18L 9s

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.

↖ 17L 8s	↑ 18L 8s	19L 8s ↗
← 17L 9s	18L 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 ¢)
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
Related to	9L 9s
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	9L 9s
Sister	9L 18s
Daughters	27L 18s, 18L 27s
Neutralized	9L 18s
2-Flought	45L 9s, 18L 36s
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 ¢)
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This MOS scale is associated with ennealimmal temperament.

Modes

Modes of 18L 9s

UDP	Cyclic order	Step pattern
18|0(9)	1	LLsLLsLLsLLsLLsLLsLLsLLsLLs
9|9(9)	2	LsLLsLLsLLsLLsLLsLLsLLsLLsL
0|18(9)	3	sLLsLLsLLsLLsLLsLLsLLsLLsLL

Intervals

Intervals of 18L 9s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 44.4 ¢
	Perfect 1-mosstep	P1ms	L	44.4 ¢ to 66.7 ¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	66.7 ¢ to 88.9 ¢
	Augmented 2-mosstep	A2ms	2L	88.9 ¢ to 133.3 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	133.3 ¢
4-mosstep	Diminished 4-mosstep	d4ms	2L + 2s	133.3 ¢ to 177.8 ¢
	Perfect 4-mosstep	P4ms	3L + s	177.8 ¢ to 200.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	3L + 2s	200.0 ¢ to 222.2 ¢
	Augmented 5-mosstep	A5ms	4L + s	222.2 ¢ to 266.7 ¢
6-mosstep	Perfect 6-mosstep	P6ms	4L + 2s	266.7 ¢
7-mosstep	Diminished 7-mosstep	d7ms	4L + 3s	266.7 ¢ to 311.1 ¢
	Perfect 7-mosstep	P7ms	5L + 2s	311.1 ¢ to 333.3 ¢
8-mosstep	Perfect 8-mosstep	P8ms	5L + 3s	333.3 ¢ to 355.6 ¢
	Augmented 8-mosstep	A8ms	6L + 2s	355.6 ¢ to 400.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	6L + 3s	400.0 ¢
10-mosstep	Diminished 10-mosstep	d10ms	6L + 4s	400.0 ¢ to 444.4 ¢
	Perfect 10-mosstep	P10ms	7L + 3s	444.4 ¢ to 466.7 ¢
11-mosstep	Perfect 11-mosstep	P11ms	7L + 4s	466.7 ¢ to 488.9 ¢
	Augmented 11-mosstep	A11ms	8L + 3s	488.9 ¢ to 533.3 ¢
12-mosstep	Perfect 12-mosstep	P12ms	8L + 4s	533.3 ¢
13-mosstep	Diminished 13-mosstep	d13ms	8L + 5s	533.3 ¢ to 577.8 ¢
	Perfect 13-mosstep	P13ms	9L + 4s	577.8 ¢ to 600.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	9L + 5s	600.0 ¢ to 622.2 ¢
	Augmented 14-mosstep	A14ms	10L + 4s	622.2 ¢ to 666.7 ¢
15-mosstep	Perfect 15-mosstep	P15ms	10L + 5s	666.7 ¢
16-mosstep	Diminished 16-mosstep	d16ms	10L + 6s	666.7 ¢ to 711.1 ¢
	Perfect 16-mosstep	P16ms	11L + 5s	711.1 ¢ to 733.3 ¢
17-mosstep	Perfect 17-mosstep	P17ms	11L + 6s	733.3 ¢ to 755.6 ¢
	Augmented 17-mosstep	A17ms	12L + 5s	755.6 ¢ to 800.0 ¢
18-mosstep	Perfect 18-mosstep	P18ms	12L + 6s	800.0 ¢
19-mosstep	Diminished 19-mosstep	d19ms	12L + 7s	800.0 ¢ to 844.4 ¢
	Perfect 19-mosstep	P19ms	13L + 6s	844.4 ¢ to 866.7 ¢
20-mosstep	Perfect 20-mosstep	P20ms	13L + 7s	866.7 ¢ to 888.9 ¢
	Augmented 20-mosstep	A20ms	14L + 6s	888.9 ¢ to 933.3 ¢
21-mosstep	Perfect 21-mosstep	P21ms	14L + 7s	933.3 ¢
22-mosstep	Diminished 22-mosstep	d22ms	14L + 8s	933.3 ¢ to 977.8 ¢
	Perfect 22-mosstep	P22ms	15L + 7s	977.8 ¢ to 1000.0 ¢
23-mosstep	Perfect 23-mosstep	P23ms	15L + 8s	1000.0 ¢ to 1022.2 ¢
	Augmented 23-mosstep	A23ms	16L + 7s	1022.2 ¢ to 1066.7 ¢
24-mosstep	Perfect 24-mosstep	P24ms	16L + 8s	1066.7 ¢
25-mosstep	Diminished 25-mosstep	d25ms	16L + 9s	1066.7 ¢ to 1111.1 ¢
	Perfect 25-mosstep	P25ms	17L + 8s	1111.1 ¢ to 1133.3 ¢
26-mosstep	Perfect 26-mosstep	P26ms	17L + 9s	1133.3 ¢ to 1155.6 ¢
	Augmented 26-mosstep	A26ms	18L + 8s	1155.6 ¢ to 1200.0 ¢
27-mosstep	Perfect 27-mosstep	P27ms	18L + 9s	1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: 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 18L 9s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						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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