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.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

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 ¢

Generator chain

Generator chain of 18L 9s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.
4	Augmented 1-mosdegree	A1md	Augmented 4-mosdegree	A4md	Augmented 7-mosdegree	A7md	Augmented 10-mosdegree	A10md	Augmented 13-mosdegree	A13md	Augmented 16-mosdegree	A16md	Augmented 19-mosdegree	A19md	Augmented 22-mosdegree	A22md	Augmented 25-mosdegree	A25md
3	Augmented 0-mosdegree	A0md	Augmented 3-mosdegree	A3md	Augmented 6-mosdegree	A6md	Augmented 9-mosdegree	A9md	Augmented 12-mosdegree	A12md	Augmented 15-mosdegree	A15md	Augmented 18-mosdegree	A18md	Augmented 21-mosdegree	A21md	Augmented 24-mosdegree	A24md
2	Augmented 2-mosdegree	A2md	Augmented 5-mosdegree	A5md	Augmented 8-mosdegree	A8md	Augmented 11-mosdegree	A11md	Augmented 14-mosdegree	A14md	Augmented 17-mosdegree	A17md	Augmented 20-mosdegree	A20md	Augmented 23-mosdegree	A23md	Augmented 26-mosdegree	A26md
1	Perfect 1-mosdegree	P1md	Perfect 4-mosdegree	P4md	Perfect 7-mosdegree	P7md	Perfect 10-mosdegree	P10md	Perfect 13-mosdegree	P13md	Perfect 16-mosdegree	P16md	Perfect 19-mosdegree	P19md	Perfect 22-mosdegree	P22md	Perfect 25-mosdegree	P25md
0	Perfect 0-mosdegree Perfect 3-mosdegree	P0md P3md	Perfect 3-mosdegree Perfect 6-mosdegree	P3md P6md	Perfect 6-mosdegree Perfect 9-mosdegree	P6md P9md	Perfect 9-mosdegree Perfect 12-mosdegree	P9md P12md	Perfect 12-mosdegree Perfect 15-mosdegree	P12md P15md	Perfect 15-mosdegree Perfect 18-mosdegree	P15md P18md	Perfect 18-mosdegree Perfect 21-mosdegree	P18md P21md	Perfect 21-mosdegree Perfect 24-mosdegree	P21md P24md	Perfect 24-mosdegree Perfect 27-mosdegree	P24md P27md
−1	Perfect 2-mosdegree	P2md	Perfect 5-mosdegree	P5md	Perfect 8-mosdegree	P8md	Perfect 11-mosdegree	P11md	Perfect 14-mosdegree	P14md	Perfect 17-mosdegree	P17md	Perfect 20-mosdegree	P20md	Perfect 23-mosdegree	P23md	Perfect 26-mosdegree	P26md
−2	Diminished 1-mosdegree	d1md	Diminished 4-mosdegree	d4md	Diminished 7-mosdegree	d7md	Diminished 10-mosdegree	d10md	Diminished 13-mosdegree	d13md	Diminished 16-mosdegree	d16md	Diminished 19-mosdegree	d19md	Diminished 22-mosdegree	d22md	Diminished 25-mosdegree	d25md
−3	Diminished 3-mosdegree	d3md	Diminished 6-mosdegree	d6md	Diminished 9-mosdegree	d9md	Diminished 12-mosdegree	d12md	Diminished 15-mosdegree	d15md	Diminished 18-mosdegree	d18md	Diminished 21-mosdegree	d21md	Diminished 24-mosdegree	d24md	Diminished 27-mosdegree	d27md
−4	Diminished 2-mosdegree	d2md	Diminished 5-mosdegree	d5md	Diminished 8-mosdegree	d8md	Diminished 11-mosdegree	d11md	Diminished 14-mosdegree	d14md	Diminished 17-mosdegree	d17md	Diminished 20-mosdegree	d20md	Diminished 23-mosdegree	d23md	Diminished 26-mosdegree	d26md

Modes

Scale degrees of the modes of 18L 9s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27
18|0(9)	1	LLsLLsLLsLLsLLsLLsLLsLLsLLs	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.
9|9(9)	2	LsLLsLLsLLsLLsLLsLLsLLsLLsL	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.
0|18(9)	3	sLLsLLsLLsLLsLLsLLsLLsLLsLL	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.

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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