18L 1s

← 17L 1s	18L 1s	19L 1s →
↙ 17L 2s	↓ 18L 2s	19L 2s ↘

┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║║║║║║║║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLLLLLLLLLLLLs sLLLLLLLLLLLLLLLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	1\19 to 1\18 (63.2¢ to 66.7¢)
Dark	17\18 to 18\19 (1133.3¢ to 1136.8¢)
TAMNAMS information
Descends from	1L 9s (antisinatonic)
Ancestor's step ratio range	9:1 to 10:1
Related MOS scales
Parent	1L 17s
Sister	1L 18s
Daughters	19L 18s, 18L 19s
Neutralized	17L 2s
2-Flought	37L 1s, 18L 20s
Equal tunings
Equalized (L:s = 1:1)	1\19 (63.2¢)
Supersoft (L:s = 4:3)	4\75 (64.0¢)
Soft (L:s = 3:2)	3\56 (64.3¢)
Semisoft (L:s = 5:3)	5\93 (64.5¢)
Basic (L:s = 2:1)	2\37 (64.9¢)
Semihard (L:s = 5:2)	5\92 (65.2¢)
Hard (L:s = 3:1)	3\55 (65.5¢)
Superhard (L:s = 4:1)	4\73 (65.8¢)
Collapsed (L:s = 1:0)	1\18 (66.7¢)

18L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 18 large steps and 1 small step, repeating every octave. 18L 1s is related to 1L 9s, expanding it by 9 tones. Generators that produce this scale range from 63.2¢ to 66.7¢, or from 1133.3¢ to 1136.8¢. Scales of this form are always proper because there is only one small step.

Modes

Modes of 18L 1s

UDP	Cyclic order	Step pattern
18|0	1	LLLLLLLLLLLLLLLLLLs
17|1	2	LLLLLLLLLLLLLLLLLsL
16|2	3	LLLLLLLLLLLLLLLLsLL
15|3	4	LLLLLLLLLLLLLLLsLLL
14|4	5	LLLLLLLLLLLLLLsLLLL
13|5	6	LLLLLLLLLLLLLsLLLLL
12|6	7	LLLLLLLLLLLLsLLLLLL
11|7	8	LLLLLLLLLLLsLLLLLLL
10|8	9	LLLLLLLLLLsLLLLLLLL
9|9	10	LLLLLLLLLsLLLLLLLLL
8|10	11	LLLLLLLLsLLLLLLLLLL
7|11	12	LLLLLLLsLLLLLLLLLLL
6|12	13	LLLLLLsLLLLLLLLLLLL
5|13	14	LLLLLsLLLLLLLLLLLLL
4|14	15	LLLLsLLLLLLLLLLLLLL
3|15	16	LLLsLLLLLLLLLLLLLLL
2|16	17	LLsLLLLLLLLLLLLLLLL
1|17	18	LsLLLLLLLLLLLLLLLLL
0|18	19	sLLLLLLLLLLLLLLLLLL

