16L 6s

↖ 15L 5s	↑ 16L 5s	17L 5s ↗
← 15L 6s	16L 6s	17L 6s →
↙ 15L 7s	↓ 16L 7s	17L 7s ↘

┌╥╥╥┬╥╥╥┬╥╥┬╥╥╥┬╥╥╥┬╥╥┬┐ │║║║│║║║│║║│║║║│║║║│║║││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLsLLLsLLsLLLsLLLsLLs sLLsLLLsLLLsLLsLLLsLLL
Equave	2/1 (1200.0¢)
Period	1\2 (600.0¢)
Generator size
Bright	4\22 to 3\16 (218.2¢ to 225.0¢)
Dark	5\16 to 7\22 (375.0¢ to 381.8¢)
TAMNAMS information
Descends from	6L 4s
Ancestor's step ratio range	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	6L 10s
Sister	6L 16s
Daughters	22L 16s, 16L 22s
Neutralized	10L 12s
2-Flought	38L 6s, 16L 28s
Equal tunings
Equalized (L:s = 1:1)	4\22 (218.2¢)
Supersoft (L:s = 4:3)	15\82 (219.5¢)
Soft (L:s = 3:2)	11\60 (220.0¢)
Semisoft (L:s = 5:3)	18\98 (220.4¢)
Basic (L:s = 2:1)	7\38 (221.1¢)
Semihard (L:s = 5:2)	17\92 (221.7¢)
Hard (L:s = 3:1)	10\54 (222.2¢)
Superhard (L:s = 4:1)	13\70 (222.9¢)
Collapsed (L:s = 1:0)	3\16 (225.0¢)

16L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 6 small steps, with a period of 8 large steps and 3 small steps that repeats every 600.0¢, or twice every octave. 16L 6s is a grandchild scale of 6L 4s, expanding it by 12 tones. Generators that produce this scale range from 218.2¢ to 225¢, or from 375¢ to 381.8¢.

Modes

Modes of 16L 6s

UDP	Cyclic order	Step pattern
20|0(2)	1	LLLsLLLsLLsLLLsLLLsLLs
18|2(2)	5	LLLsLLsLLLsLLLsLLsLLLs
16|4(2)	9	LLsLLLsLLLsLLsLLLsLLLs
14|6(2)	2	LLsLLLsLLsLLLsLLLsLLsL
12|8(2)	6	LLsLLsLLLsLLLsLLsLLLsL
10|10(2)	10	LsLLLsLLLsLLsLLLsLLLsL
8|12(2)	3	LsLLLsLLsLLLsLLLsLLsLL
6|14(2)	7	LsLLsLLLsLLLsLLsLLLsLL
4|16(2)	11	sLLLsLLLsLLsLLLsLLLsLL
2|18(2)	4	sLLLsLLsLLLsLLLsLLsLLL
0|20(2)	8	sLLsLLLsLLLsLLsLLLsLLL

