15L 6s

↖ 14L 5s	↑ 15L 5s	16L 5s ↗
← 14L 6s	15L 6s	16L 6s →
↙ 14L 7s	↓ 15L 7s	16L 7s ↘

┌╥╥╥┬╥╥┬╥╥╥┬╥╥┬╥╥╥┬╥╥┬┐ │║║║│║║│║║║│║║│║║║│║║││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLsLLsLLLsLLsLLLsLLs sLLsLLLsLLsLLLsLLsLLL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	4\21 to 3\15 (228.6 ¢ to 240.0 ¢)
Dark	2\15 to 3\21 (160.0 ¢ to 171.4 ¢)
TAMNAMS information
Related to	6L 3s (hyrulic)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	6L 9s
Sister	6L 15s
Daughters	21L 15s, 15L 21s
Neutralized	9L 12s
2-Flought	36L 6s, 15L 27s
Equal tunings
Equalized (L:s = 1:1)	4\21 (228.6 ¢)
Supersoft (L:s = 4:3)	15\78 (230.8 ¢)
Soft (L:s = 3:2)	11\57 (231.6 ¢)
Semisoft (L:s = 5:3)	18\93 (232.3 ¢)
Basic (L:s = 2:1)	7\36 (233.3 ¢)
Semihard (L:s = 5:2)	17\87 (234.5 ¢)
Hard (L:s = 3:1)	10\51 (235.3 ¢)
Superhard (L:s = 4:1)	13\66 (236.4 ¢)
Collapsed (L:s = 1:0)	3\15 (240.0 ¢)

15L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 6 small steps, with a period of 5 large steps and 2 small steps that repeats every 400.0 ¢, or 3 times every octave. 15L 6s is a grandchild scale of 6L 3s, expanding it by 12 tones. Generators that produce this scale range from 228.6 ¢ to 240 ¢, or from 160 ¢ to 171.4 ¢.

Modes

Modes of 15L 6s

UDP	Cyclic order	Step pattern
18|0(3)	1	LLLsLLsLLLsLLsLLLsLLs
15|3(3)	5	LLsLLLsLLsLLLsLLsLLLs
12|6(3)	2	LLsLLsLLLsLLsLLLsLLsL
9|9(3)	6	LsLLLsLLsLLLsLLsLLLsL
6|12(3)	3	LsLLsLLLsLLsLLLsLLsLL
3|15(3)	7	sLLLsLLsLLLsLLsLLLsLL
0|18(3)	4	sLLsLLLsLLsLLLsLLsLLL

Intervals

Intervals of 15L 6s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 57.1 ¢
	Major 1-mosstep	M1ms	L	57.1 ¢ to 80.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	80.0 ¢ to 114.3 ¢
	Major 2-mosstep	M2ms	2L	114.3 ¢ to 160.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	160.0 ¢ to 171.4 ¢
	Augmented 3-mosstep	A3ms	3L	171.4 ¢ to 240.0 ¢
4-mosstep	Diminished 4-mosstep	d4ms	2L + 2s	160.0 ¢ to 228.6 ¢
	Perfect 4-mosstep	P4ms	3L + s	228.6 ¢ to 240.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	240.0 ¢ to 285.7 ¢
	Major 5-mosstep	M5ms	4L + s	285.7 ¢ to 320.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	320.0 ¢ to 342.9 ¢
	Major 6-mosstep	M6ms	5L + s	342.9 ¢ to 400.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	400.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	400.0 ¢ to 457.1 ¢
	Major 8-mosstep	M8ms	6L + 2s	457.1 ¢ to 480.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	480.0 ¢ to 514.3 ¢
	Major 9-mosstep	M9ms	7L + 2s	514.3 ¢ to 560.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	7L + 3s	560.0 ¢ to 571.4 ¢
	Augmented 10-mosstep	A10ms	8L + 2s	571.4 ¢ to 640.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	7L + 4s	560.0 ¢ to 628.6 ¢
	Perfect 11-mosstep	P11ms	8L + 3s	628.6 ¢ to 640.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	640.0 ¢ to 685.7 ¢
	Major 12-mosstep	M12ms	9L + 3s	685.7 ¢ to 720.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	720.0 ¢ to 742.9 ¢
	Major 13-mosstep	M13ms	10L + 3s	742.9 ¢ to 800.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	10L + 4s	800.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	10L + 5s	800.0 ¢ to 857.1 ¢
	Major 15-mosstep	M15ms	11L + 4s	857.1 ¢ to 880.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	11L + 5s	880.0 ¢ to 914.3 ¢
	Major 16-mosstep	M16ms	12L + 4s	914.3 ¢ to 960.0 ¢
17-mosstep	Perfect 17-mosstep	P17ms	12L + 5s	960.0 ¢ to 971.4 ¢
	Augmented 17-mosstep	A17ms	13L + 4s	971.4 ¢ to 1040.0 ¢
18-mosstep	Diminished 18-mosstep	d18ms	12L + 6s	960.0 ¢ to 1028.6 ¢
	Perfect 18-mosstep	P18ms	13L + 5s	1028.6 ¢ to 1040.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	13L + 6s	1040.0 ¢ to 1085.7 ¢
	Major 19-mosstep	M19ms	14L + 5s	1085.7 ¢ to 1120.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	14L + 6s	1120.0 ¢ to 1142.9 ¢
	Major 20-mosstep	M20ms	15L + 5s	1142.9 ¢ to 1200.0 ¢
21-mosstep	Perfect 21-mosstep	P21ms	15L + 6s	1200.0 ¢

Scale tree

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