3L 22s

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↖ 2L 21s ↑ 3L 21s 4L 21s ↗
← 2L 22s 3L 22s 4L 22s →
↙ 2L 23s ↓ 3L 23s 4L 23s ↘ 
┌╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┐
│║│││││││║│││││││║│││││││││
│││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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¢)

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

Modes of 3L 22s
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

Intervals

Intervals of 3L 22s
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 400.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 96.0¢
Major 2-mosstep M2ms L + s 96.0¢ to 400.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 144.0¢
Major 3-mosstep M3ms L + 2s 144.0¢ to 400.0¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0¢ to 192.0¢
Major 4-mosstep M4ms L + 3s 192.0¢ to 400.0¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0¢ to 240.0¢
Major 5-mosstep M5ms L + 4s 240.0¢ to 400.0¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0¢ to 288.0¢
Major 6-mosstep M6ms L + 5s 288.0¢ to 400.0¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0¢ to 336.0¢
Major 7-mosstep M7ms L + 6s 336.0¢ to 400.0¢
8-mosstep Diminished 8-mosstep d8ms 8s 0.0¢ to 384.0¢
Perfect 8-mosstep P8ms L + 7s 384.0¢ to 400.0¢
9-mosstep Minor 9-mosstep m9ms L + 8s 400.0¢ to 432.0¢
Major 9-mosstep M9ms 2L + 7s 432.0¢ to 800.0¢
10-mosstep Minor 10-mosstep m10ms L + 9s 400.0¢ to 480.0¢
Major 10-mosstep M10ms 2L + 8s 480.0¢ to 800.0¢
11-mosstep Minor 11-mosstep m11ms L + 10s 400.0¢ to 528.0¢
Major 11-mosstep M11ms 2L + 9s 528.0¢ to 800.0¢
12-mosstep Minor 12-mosstep m12ms L + 11s 400.0¢ to 576.0¢
Major 12-mosstep M12ms 2L + 10s 576.0¢ to 800.0¢
13-mosstep Minor 13-mosstep m13ms L + 12s 400.0¢ to 624.0¢
Major 13-mosstep M13ms 2L + 11s 624.0¢ to 800.0¢
14-mosstep Minor 14-mosstep m14ms L + 13s 400.0¢ to 672.0¢
Major 14-mosstep M14ms 2L + 12s 672.0¢ to 800.0¢
15-mosstep Minor 15-mosstep m15ms L + 14s 400.0¢ to 720.0¢
Major 15-mosstep M15ms 2L + 13s 720.0¢ to 800.0¢
16-mosstep Minor 16-mosstep m16ms L + 15s 400.0¢ to 768.0¢
Major 16-mosstep M16ms 2L + 14s 768.0¢ to 800.0¢
17-mosstep Perfect 17-mosstep P17ms 2L + 15s 800.0¢ to 816.0¢
Augmented 17-mosstep A17ms 3L + 14s 816.0¢ to 1200.0¢
18-mosstep Minor 18-mosstep m18ms 2L + 16s 800.0¢ to 864.0¢
Major 18-mosstep M18ms 3L + 15s 864.0¢ to 1200.0¢
19-mosstep Minor 19-mosstep m19ms 2L + 17s 800.0¢ to 912.0¢
Major 19-mosstep M19ms 3L + 16s 912.0¢ to 1200.0¢
20-mosstep Minor 20-mosstep m20ms 2L + 18s 800.0¢ to 960.0¢
Major 20-mosstep M20ms 3L + 17s 960.0¢ to 1200.0¢
21-mosstep Minor 21-mosstep m21ms 2L + 19s 800.0¢ to 1008.0¢
Major 21-mosstep M21ms 3L + 18s 1008.0¢ to 1200.0¢
22-mosstep Minor 22-mosstep m22ms 2L + 20s 800.0¢ to 1056.0¢
Major 22-mosstep M22ms 3L + 19s 1056.0¢ to 1200.0¢
23-mosstep Minor 23-mosstep m23ms 2L + 21s 800.0¢ to 1104.0¢
Major 23-mosstep M23ms 3L + 20s 1104.0¢ to 1200.0¢
24-mosstep Minor 24-mosstep m24ms 2L + 22s 800.0¢ to 1152.0¢
Major 24-mosstep M24ms 3L + 21s 1152.0¢ to 1200.0¢
25-mosstep Perfect 25-mosstep P25ms 3L + 22s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 3L 22s
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
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