3L 18s

3L 18s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 18 small steps, with a period of 1 large step and 6 small steps that repeats every 400.0 ¢, or 3 times every octave. 3L 18s is related to 3L 6s, expanding it by 12 tones. Generators that produce this scale range from 342.9 ¢ to 400 ¢, or from 0 ¢ to 57.1 ¢.

↖ 2L 17s	↑ 3L 17s	4L 17s ↗
← 2L 18s	3L 18s	4L 18s →
↙ 2L 19s	↓ 3L 19s	4L 19s ↘

Scale structure
Step pattern	LssssssLssssssLssssss ssssssLssssssLssssssL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	6\21 to 1\3 (342.9 ¢ to 400.0 ¢)
Dark	0\3 to 1\21 (0.0 ¢ to 57.1 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	5:1 to 1:0
Related MOS scales
Parent	3L 15s
Sister	18L 3s
Daughters	21L 3s, 3L 21s
Neutralized	6L 15s
2-Flought	24L 18s, 3L 39s
Equal tunings
Equalized (L:s = 1:1)	6\21 (342.9 ¢)
Supersoft (L:s = 4:3)	19\66 (345.5 ¢)
Soft (L:s = 3:2)	13\45 (346.7 ¢)
Semisoft (L:s = 5:3)	20\69 (347.8 ¢)
Basic (L:s = 2:1)	7\24 (350.0 ¢)
Semihard (L:s = 5:2)	15\51 (352.9 ¢)
Hard (L:s = 3:1)	8\27 (355.6 ¢)
Superhard (L:s = 4:1)	9\30 (360.0 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)
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Modes

Modes of 3L 18s

UDP	Cyclic order	Step pattern
18|0(3)	1	LssssssLssssssLssssss
15|3(3)	7	sLssssssLssssssLsssss
12|6(3)	6	ssLssssssLssssssLssss
9|9(3)	5	sssLssssssLssssssLsss
6|12(3)	4	ssssLssssssLssssssLss
3|15(3)	3	sssssLssssssLssssssLs
0|18(3)	2	ssssssLssssssLssssssL

Intervals

Intervals of 3L 18s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 57.1 ¢
	Augmented 1-mosstep	A1ms	L	57.1 ¢ to 400.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 114.3 ¢
	Major 2-mosstep	M2ms	L + s	114.3 ¢ to 400.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 171.4 ¢
	Major 3-mosstep	M3ms	L + 2s	171.4 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 228.6 ¢
	Major 4-mosstep	M4ms	L + 3s	228.6 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 285.7 ¢
	Major 5-mosstep	M5ms	L + 4s	285.7 ¢ to 400.0 ¢
6-mosstep	Diminished 6-mosstep	d6ms	6s	0.0 ¢ to 342.9 ¢
	Perfect 6-mosstep	P6ms	L + 5s	342.9 ¢ to 400.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	L + 6s	400.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	L + 7s	400.0 ¢ to 457.1 ¢
	Augmented 8-mosstep	A8ms	2L + 6s	457.1 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	400.0 ¢ to 514.3 ¢
	Major 9-mosstep	M9ms	2L + 7s	514.3 ¢ to 800.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	400.0 ¢ to 571.4 ¢
	Major 10-mosstep	M10ms	2L + 8s	571.4 ¢ to 800.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	400.0 ¢ to 628.6 ¢
	Major 11-mosstep	M11ms	2L + 9s	628.6 ¢ to 800.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	400.0 ¢ to 685.7 ¢
	Major 12-mosstep	M12ms	2L + 10s	685.7 ¢ to 800.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	L + 12s	400.0 ¢ to 742.9 ¢
	Perfect 13-mosstep	P13ms	2L + 11s	742.9 ¢ to 800.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	2L + 12s	800.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	2L + 13s	800.0 ¢ to 857.1 ¢
	Augmented 15-mosstep	A15ms	3L + 12s	857.1 ¢ to 1200.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	2L + 14s	800.0 ¢ to 914.3 ¢
	Major 16-mosstep	M16ms	3L + 13s	914.3 ¢ to 1200.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	2L + 15s	800.0 ¢ to 971.4 ¢
	Major 17-mosstep	M17ms	3L + 14s	971.4 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	2L + 16s	800.0 ¢ to 1028.6 ¢
	Major 18-mosstep	M18ms	3L + 15s	1028.6 ¢ to 1200.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	2L + 17s	800.0 ¢ to 1085.7 ¢
	Major 19-mosstep	M19ms	3L + 16s	1085.7 ¢ to 1200.0 ¢
20-mosstep	Diminished 20-mosstep	d20ms	2L + 18s	800.0 ¢ to 1142.9 ¢
	Perfect 20-mosstep	P20ms	3L + 17s	1142.9 ¢ to 1200.0 ¢
21-mosstep	Perfect 21-mosstep	P21ms	3L + 18s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 3L 18s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
6\21						342.857	57.143	1:1	1.000	Equalized 3L 18s
					31\108	344.444	55.556	6:5	1.200
				25\87		344.828	55.172	5:4	1.250
					44\153	345.098	54.902	9:7	1.286
			19\66			345.455	54.545	4:3	1.333	Supersoft 3L 18s
					51\177	345.763	54.237	11:8	1.375
				32\111		345.946	54.054	7:5	1.400
					45\156	346.154	53.846	10:7	1.429
		13\45				346.667	53.333	3:2	1.500	Soft 3L 18s
					46\159	347.170	52.830	11:7	1.571
				33\114		347.368	52.632	8:5	1.600
					53\183	347.541	52.459	13:8	1.625
			20\69			347.826	52.174	5:3	1.667	Semisoft 3L 18s
					47\162	348.148	51.852	12:7	1.714
				27\93		348.387	51.613	7:4	1.750
					34\117	348.718	51.282	9:5	1.800
	7\24					350.000	50.000	2:1	2.000	Basic 3L 18s Scales with tunings softer than this are proper
					29\99	351.515	48.485	9:4	2.250
				22\75		352.000	48.000	7:3	2.333
					37\126	352.381	47.619	12:5	2.400
			15\51			352.941	47.059	5:2	2.500	Semihard 3L 18s
					38\129	353.488	46.512	13:5	2.600
				23\78		353.846	46.154	8:3	2.667
					31\105	354.286	45.714	11:4	2.750
		8\27				355.556	44.444	3:1	3.000	Hard 3L 18s
					25\84	357.143	42.857	10:3	3.333
				17\57		357.895	42.105	7:2	3.500
					26\87	358.621	41.379	11:3	3.667
			9\30			360.000	40.000	4:1	4.000	Superhard 3L 18s
					19\63	361.905	38.095	9:2	4.500
				10\33		363.636	36.364	5:1	5.000
					11\36	366.667	33.333	6:1	6.000
1\3						400.000	0.000	1:0	→ ∞	Collapsed 3L 18s

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