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