18L 9s

↖17L 8s	↑18L 8s	19L 8s↗
←17L 9s	18L 9s	19L 9s→
↙17L 10s	↓18L 10s	19L 10s↘

┌╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬┐
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LLsLLsLLsLLsLLsLLsLLsLLsLLs
sLLsLLsLLsLLsLLsLLsLLsLLsLL

Equave

2/1 (1200.0¢)

Period

1\9 (133.3¢)

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

Required step ratio range

1:1 to 2:1 (soft-of-basic)

Related MOS scales

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^(edo)						Cents		Step Ratio		Comments^{(always proper)}
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments^{(always proper)}
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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18L 9s

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