18L 9s

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↖17L 8s ↑18L 8s 19L 8s↗
←17L 9s18L 9s 19L 9s→
↙17L 10s ↓18L 10s 19L 10s↘
┌╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬┐
│║║│║║│║║│║║│║║│║║│║║│║║│║║││
│││││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLsLLsLLsLLsLLsLLsLLs
sLLsLLsLLsLLsLLsLLsLLsLLsLL
Equave 2/1 (1200.0¢)
Period 1\9 (133.3¢)
Step size ranges
Large 1\27 to 1\18 (44.4¢ to 66.7¢)
Small 0\18 to 1\27 (0.0¢ to 44.4¢)
Generator size
Bright 1\27 to 1\18 (44.4¢ to 66.7¢)
Dark 1\18 to 2\27 (66.7¢ to 88.9¢)
TAMNAMS information
Descends from 9L 9s
Related MOS scales
Parent 9L 9s
Sister 9L 18s
Daughters 27L 18s
18L 27s
Equal tunings
Equalized (L:s = 1:1) 1\27 (44.4¢)
Supersoft (L:s = 4:3) 4\99 (48.5¢)
Soft (L:s = 3:2) 3\72 (50.0¢)
Semisoft (L:s = 5:3) 5\117 (51.3¢)
Basic (L:s = 2:1) 2\45 (53.3¢)
Semihard (L:s = 5:2) 5\108 (55.6¢)
Hard (L:s = 3:1) 3\63 (57.1¢)
Superhard (L:s = 4:1) 4\81 (59.3¢)
Collapsed (L:s = 1:0) 1\18 (66.7¢)

18L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 18 large steps and 9 small steps, with a period of 2 large steps and 1 small step that repeats every 133.3¢, or 9 times every octave. 18L 9s is a child scale of 9L 9s, expanding it by 9 tones. Generators that produce this scale range from 44.4¢ to 66.7¢, or from 66.7¢ to 88.9¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.


Scale tree and tuning spectrum of 18L 9s
Generator (in steps of edo) Cents Step ratio Comments
(Every true-MOS tuning produces a proper scale)
Bright Dark L:s Hardness
1\27 44.444 88.889 1:1 1.000 Equalized 18L 9s
6\153 47.059 86.275 6:5 1.200
5\126 47.619 85.714 5:4 1.250
9\225 48.000 85.333 9:7 1.286
4\99 48.485 84.848 4:3 1.333 Supersoft 18L 9s
11\270 48.889 84.444 11:8 1.375
7\171 49.123 84.211 7:5 1.400
10\243 49.383 83.951 10:7 1.429
3\72 50.000 83.333 3:2 1.500 Soft 18L 9s
11\261 50.575 82.759 11:7 1.571
8\189 50.794 82.540 8:5 1.600
13\306 50.980 82.353 13:8 1.625
5\117 51.282 82.051 5:3 1.667 Semisoft 18L 9s
12\279 51.613 81.720 12:7 1.714
7\162 51.852 81.481 7:4 1.750
9\207 52.174 81.159 9:5 1.800
2\45 53.333 80.000 2:1 2.000 Basic 18L 9s
9\198 54.545 78.788 9:4 2.250
7\153 54.902 78.431 7:3 2.333
12\261 55.172 78.161 12:5 2.400
5\108 55.556 77.778 5:2 2.500 Semihard 18L 9s
13\279 55.914 77.419 13:5 2.600
8\171 56.140 77.193 8:3 2.667
11\234 56.410 76.923 11:4 2.750
3\63 57.143 76.190 3:1 3.000 Hard 18L 9s
10\207 57.971 75.362 10:3 3.333
7\144 58.333 75.000 7:2 3.500
11\225 58.667 74.667 11:3 3.667
4\81 59.259 74.074 4:1 4.000 Superhard 18L 9s
9\180 60.000 73.333 9:2 4.500
5\99 60.606 72.727 5:1 5.000
6\117 61.538 71.795 6:1 6.000
1\18 66.667 66.667 1:0 → ∞ Collapsed 18L 9s

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