6L 15s

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

┌╥┬┬╥┬┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐ │║││║│││║││║│││║││║││││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssLsssLssLsssLssLsss sssLssLsssLssLsssLssL
Equave	2/1 (1200.0¢)
Period	1\3 (400.0¢)
Generator size
Bright	3\21 to 1\6 (171.4¢ to 200.0¢)
Dark	1\6 to 4\21 (200.0¢ to 228.6¢)
TAMNAMS information
Descends from	6L 3s (hyrulic)
Ancestor's step ratio range	3:1 to 1:0 (hard)
Related MOS scales
Parent	6L 9s
Sister	15L 6s
Daughters	21L 6s, 6L 21s
Neutralized	12L 9s
2-Flought	27L 15s, 6L 36s
Equal tunings
Equalized (L:s = 1:1)	3\21 (171.4¢)
Supersoft (L:s = 4:3)	10\69 (173.9¢)
Soft (L:s = 3:2)	7\48 (175.0¢)
Semisoft (L:s = 5:3)	11\75 (176.0¢)
Basic (L:s = 2:1)	4\27 (177.8¢)
Semihard (L:s = 5:2)	9\60 (180.0¢)
Hard (L:s = 3:1)	5\33 (181.8¢)
Superhard (L:s = 4:1)	6\39 (184.6¢)
Collapsed (L:s = 1:0)	1\6 (200.0¢)

6L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 15 small steps, with a period of 2 large steps and 5 small steps that repeats every 400.0¢, or 3 times every octave. 6L 15s is a grandchild scale of 6L 3s, expanding it by 12 tones. Generators that produce this scale range from 171.4¢ to 200¢, or from 200¢ to 228.6¢.

Modes

Modes of 6L 15s

UDP	Cyclic order	Step pattern
18|0(3)	1	LssLsssLssLsssLssLsss
15|3(3)	4	LsssLssLsssLssLsssLss
12|6(3)	7	sLssLsssLssLsssLssLss
9|9(3)	3	sLsssLssLsssLssLsssLs
6|12(3)	6	ssLssLsssLssLsssLssLs
3|15(3)	2	ssLsssLssLsssLssLsssL
0|18(3)	5	sssLssLsssLssLsssLssL

Intervals

Intervals of 6L 15s

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 200.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 114.3¢
	Major 2-mosstep	M2ms	L + s	114.3¢ to 200.0¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0¢ to 171.4¢
	Perfect 3-mosstep	P3ms	L + 2s	171.4¢ to 200.0¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	200.0¢ to 228.6¢
	Augmented 4-mosstep	A4ms	2L + 2s	228.6¢ to 400.0¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	200.0¢ to 285.7¢
	Major 5-mosstep	M5ms	2L + 3s	285.7¢ to 400.0¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	200.0¢ to 342.9¢
	Major 6-mosstep	M6ms	2L + 4s	342.9¢ to 400.0¢
7-mosstep	Perfect 7-mosstep	P7ms	2L + 5s	400.0¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	400.0¢ to 457.1¢
	Major 8-mosstep	M8ms	3L + 5s	457.1¢ to 600.0¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	400.0¢ to 514.3¢
	Major 9-mosstep	M9ms	3L + 6s	514.3¢ to 600.0¢
10-mosstep	Diminished 10-mosstep	d10ms	2L + 8s	400.0¢ to 571.4¢
	Perfect 10-mosstep	P10ms	3L + 7s	571.4¢ to 600.0¢
11-mosstep	Perfect 11-mosstep	P11ms	3L + 8s	600.0¢ to 628.6¢
	Augmented 11-mosstep	A11ms	4L + 7s	628.6¢ to 800.0¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	600.0¢ to 685.7¢
	Major 12-mosstep	M12ms	4L + 8s	685.7¢ to 800.0¢
13-mosstep	Minor 13-mosstep	m13ms	3L + 10s	600.0¢ to 742.9¢
	Major 13-mosstep	M13ms	4L + 9s	742.9¢ to 800.0¢
14-mosstep	Perfect 14-mosstep	P14ms	4L + 10s	800.0¢
15-mosstep	Minor 15-mosstep	m15ms	4L + 11s	800.0¢ to 857.1¢
	Major 15-mosstep	M15ms	5L + 10s	857.1¢ to 1000.0¢
16-mosstep	Minor 16-mosstep	m16ms	4L + 12s	800.0¢ to 914.3¢
	Major 16-mosstep	M16ms	5L + 11s	914.3¢ to 1000.0¢
17-mosstep	Diminished 17-mosstep	d17ms	4L + 13s	800.0¢ to 971.4¢
	Perfect 17-mosstep	P17ms	5L + 12s	971.4¢ to 1000.0¢
18-mosstep	Perfect 18-mosstep	P18ms	5L + 13s	1000.0¢ to 1028.6¢
	Augmented 18-mosstep	A18ms	6L + 12s	1028.6¢ to 1200.0¢
19-mosstep	Minor 19-mosstep	m19ms	5L + 14s	1000.0¢ to 1085.7¢
	Major 19-mosstep	M19ms	6L + 13s	1085.7¢ to 1200.0¢
20-mosstep	Minor 20-mosstep	m20ms	5L + 15s	1000.0¢ to 1142.9¢
	Major 20-mosstep	M20ms	6L + 14s	1142.9¢ to 1200.0¢
21-mosstep	Perfect 21-mosstep	P21ms	6L + 15s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 6L 15s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\21						171.429	228.571	1:1	1.000	Equalized 6L 15s
					16\111	172.973	227.027	6:5	1.200
				13\90		173.333	226.667	5:4	1.250
					23\159	173.585	226.415	9:7	1.286
			10\69			173.913	226.087	4:3	1.333	Supersoft 6L 15s
					27\186	174.194	225.806	11:8	1.375
				17\117		174.359	225.641	7:5	1.400
					24\165	174.545	225.455	10:7	1.429
		7\48				175.000	225.000	3:2	1.500	Soft 6L 15s
					25\171	175.439	224.561	11:7	1.571
				18\123		175.610	224.390	8:5	1.600
					29\198	175.758	224.242	13:8	1.625
			11\75			176.000	224.000	5:3	1.667	Semisoft 6L 15s
					26\177	176.271	223.729	12:7	1.714
				15\102		176.471	223.529	7:4	1.750
					19\129	176.744	223.256	9:5	1.800
	4\27					177.778	222.222	2:1	2.000	Basic 6L 15s Scales with tunings softer than this are proper
					17\114	178.947	221.053	9:4	2.250
				13\87		179.310	220.690	7:3	2.333
					22\147	179.592	220.408	12:5	2.400
			9\60			180.000	220.000	5:2	2.500	Semihard 6L 15s
					23\153	180.392	219.608	13:5	2.600
				14\93		180.645	219.355	8:3	2.667
					19\126	180.952	219.048	11:4	2.750
		5\33				181.818	218.182	3:1	3.000	Hard 6L 15s
					16\105	182.857	217.143	10:3	3.333
				11\72		183.333	216.667	7:2	3.500
					17\111	183.784	216.216	11:3	3.667
			6\39			184.615	215.385	4:1	4.000	Superhard 6L 15s
					13\84	185.714	214.286	9:2	4.500
				7\45		186.667	213.333	5:1	5.000
					8\51	188.235	211.765	6:1	6.000
1\6						200.000	200.000	1:0	→ ∞	Collapsed 6L 15s

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