16L 2s

↖ 15L 1s	↑ 16L 1s	17L 1s ↗
← 15L 2s	16L 2s	17L 2s →
↙ 15L 3s	↓ 16L 3s	17L 3s ↘

┌╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║│║║║║║║║║││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLLsLLLLLLLLs sLLLLLLLLsLLLLLLLL
Equave	2/1 (1200.0¢)
Period	1\2 (600.0¢)
Generator size
Bright	1\18 to 1\16 (66.7¢ to 75.0¢)
Dark	7\16 to 8\18 (525.0¢ to 533.3¢)
TAMNAMS information
Descends from	2L 8s (jaric)
Ancestor's step ratio range	4:1 to 5:1
Related MOS scales
Parent	2L 14s
Sister	2L 16s
Daughters	18L 16s, 16L 18s
Neutralized	14L 4s
2-Flought	34L 2s, 16L 20s
Equal tunings
Equalized (L:s = 1:1)	1\18 (66.7¢)
Supersoft (L:s = 4:3)	4\70 (68.6¢)
Soft (L:s = 3:2)	3\52 (69.2¢)
Semisoft (L:s = 5:3)	5\86 (69.8¢)
Basic (L:s = 2:1)	2\34 (70.6¢)
Semihard (L:s = 5:2)	5\84 (71.4¢)
Hard (L:s = 3:1)	3\50 (72.0¢)
Superhard (L:s = 4:1)	4\66 (72.7¢)
Collapsed (L:s = 1:0)	1\16 (75.0¢)

16L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 2 small steps, with a period of 8 large steps and 1 small step that repeats every 600.0¢, or twice every octave. 16L 2s is related to 2L 8s, expanding it by 8 tones. Generators that produce this scale range from 66.7¢ to 75¢, or from 525¢ to 533.3¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Modes

Modes of 16L 2s

UDP	Cyclic order	Step pattern
16|0(2)	1	LLLLLLLLsLLLLLLLLs
14|2(2)	2	LLLLLLLsLLLLLLLLsL
12|4(2)	3	LLLLLLsLLLLLLLLsLL
10|6(2)	4	LLLLLsLLLLLLLLsLLL
8|8(2)	5	LLLLsLLLLLLLLsLLLL
6|10(2)	6	LLLsLLLLLLLLsLLLLL
4|12(2)	7	LLsLLLLLLLLsLLLLLL
2|14(2)	8	LsLLLLLLLLsLLLLLLL
0|16(2)	9	sLLLLLLLLsLLLLLLLL

Intervals

Intervals of 16L 2s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0¢ to 66.7¢
	Perfect 1-mosstep	P1ms	L	66.7¢ to 75.0¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	75.0¢ to 133.3¢
	Major 2-mosstep	M2ms	2L	133.3¢ to 150.0¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	150.0¢ to 200.0¢
	Major 3-mosstep	M3ms	3L	200.0¢ to 225.0¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	225.0¢ to 266.7¢
	Major 4-mosstep	M4ms	4L	266.7¢ to 300.0¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	300.0¢ to 333.3¢
	Major 5-mosstep	M5ms	5L	333.3¢ to 375.0¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	375.0¢ to 400.0¢
	Major 6-mosstep	M6ms	6L	400.0¢ to 450.0¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	450.0¢ to 466.7¢
	Major 7-mosstep	M7ms	7L	466.7¢ to 525.0¢
8-mosstep	Perfect 8-mosstep	P8ms	7L + s	525.0¢ to 533.3¢
	Augmented 8-mosstep	A8ms	8L	533.3¢ to 600.0¢
9-mosstep	Perfect 9-mosstep	P9ms	8L + s	600.0¢
10-mosstep	Diminished 10-mosstep	d10ms	8L + 2s	600.0¢ to 666.7¢
	Perfect 10-mosstep	P10ms	9L + s	666.7¢ to 675.0¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	675.0¢ to 733.3¢
	Major 11-mosstep	M11ms	10L + s	733.3¢ to 750.0¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	750.0¢ to 800.0¢
	Major 12-mosstep	M12ms	11L + s	800.0¢ to 825.0¢
13-mosstep	Minor 13-mosstep	m13ms	11L + 2s	825.0¢ to 866.7¢
	Major 13-mosstep	M13ms	12L + s	866.7¢ to 900.0¢
14-mosstep	Minor 14-mosstep	m14ms	12L + 2s	900.0¢ to 933.3¢
	Major 14-mosstep	M14ms	13L + s	933.3¢ to 975.0¢
15-mosstep	Minor 15-mosstep	m15ms	13L + 2s	975.0¢ to 1000.0¢
	Major 15-mosstep	M15ms	14L + s	1000.0¢ to 1050.0¢
16-mosstep	Minor 16-mosstep	m16ms	14L + 2s	1050.0¢ to 1066.7¢
	Major 16-mosstep	M16ms	15L + s	1066.7¢ to 1125.0¢
17-mosstep	Perfect 17-mosstep	P17ms	15L + 2s	1125.0¢ to 1133.3¢
	Augmented 17-mosstep	A17ms	16L + s	1133.3¢ to 1200.0¢
18-mosstep	Perfect 18-mosstep	P18ms	16L + 2s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 16L 2s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\18						66.667	533.333	1:1	1.000	Equalized 16L 2s
					6\106	67.925	532.075	6:5	1.200
				5\88		68.182	531.818	5:4	1.250
					9\158	68.354	531.646	9:7	1.286
			4\70			68.571	531.429	4:3	1.333	Supersoft 16L 2s
					11\192	68.750	531.250	11:8	1.375
				7\122		68.852	531.148	7:5	1.400
					10\174	68.966	531.034	10:7	1.429
		3\52				69.231	530.769	3:2	1.500	Soft 16L 2s
					11\190	69.474	530.526	11:7	1.571
				8\138		69.565	530.435	8:5	1.600
					13\224	69.643	530.357	13:8	1.625
			5\86			69.767	530.233	5:3	1.667	Semisoft 16L 2s
					12\206	69.903	530.097	12:7	1.714
				7\120		70.000	530.000	7:4	1.750
					9\154	70.130	529.870	9:5	1.800
	2\34					70.588	529.412	2:1	2.000	Basic 16L 2s
					9\152	71.053	528.947	9:4	2.250
				7\118		71.186	528.814	7:3	2.333
					12\202	71.287	528.713	12:5	2.400
			5\84			71.429	528.571	5:2	2.500	Semihard 16L 2s
					13\218	71.560	528.440	13:5	2.600
				8\134		71.642	528.358	8:3	2.667
					11\184	71.739	528.261	11:4	2.750
		3\50				72.000	528.000	3:1	3.000	Hard 16L 2s
					10\166	72.289	527.711	10:3	3.333
				7\116		72.414	527.586	7:2	3.500
					11\182	72.527	527.473	11:3	3.667
			4\66			72.727	527.273	4:1	4.000	Superhard 16L 2s
					9\148	72.973	527.027	9:2	4.500
				5\82		73.171	526.829	5:1	5.000
					6\98	73.469	526.531	6:1	6.000
1\16						75.000	525.000	1:0	→ ∞	Collapsed 16L 2s

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