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
Ancestor's step ratio range	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¢)

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.

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

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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