11:3 | 3.667 | ||||||
| 11\34 | 388.235 | 811.765 | 4:1 | 4.000 | Superhard 3L 22s | |||||
| 23\71 | 388.732 | 811.268 | 9:2 | 4.500 | ||||||
| 12\37 | 389.189 | 810.811 | 5:1 | 5.000 | ||||||
| 13\40 | 390.000 | 810.000 | 6:1 | 6.000 | ||||||
| 1\3 | 400.000 | 800.000 | 1:0 | → ∞ | Collapsed 3L 22s | |||||