3L 21s

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↖ 2L 20s ↑ 3L 20s 4L 20s ↗
← 2L 21s 3L 21s 4L 21s →
↙ 2L 22s ↓ 3L 22s 4L 22s ↘ 
┌╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┐
│║│││││││║│││││││║││││││││
││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssssssLsssssssLsssssss
sssssssLsssssssLsssssssL
Equave 2/1 (1200.0¢)
Period 1\3 (400.0¢)
Generator size
Bright 7\24 to 1\3 (350.0¢ to 400.0¢)
Dark 0\3 to 1\24 (0.0¢ to 50.0¢)
TAMNAMS information
Descends from 3L 6s (tcherepnin)
Ancestor's step ratio range 6:1 to 1:0
Related MOS scales
Parent 3L 18s
Sister 21L 3s
Daughters 24L 3s, 3L 24s
Neutralized 6L 18s
2-Flought 27L 21s, 3L 45s
Equal tunings
Equalized (L:s = 1:1) 7\24 (350.0¢)
Supersoft (L:s = 4:3) 22\75 (352.0¢)
Soft (L:s = 3:2) 15\51 (352.9¢)
Semisoft (L:s = 5:3) 23\78 (353.8¢)
Basic (L:s = 2:1) 8\27 (355.6¢)
Semihard (L:s = 5:2) 17\57 (357.9¢)
Hard (L:s = 3:1) 9\30 (360.0¢)
Superhard (L:s = 4:1) 10\33 (363.6¢)
Collapsed (L:s = 1:0) 1\3 (400.0¢)

3L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 21 small steps, with a period of 1 large step and 7 small steps that repeats every 400.0¢, or 3 times every octave. 3L 21s is related to 3L 6s, expanding it by 15 tones. Generators that produce this scale range from 350¢ to 400¢, or from 0¢ to 50¢.

Modes

Modes of 3L 21s
UDP Cyclic
order		 Step
pattern
21|0(3) 1 LsssssssLsssssssLsssssss
18|3(3) 8 sLsssssssLsssssssLssssss
15|6(3) 7 ssLsssssssLsssssssLsssss
12|9(3) 6 sssLsssssssLsssssssLssss
9|12(3) 5 ssssLsssssssLsssssssLsss
6|15(3) 4 sssssLsssssssLsssssssLss
3|18(3) 3 ssssssLsssssssLsssssssLs
0|21(3) 2 sssssssLsssssssLsssssssL

