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
Related to	3L 6s (tcherepnin)
With tunings	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

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