18L 1s
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Scale structure
Step pattern
LLLLLLLLLLLLLLLLLLs
sLLLLLLLLLLLLLLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
1\19 to 1\18 (63.2¢ to 66.7¢)
Dark
17\18 to 18\19 (1133.3¢ to 1136.8¢)
TAMNAMS information
Descends from
1L 9s (antisinatonic)
Ancestor's step ratio range
9:1 to 10:1
Related MOS scales
Parent
1L 17s
Sister
1L 18s
Daughters
19L 18s, 18L 19s
Neutralized
17L 2s
2-Flought
37L 1s, 18L 20s
Equal tunings
Equalized (L:s = 1:1)
1\19 (63.2¢)
Supersoft (L:s = 4:3)
4\75 (64.0¢)
Soft (L:s = 3:2)
3\56 (64.3¢)
Semisoft (L:s = 5:3)
5\93 (64.5¢)
Basic (L:s = 2:1)
2\37 (64.9¢)
Semihard (L:s = 5:2)
5\92 (65.2¢)
Hard (L:s = 3:1)
3\55 (65.5¢)
Superhard (L:s = 4:1)
4\73 (65.8¢)
Collapsed (L:s = 1:0)
1\18 (66.7¢)
| ← 17L 1s | 18L 1s | 19L 1s → |
| ↙ 17L 2s | ↓ 18L 2s | 19L 2s ↘ |
┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║║║║║║║║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLLLLLLLLLLLLL
18L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 18 large steps and 1 small step, repeating every octave. 18L 1s is related to 1L 9s, expanding it by 9 tones. Generators that produce this scale range from 63.2¢ to 66.7¢, or from 1133.3¢ to 1136.8¢. Scales of this form are always proper because there is only one small step.
Modes
| UDP | Cyclic Order |
Step Pattern |
|---|---|---|
| 18|0 | 1 | LLLLLLLLLLLLLLLLLLs |
| 17|1 | 2 | LLLLLLLLLLLLLLLLLsL |
| 16|2 | 3 | LLLLLLLLLLLLLLLLsLL |
| 15|3 | 4 | LLLLLLLLLLLLLLLsLLL |
| 14|4 | 5 | LLLLLLLLLLLLLLsLLLL |
| 13|5 | 6 | LLLLLLLLLLLLLsLLLLL |
| 12|6 | 7 | LLLLLLLLLLLLsLLLLLL |
| 11|7 | 8 | LLLLLLLLLLLsLLLLLLL |
| 10|8 | 9 | LLLLLLLLLLsLLLLLLLL |
| 9|9 | 10 | LLLLLLLLLsLLLLLLLLL |
| 8|10 | 11 | LLLLLLLLsLLLLLLLLLL |
| 7|11 | 12 | LLLLLLLsLLLLLLLLLLL |
| 6|12 | 13 | LLLLLLsLLLLLLLLLLLL |
| 5|13 | 14 | LLLLLsLLLLLLLLLLLLL |
| 4|14 | 15 | LLLLsLLLLLLLLLLLLLL |
| 3|15 | 16 | LLLsLLLLLLLLLLLLLLL |
| 2|16 | 17 | LLsLLLLLLLLLLLLLLLL |
| 1|17 | 18 | LsLLLLLLLLLLLLLLLLL |
| 0|18 | 19 | sLLLLLLLLLLLLLLLLLL |
Scale tree
| Generator(edo) | Cents | Step Ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\19 | 63.158 | 1136.842 | 1:1 | 1.000 | Equalized 18L 1s | |||||
| 6\113 | 63.717 | 1136.283 | 6:5 | 1.200 | ||||||
| 5\94 | 63.830 | 1136.170 | 5:4 | 1.250 | ||||||
| 9\169 | 63.905 | 1136.095 | 9:7 | 1.286 | ||||||
| 4\75 | 64.000 | 1136.000 | 4:3 | 1.333 | Supersoft 18L 1s | |||||
| 11\206 | 64.078 | 1135.922 | 11:8 | 1.375 | ||||||
| 7\131 | 64.122 | 1135.878 | 7:5 | 1.400 | ||||||
| 10\187 | 64.171 | 1135.829 | 10:7 | 1.429 | ||||||
| 3\56 | 64.286 | 1135.714 | 3:2 | 1.500 | Soft 18L 1s | |||||
| 11\205 | 64.390 | 1135.610 | 11:7 | 1.571 | ||||||
| 8\149 | 64.430 | 1135.570 | 8:5 | 1.600 | ||||||
| 13\242 | 64.463 | 1135.537 | 13:8 | 1.625 | ||||||
| 5\93 | 64.516 | 1135.484 | 5:3 | 1.667 | Semisoft 18L 1s | |||||
| 12\223 | 64.574 | 1135.426 | 12:7 | 1.714 | ||||||
| 7\130 | 64.615 | 1135.385 | 7:4 | 1.750 | ||||||
| 9\167 | 64.671 | 1135.329 | 9:5 | 1.800 | ||||||
| 2\37 | 64.865 | 1135.135 | 2:1 | 2.000 | Basic 18L 1s | |||||
| 9\166 | 65.060 | 1134.940 | 9:4 | 2.250 | ||||||
| 7\129 | 65.116 | 1134.884 | 7:3 | 2.333 | ||||||
| 12\221 | 65.158 | 1134.842 | 12:5 | 2.400 | ||||||
| 5\92 | 65.217 | 1134.783 | 5:2 | 2.500 | Semihard 18L 1s | |||||
| 13\239 | 65.272 | 1134.728 | 13:5 | 2.600 | ||||||
| 8\147 | 65.306 | 1134.694 | 8:3 | 2.667 | ||||||
| 11\202 | 65.347 | 1134.653 | 11:4 | 2.750 | ||||||
| 3\55 | 65.455 | 1134.545 | 3:1 | 3.000 | Hard 18L 1s | |||||
| 10\183 | 65.574 | 1134.426 | 10:3 | 3.333 | ||||||
| 7\128 | 65.625 | 1134.375 | 7:2 | 3.500 | ||||||
| 11\201 | 65.672 | 1134.328 | 11:3 | 3.667 | ||||||
| 4\73 | 65.753 | 1134.247 | 4:1 | 4.000 | Superhard 18L 1s | |||||
| 9\164 | 65.854 | 1134.146 | 9:2 | 4.500 | ||||||
| 5\91 | 65.934 | 1134.066 | 5:1 | 5.000 | ||||||
| 6\109 | 66.055 | 1133.945 | 6:1 | 6.000 | ||||||
| 1\18 | 66.667 | 1133.333 | 1:0 | → ∞ | Collapsed 18L 1s | |||||