3L 18s

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↖ 2L 17s ↑ 3L 17s 4L 17s ↗
← 2L 18s 3L 18s 4L 18s →
↙ 2L 19s ↓ 3L 19s 4L 19s ↘
┌╥┬┬┬┬┬┬╥┬┬┬┬┬┬╥┬┬┬┬┬┬┐
│║││││││║││││││║│││││││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssssLssssssLssssss
ssssssLssssssLssssssL
Equave 2/1 (1200.0¢)
Period 1\3 (400.0¢)
Generator size
Bright 6\21 to 1\3 (342.9¢ to 400.0¢)
Dark 0\3 to 1\21 (0.0¢ to 57.1¢)
TAMNAMS information
Descends from 3L 6s (tcherepnin)
Ancestor's step ratio range 5:1 to 1:0
Related MOS scales
Parent 3L 15s
Sister 18L 3s
Daughters 21L 3s, 3L 21s
Neutralized 6L 15s
2-Flought 24L 18s, 3L 39s
Equal tunings
Equalized (L:s = 1:1) 6\21 (342.9¢)
Supersoft (L:s = 4:3) 19\66 (345.5¢)
Soft (L:s = 3:2) 13\45 (346.7¢)
Semisoft (L:s = 5:3) 20\69 (347.8¢)
Basic (L:s = 2:1) 7\24 (350.0¢)
Semihard (L:s = 5:2) 15\51 (352.9¢)
Hard (L:s = 3:1) 8\27 (355.6¢)
Superhard (L:s = 4:1) 9\30 (360.0¢)
Collapsed (L:s = 1:0) 1\3 (400.0¢)

3L 18s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 18 small steps, with a period of 1 large step and 6 small steps that repeats every 400.0¢, or 3 times every octave. 3L 18s is related to 3L 6s, expanding it by 12 tones. Generators that produce this scale range from 342.9¢ to 400¢, or from 0¢ to 57.1¢.

Modes

Modes of 3L 18s
UDP Cyclic
order
Step
pattern
18|0(3) 1 LssssssLssssssLssssss
15|3(3) 7 sLssssssLssssssLsssss
12|6(3) 6 ssLssssssLssssssLssss
9|9(3) 5 sssLssssssLssssssLsss
6|12(3) 4 ssssLssssssLssssssLss
3|15(3) 3 sssssLssssssLssssssLs
0|18(3) 2 ssssssLssssssLssssssL

Scale tree

Scale Tree and Tuning Spectrum of 3L 18s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
6\21 342.857 57.143 1:1 1.000 Equalized 3L 18s
31\108 344.444 55.556 6:5 1.200
25\87 344.828 55.172 5:4 1.250
44\153 345.098 54.902 9:7 1.286
19\66 345.455 54.545 4:3 1.333 Supersoft 3L 18s
51\177 345.763 54.237 11:8 1.375
32\111 345.946 54.054 7:5 1.400
45\156 346.154 53.846 10:7 1.429
13\45 346.667 53.333 3:2 1.500 Soft 3L 18s
46\159 347.170 52.830 11:7 1.571
33\114 347.368 52.632 8:5 1.600
53\183 347.541 52.459 13:8 1.625
20\69 347.826 52.174 5:3 1.667 Semisoft 3L 18s
47\162 348.148 51.852 12:7 1.714
27\93 348.387 51.613 7:4 1.750
34\117 348.718 51.282 9:5 1.800
7\24 350.000 50.000 2:1 2.000 Basic 3L 18s
Scales with tunings softer than this are proper
29\99 351.515 48.485 9:4 2.250
22\75 352.000 48.000 7:3 2.333
37\126 352.381 47.619 12:5 2.400
15\51 352.941 47.059 5:2 2.500 Semihard 3L 18s
38\129 353.488 46.512 13:5 2.600
23\78 353.846 46.154 8:3 2.667
31\105 354.286 45.714 11:4 2.750
8\27 355.556 44.444 3:1 3.000 Hard 3L 18s
25\84 357.143 42.857 10:3 3.333
17\57 357.895 42.105 7:2 3.500
26\87 358.621 41.379 11:3 3.667
9\30 360.000 40.000 4:1 4.000 Superhard 3L 18s
19\63 361.905 38.095 9:2 4.500
10\33 363.636 36.364 5:1 5.000
11\36 366.667 33.333 6:1 6.000
1\3 400.000 0.000 1:0 → ∞ Collapsed 3L 18s