16L 2s

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.

↖ 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
Related to	2L 8s (jaric)
With tunings	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 ¢)
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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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