Intervals

Intervals of 16L 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 54.5¢
	Major 1-mosstep	M1ms	L	54.5¢ to 75.0¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	75.0¢ to 109.1¢
	Major 2-mosstep	M2ms	2L	109.1¢ to 150.0¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	150.0¢ to 163.6¢
	Major 3-mosstep	M3ms	3L	163.6¢ to 225.0¢
4-mosstep	Diminished 4-mosstep	d4ms	2L + 2s	150.0¢ to 218.2¢
	Perfect 4-mosstep	P4ms	3L + s	218.2¢ to 225.0¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	225.0¢ to 272.7¢
	Major 5-mosstep	M5ms	4L + s	272.7¢ to 300.0¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	300.0¢ to 327.3¢
	Major 6-mosstep	M6ms	5L + s	327.3¢ to 375.0¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	375.0¢ to 381.8¢
	Augmented 7-mosstep	A7ms	6L + s	381.8¢ to 450.0¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	375.0¢ to 436.4¢
	Major 8-mosstep	M8ms	6L + 2s	436.4¢ to 450.0¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	450.0¢ to 490.9¢
	Major 9-mosstep	M9ms	7L + 2s	490.9¢ to 525.0¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	525.0¢ to 545.5¢
	Major 10-mosstep	M10ms	8L + 2s	545.5¢ to 600.0¢
11-mosstep	Perfect 11-mosstep	P11ms	8L + 3s	600.0¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	600.0¢ to 654.5¢
	Major 12-mosstep	M12ms	9L + 3s	654.5¢ to 675.0¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	675.0¢ to 709.1¢
	Major 13-mosstep	M13ms	10L + 3s	709.1¢ to 750.0¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	750.0¢ to 763.6¢
	Major 14-mosstep	M14ms	11L + 3s	763.6¢ to 825.0¢
15-mosstep	Diminished 15-mosstep	d15ms	10L + 5s	750.0¢ to 818.2¢
	Perfect 15-mosstep	P15ms	11L + 4s	818.2¢ to 825.0¢
16-mosstep	Minor 16-mosstep	m16ms	11L + 5s	825.0¢ to 872.7¢
	Major 16-mosstep	M16ms	12L + 4s	872.7¢ to 900.0¢
17-mosstep	Minor 17-mosstep	m17ms	12L + 5s	900.0¢ to 927.3¢
	Major 17-mosstep	M17ms	13L + 4s	927.3¢ to 975.0¢
18-mosstep	Perfect 18-mosstep	P18ms	13L + 5s	975.0¢ to 981.8¢
	Augmented 18-mosstep	A18ms	14L + 4s	981.8¢ to 1050.0¢
19-mosstep	Minor 19-mosstep	m19ms	13L + 6s	975.0¢ to 1036.4¢
	Major 19-mosstep	M19ms	14L + 5s	1036.4¢ to 1050.0¢
20-mosstep	Minor 20-mosstep	m20ms	14L + 6s	1050.0¢ to 1090.9¢
	Major 20-mosstep	M20ms	15L + 5s	1090.9¢ to 1125.0¢
21-mosstep	Minor 21-mosstep	m21ms	15L + 6s	1125.0¢ to 1145.5¢
	Major 21-mosstep	M21ms	16L + 5s	1145.5¢ to 1200.0¢
22-mosstep	Perfect 22-mosstep	P22ms	16L + 6s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 16L 6s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\22						218.182	381.818	1:1	1.000	Equalized 16L 6s
					23\126	219.048	380.952	6:5	1.200
				19\104		219.231	380.769	5:4	1.250
					34\186	219.355	380.645	9:7	1.286
			15\82			219.512	380.488	4:3	1.333	Supersoft 16L 6s
					41\224	219.643	380.357	11:8	1.375
				26\142		219.718	380.282	7:5	1.400
					37\202	219.802	380.198	10:7	1.429
		11\60				220.000	380.000	3:2	1.500	Soft 16L 6s
					40\218	220.183	379.817	11:7	1.571
				29\158		220.253	379.747	8:5	1.600
					47\256	220.312	379.688	13:8	1.625
			18\98			220.408	379.592	5:3	1.667	Semisoft 16L 6s
					43\234	220.513	379.487	12:7	1.714
				25\136		220.588	379.412	7:4	1.750
					32\174	220.690	379.310	9:5	1.800
	7\38					221.053	378.947	2:1	2.000	Basic 16L 6s Scales with tunings softer than this are proper
					31\168	221.429	378.571	9:4	2.250
				24\130		221.538	378.462	7:3	2.333
					41\222	221.622	378.378	12:5	2.400
			17\92			221.739	378.261	5:2	2.500	Semihard 16L 6s
					44\238	221.849	378.151	13:5	2.600
				27\146		221.918	378.082	8:3	2.667
					37\200	222.000	378.000	11:4	2.750
		10\54				222.222	377.778	3:1	3.000	Hard 16L 6s
					33\178	222.472	377.528	10:3	3.333
				23\124		222.581	377.419	7:2	3.500
					36\194	222.680	377.320	11:3	3.667
			13\70			222.857	377.143	4:1	4.000	Superhard 16L 6s
					29\156	223.077	376.923	9:2	4.500
				16\86		223.256	376.744	5:1	5.000
					19\102	223.529	376.471	6:1	6.000
3\16						225.000	375.000	1:0	→ ∞	Collapsed 16L 6s

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