Intervals

Intervals of 3L 21s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0¢
1-mosstep Perfect 1-mosstep P1ms s 0.0¢ to 50.0¢
Augmented 1-mosstep A1ms L 50.0¢ to 400.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 100.0¢
Major 2-mosstep M2ms L + s 100.0¢ to 400.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 150.0¢
Major 3-mosstep M3ms L + 2s 150.0¢ to 400.0¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0¢ to 200.0¢
Major 4-mosstep M4ms L + 3s 200.0¢ to 400.0¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0¢ to 250.0¢
Major 5-mosstep M5ms L + 4s 250.0¢ to 400.0¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0¢ to 300.0¢
Major 6-mosstep M6ms L + 5s 300.0¢ to 400.0¢
7-mosstep Diminished 7-mosstep d7ms 7s 0.0¢ to 350.0¢
Perfect 7-mosstep P7ms L + 6s 350.0¢ to 400.0¢
8-mosstep Perfect 8-mosstep P8ms L + 7s 400.0¢
9-mosstep Perfect 9-mosstep P9ms L + 8s 400.0¢ to 450.0¢
Augmented 9-mosstep A9ms 2L + 7s 450.0¢ to 800.0¢
10-mosstep Minor 10-mosstep m10ms L + 9s 400.0¢ to 500.0¢
Major 10-mosstep M10ms 2L + 8s 500.0¢ to 800.0¢
11-mosstep Minor 11-mosstep m11ms L + 10s 400.0¢ to 550.0¢
Major 11-mosstep M11ms 2L + 9s 550.0¢ to 800.0¢
12-mosstep Minor 12-mosstep m12ms L + 11s 400.0¢ to 600.0¢
Major 12-mosstep M12ms 2L + 10s 600.0¢ to 800.0¢
13-mosstep Minor 13-mosstep m13ms L + 12s 400.0¢ to 650.0¢
Major 13-mosstep M13ms 2L + 11s 650.0¢ to 800.0¢
14-mosstep Minor 14-mosstep m14ms L + 13s 400.0¢ to 700.0¢
Major 14-mosstep M14ms 2L + 12s 700.0¢ to 800.0¢
15-mosstep Diminished 15-mosstep d15ms L + 14s 400.0¢ to 750.0¢
Perfect 15-mosstep P15ms 2L + 13s 750.0¢ to 800.0¢
16-mosstep Perfect 16-mosstep P16ms 2L + 14s 800.0¢
17-mosstep Perfect 17-mosstep P17ms 2L + 15s 800.0¢ to 850.0¢
Augmented 17-mosstep A17ms 3L + 14s 850.0¢ to 1200.0¢
18-mosstep Minor 18-mosstep m18ms 2L + 16s 800.0¢ to 900.0¢
Major 18-mosstep M18ms 3L + 15s 900.0¢ to 1200.0¢
19-mosstep Minor 19-mosstep m19ms 2L + 17s 800.0¢ to 950.0¢
Major 19-mosstep M19ms 3L + 16s 950.0¢ to 1200.0¢
20-mosstep Minor 20-mosstep m20ms 2L + 18s 800.0¢ to 1000.0¢
Major 20-mosstep M20ms 3L + 17s 1000.0¢ to 1200.0¢
21-mosstep Minor 21-mosstep m21ms 2L + 19s 800.0¢ to 1050.0¢
Major 21-mosstep M21ms 3L + 18s 1050.0¢ to 1200.0¢
22-mosstep Minor 22-mosstep m22ms 2L + 20s 800.0¢ to 1100.0¢
Major 22-mosstep M22ms 3L + 19s 1100.0¢ to 1200.0¢
23-mosstep Diminished 23-mosstep d23ms 2L + 21s 800.0¢ to 1150.0¢
Perfect 23-mosstep P23ms 3L + 20s 1150.0¢ to 1200.0¢
24-mosstep Perfect 24-mosstep P24ms 3L + 21s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 3L 21s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\24 350.000 50.000 1:1 1.000 Equalized 3L 21s
36\123 351.220 48.780 6:5 1.200
29\99 351.515 48.485 5:4 1.250
51\174 351.724 48.276 9:7 1.286
22\75 352.000 48.000 4:3 1.333 Supersoft 3L 21s
59\201 352.239 47.761 11:8 1.375
37\126 352.381 47.619 7:5 1.400
52\177 352.542 47.458 10:7 1.429
15\51 352.941 47.059 3:2 1.500 Soft 3L 21s
53\180 353.333 46.667 11:7 1.571
38\129 353.488 46.512 8:5 1.600
61\207 353.623 46.377 13:8 1.625
23\78 353.846 46.154 5:3 1.667 Semisoft 3L 21s
54\183 354.098 45.902 12:7 1.714
31\105 354.286 45.714 7:4 1.750
39\132 354.545 45.455 9:5 1.800
8\27 355.556 44.444 2:1 2.000 Basic 3L 21s
Scales with tunings softer than this are proper
33\111 356.757 43.243 9:4 2.250
25\84 357.143 42.857 7:3 2.333
42\141 357.447 42.553 12:5 2.400
17\57 357.895 42.105 5:2 2.500 Semihard 3L 21s
43\144 358.333 41.667 13:5 2.600
26\87 358.621 41.379 8:3 2.667
35\117 358.974 41.026 11:4 2.750
9\30 360.000 40.000 3:1 3.000 Hard 3L 21s
28\93 361.290 38.710 10:3 3.333
19\63 361.905 38.095 7:2 3.500
29\96 362.500 37.500 11:3 3.667
10\33 363.636 36.364 4:1 4.000 Superhard 3L 21s
21\69 365.217 34.783 9:2 4.500
11\36 366.667 33.333 5:1 5.000
12\39 369.231 30.769 6:1 6.000
1\3 400.000 0.000 1:0 → ∞ Collapsed 3L 21s


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