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
Descends from	6L 3s (hyrulic)
Ancestor's step ratio range	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

Scale Tree and Tuning Spectrum of 15L 6s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\21						228.571	171.429	1:1	1.000	Equalized 15L 6s
					23\120	230.000	170.000	6:5	1.200
				19\99		230.303	169.697	5:4	1.250
					34\177	230.508	169.492	9:7	1.286
			15\78			230.769	169.231	4:3	1.333	Supersoft 15L 6s
					41\213	230.986	169.014	11:8	1.375
				26\135		231.111	168.889	7:5	1.400
					37\192	231.250	168.750	10:7	1.429
		11\57				231.579	168.421	3:2	1.500	Soft 15L 6s
					40\207	231.884	168.116	11:7	1.571
				29\150		232.000	168.000	8:5	1.600
					47\243	232.099	167.901	13:8	1.625
			18\93			232.258	167.742	5:3	1.667	Semisoft 15L 6s
					43\222	232.432	167.568	12:7	1.714
				25\129		232.558	167.442	7:4	1.750
					32\165	232.727	167.273	9:5	1.800
	7\36					233.333	166.667	2:1	2.000	Basic 15L 6s Scales with tunings softer than this are proper
					31\159	233.962	166.038	9:4	2.250
				24\123		234.146	165.854	7:3	2.333
					41\210	234.286	165.714	12:5	2.400
			17\87			234.483	165.517	5:2	2.500	Semihard 15L 6s
					44\225	234.667	165.333	13:5	2.600
				27\138		234.783	165.217	8:3	2.667
					37\189	234.921	165.079	11:4	2.750
		10\51				235.294	164.706	3:1	3.000	Hard 15L 6s
					33\168	235.714	164.286	10:3	3.333
				23\117		235.897	164.103	7:2	3.500
					36\183	236.066	163.934	11:3	3.667
			13\66			236.364	163.636	4:1	4.000	Superhard 15L 6s
					29\147	236.735	163.265	9:2	4.500
				16\81		237.037	162.963	5:1	5.000
					19\96	237.500	162.500	6:1	6.000
3\15						240.000	160.000	1:0	→ ∞	Collapsed 15L 6s

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