3L 18s

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↖ 2L 17s ↑ 3L 17s 4L 17s ↗
← 2L 18s 3L 18s 4L 18s →
↙ 2L 19s ↓ 3L 19s 4L 19s ↘ 
┌╥┬┬┬┬┬┬╥┬┬┬┬┬┬╥┬┬┬┬┬┬┐
│║││││││║││││││║│││││││
│││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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

Intervals

Intervals of 3L 18s
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 57.1 ¢
Augmented 1-mosstep A1ms L 57.1 ¢ to 400.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 114.3 ¢
Major 2-mosstep M2ms L + s 114.3 ¢ to 400.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 171.4 ¢
Major 3-mosstep M3ms L + 2s 171.4 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 228.6 ¢
Major 4-mosstep M4ms L + 3s 228.6 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 285.7 ¢
Major 5-mosstep M5ms L + 4s 285.7 ¢ to 400.0 ¢
6-mosstep Diminished 6-mosstep d6ms 6s 0.0 ¢ to 342.9 ¢
Perfect 6-mosstep P6ms L + 5s 342.9 ¢ to 400.0 ¢
7-mosstep Perfect 7-mosstep P7ms L + 6s 400.0 ¢
8-mosstep Perfect 8-mosstep P8ms L + 7s 400.0 ¢ to 457.1 ¢
Augmented 8-mosstep A8ms 2L + 6s 457.1 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 400.0 ¢ to 514.3 ¢
Major 9-mosstep M9ms 2L + 7s 514.3 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 400.0 ¢ to 571.4 ¢
Major 10-mosstep M10ms 2L + 8s 571.4 ¢ to 800.0 ¢
11-mosstep Minor 11-mosstep m11ms L + 10s 400.0 ¢ to 628.6 ¢
Major 11-mosstep M11ms 2L + 9s 628.6 ¢ to 800.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 400.0 ¢ to 685.7 ¢
Major 12-mosstep M12ms 2L + 10s 685.7 ¢ to 800.0 ¢
13-mosstep Diminished 13-mosstep d13ms L + 12s 400.0 ¢ to 742.9 ¢
Perfect 13-mosstep P13ms 2L + 11s 742.9 ¢ to 800.0 ¢
14-mosstep Perfect 14-mosstep P14ms 2L + 12s 800.0 ¢
15-mosstep Perfect 15-mosstep P15ms 2L + 13s 800.0 ¢ to 857.1 ¢
Augmented 15-mosstep A15ms 3L + 12s 857.1 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 2L + 14s 800.0 ¢ to 914.3 ¢
Major 16-mosstep M16ms 3L + 13s 914.3 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms 2L + 15s 800.0 ¢ to 971.4 ¢
Major 17-mosstep M17ms 3L + 14s 971.4 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms 2L + 16s 800.0 ¢ to 1028.6 ¢
Major 18-mosstep M18ms 3L + 15s 1028.6 ¢ to 1200.0 ¢
19-mosstep Minor 19-mosstep m19ms 2L + 17s 800.0 ¢ to 1085.7 ¢
Major 19-mosstep M19ms 3L + 16s 1085.7 ¢ to 1200.0 ¢
20-mosstep Diminished 20-mosstep d20ms 2L + 18s 800.0 ¢ to 1142.9 ¢
Perfect 20-mosstep P20ms 3L + 17s 1142.9 ¢ to 1200.0 ¢
21-mosstep Perfect 21-mosstep P21ms 3L + 18s 1200.0 ¢

Scale tree

Icon-Deprecated.png Scale tree is deprecated. Please use Template: MOS tuning spectrum instead.
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


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


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