Intervals

Intervals of 18L 1s

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 63.2¢
	Perfect 1-mosstep	P1ms	L	63.2¢ to 66.7¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	66.7¢ to 126.3¢
	Major 2-mosstep	M2ms	2L	126.3¢ to 133.3¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	133.3¢ to 189.5¢
	Major 3-mosstep	M3ms	3L	189.5¢ to 200.0¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	200.0¢ to 252.6¢
	Major 4-mosstep	M4ms	4L	252.6¢ to 266.7¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	266.7¢ to 315.8¢
	Major 5-mosstep	M5ms	5L	315.8¢ to 333.3¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	333.3¢ to 378.9¢
	Major 6-mosstep	M6ms	6L	378.9¢ to 400.0¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	400.0¢ to 442.1¢
	Major 7-mosstep	M7ms	7L	442.1¢ to 466.7¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	466.7¢ to 505.3¢
	Major 8-mosstep	M8ms	8L	505.3¢ to 533.3¢
9-mosstep	Minor 9-mosstep	m9ms	8L + s	533.3¢ to 568.4¢
	Major 9-mosstep	M9ms	9L	568.4¢ to 600.0¢
10-mosstep	Minor 10-mosstep	m10ms	9L + s	600.0¢ to 631.6¢
	Major 10-mosstep	M10ms	10L	631.6¢ to 666.7¢
11-mosstep	Minor 11-mosstep	m11ms	10L + s	666.7¢ to 694.7¢
	Major 11-mosstep	M11ms	11L	694.7¢ to 733.3¢
12-mosstep	Minor 12-mosstep	m12ms	11L + s	733.3¢ to 757.9¢
	Major 12-mosstep	M12ms	12L	757.9¢ to 800.0¢
13-mosstep	Minor 13-mosstep	m13ms	12L + s	800.0¢ to 821.1¢
	Major 13-mosstep	M13ms	13L	821.1¢ to 866.7¢
14-mosstep	Minor 14-mosstep	m14ms	13L + s	866.7¢ to 884.2¢
	Major 14-mosstep	M14ms	14L	884.2¢ to 933.3¢
15-mosstep	Minor 15-mosstep	m15ms	14L + s	933.3¢ to 947.4¢
	Major 15-mosstep	M15ms	15L	947.4¢ to 1000.0¢
16-mosstep	Minor 16-mosstep	m16ms	15L + s	1000.0¢ to 1010.5¢
	Major 16-mosstep	M16ms	16L	1010.5¢ to 1066.7¢
17-mosstep	Minor 17-mosstep	m17ms	16L + s	1066.7¢ to 1073.7¢
	Major 17-mosstep	M17ms	17L	1073.7¢ to 1133.3¢
18-mosstep	Perfect 18-mosstep	P18ms	17L + s	1133.3¢ to 1136.8¢
	Augmented 18-mosstep	A18ms	18L	1136.8¢ to 1200.0¢
19-mosstep	Perfect 19-mosstep	P19ms	18L + s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 18L 1s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\19						63.158	1136.842	1:1	1.000	Equalized 18L 1s
					6\113	63.717	1136.283	6:5	1.200
				5\94		63.830	1136.170	5:4	1.250
					9\169	63.905	1136.095	9:7	1.286
			4\75			64.000	1136.000	4:3	1.333	Supersoft 18L 1s
					11\206	64.078	1135.922	11:8	1.375
				7\131		64.122	1135.878	7:5	1.400
					10\187	64.171	1135.829	10:7	1.429
		3\56				64.286	1135.714	3:2	1.500	Soft 18L 1s
					11\205	64.390	1135.610	11:7	1.571
				8\149		64.430	1135.570	8:5	1.600
					13\242	64.463	1135.537	13:8	1.625
			5\93			64.516	1135.484	5:3	1.667	Semisoft 18L 1s
					12\223	64.574	1135.426	12:7	1.714
				7\130		64.615	1135.385	7:4	1.750
					9\167	64.671	1135.329	9:5	1.800
	2\37					64.865	1135.135	2:1	2.000	Basic 18L 1s
					9\166	65.060	1134.940	9:4	2.250
				7\129		65.116	1134.884	7:3	2.333
					12\221	65.158	1134.842	12:5	2.400
			5\92			65.217	1134.783	5:2	2.500	Semihard 18L 1s
					13\239	65.272	1134.728	13:5	2.600
				8\147		65.306	1134.694	8:3	2.667
					11\202	65.347	1134.653	11:4	2.750
		3\55				65.455	1134.545	3:1	3.000	Hard 18L 1s
					10\183	65.574	1134.426	10:3	3.333
				7\128		65.625	1134.375	7:2	3.500
					11\201	65.672	1134.328	11:3	3.667
			4\73			65.753	1134.247	4:1	4.000	Superhard 18L 1s
					9\164	65.854	1134.146	9:2	4.500
				5\91		65.934	1134.066	5:1	5.000
					6\109	66.055	1133.945	6:1	6.000
1\18						66.667	1133.333	1:0	→ ∞	Collapsed 18L 1s

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