3L 15s

↖ 2L 14s	↑ 3L 14s	4L 14s ↗
← 2L 15s	3L 15s	4L 15s →
↙ 2L 16s	↓ 3L 16s	4L 16s ↘

┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┐ │║│││││║│││││║││││││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsssssLsssssLsssss sssssLsssssLsssssL
Equave	2/1 (1200.0¢)
Period	1\3 (400.0¢)
Generator size
Bright	5\18 to 1\3 (333.3¢ to 400.0¢)
Dark	0\3 to 1\18 (0.0¢ to 66.7¢)
TAMNAMS information
Descends from	3L 6s (tcherepnin)
Ancestor's step ratio range	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	3L 12s
Sister	15L 3s
Daughters	18L 3s, 3L 18s
Neutralized	6L 12s
2-Flought	21L 15s, 3L 33s
Equal tunings
Equalized (L:s = 1:1)	5\18 (333.3¢)
Supersoft (L:s = 4:3)	16\57 (336.8¢)
Soft (L:s = 3:2)	11\39 (338.5¢)
Semisoft (L:s = 5:3)	17\60 (340.0¢)
Basic (L:s = 2:1)	6\21 (342.9¢)
Semihard (L:s = 5:2)	13\45 (346.7¢)
Hard (L:s = 3:1)	7\24 (350.0¢)
Superhard (L:s = 4:1)	8\27 (355.6¢)
Collapsed (L:s = 1:0)	1\3 (400.0¢)

3L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 15 small steps, with a period of 1 large step and 5 small steps that repeats every 400.0¢, or 3 times every octave. 3L 15s is a great-grandchild scale of 3L 6s, expanding it by 9 tones. Generators that produce this scale range from 333.3¢ to 400¢, or from 0¢ to 66.7¢.

Modes

Modes of 3L 15s

UDP	Cyclic order	Step pattern
15|0(3)	1	LsssssLsssssLsssss
12|3(3)	6	sLsssssLsssssLssss
9|6(3)	5	ssLsssssLsssssLsss
6|9(3)	4	sssLsssssLsssssLss
3|12(3)	3	ssssLsssssLsssssLs
0|15(3)	2	sssssLsssssLsssssL

Intervals

Intervals of 3L 15s

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 66.7¢
	Augmented 1-mosstep	A1ms	L	66.7¢ to 400.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 133.3¢
	Major 2-mosstep	M2ms	L + s	133.3¢ to 400.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 200.0¢
	Major 3-mosstep	M3ms	L + 2s	200.0¢ to 400.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 266.7¢
	Major 4-mosstep	M4ms	L + 3s	266.7¢ to 400.0¢
5-mosstep	Diminished 5-mosstep	d5ms	5s	0.0¢ to 333.3¢
	Perfect 5-mosstep	P5ms	L + 4s	333.3¢ to 400.0¢
6-mosstep	Perfect 6-mosstep	P6ms	L + 5s	400.0¢
7-mosstep	Perfect 7-mosstep	P7ms	L + 6s	400.0¢ to 466.7¢
	Augmented 7-mosstep	A7ms	2L + 5s	466.7¢ to 800.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	400.0¢ to 533.3¢
	Major 8-mosstep	M8ms	2L + 6s	533.3¢ to 800.0¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	400.0¢ to 600.0¢
	Major 9-mosstep	M9ms	2L + 7s	600.0¢ to 800.0¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	400.0¢ to 666.7¢
	Major 10-mosstep	M10ms	2L + 8s	666.7¢ to 800.0¢
11-mosstep	Diminished 11-mosstep	d11ms	L + 10s	400.0¢ to 733.3¢
	Perfect 11-mosstep	P11ms	2L + 9s	733.3¢ to 800.0¢
12-mosstep	Perfect 12-mosstep	P12ms	2L + 10s	800.0¢
13-mosstep	Perfect 13-mosstep	P13ms	2L + 11s	800.0¢ to 866.7¢
	Augmented 13-mosstep	A13ms	3L + 10s	866.7¢ to 1200.0¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	800.0¢ to 933.3¢
	Major 14-mosstep	M14ms	3L + 11s	933.3¢ to 1200.0¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	800.0¢ to 1000.0¢
	Major 15-mosstep	M15ms	3L + 12s	1000.0¢ to 1200.0¢
16-mosstep	Minor 16-mosstep	m16ms	2L + 14s	800.0¢ to 1066.7¢
	Major 16-mosstep	M16ms	3L + 13s	1066.7¢ to 1200.0¢
17-mosstep	Diminished 17-mosstep	d17ms	2L + 15s	800.0¢ to 1133.3¢
	Perfect 17-mosstep	P17ms	3L + 14s	1133.3¢ to 1200.0¢
18-mosstep	Perfect 18-mosstep	P18ms	3L + 15s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 3L 15s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\18						333.333	66.667	1:1	1.000	Equalized 3L 15s
					26\93	335.484	64.516	6:5	1.200
				21\75		336.000	64.000	5:4	1.250
					37\132	336.364	63.636	9:7	1.286
			16\57			336.842	63.158	4:3	1.333	Supersoft 3L 15s
					43\153	337.255	62.745	11:8	1.375
				27\96		337.500	62.500	7:5	1.400
					38\135	337.778	62.222	10:7	1.429
		11\39				338.462	61.538	3:2	1.500	Soft 3L 15s
					39\138	339.130	60.870	11:7	1.571
				28\99		339.394	60.606	8:5	1.600
					45\159	339.623	60.377	13:8	1.625
			17\60			340.000	60.000	5:3	1.667	Semisoft 3L 15s
					40\141	340.426	59.574	12:7	1.714
				23\81		340.741	59.259	7:4	1.750
					29\102	341.176	58.824	9:5	1.800
	6\21					342.857	57.143	2:1	2.000	Basic 3L 15s Scales with tunings softer than this are proper
					25\87	344.828	55.172	9:4	2.250
				19\66		345.455	54.545	7:3	2.333
					32\111	345.946	54.054	12:5	2.400
			13\45			346.667	53.333	5:2	2.500	Semihard 3L 15s
					33\114	347.368	52.632	13:5	2.600
				20\69		347.826	52.174	8:3	2.667
					27\93	348.387	51.613	11:4	2.750
		7\24				350.000	50.000	3:1	3.000	Hard 3L 15s
					22\75	352.000	48.000	10:3	3.333
				15\51		352.941	47.059	7:2	3.500
					23\78	353.846	46.154	11:3	3.667
			8\27			355.556	44.444	4:1	4.000	Superhard 3L 15s
					17\57	357.895	42.105	9:2	4.500
				9\30		360.000	40.000	5:1	5.000
					10\33	363.636	36.364	6:1	6.000
1\3						400.000	0.000	1:0	→ ∞	Collapsed 3L 15s

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