16L 4s

16L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 4 small steps, with a period of 4 large steps and 1 small step that repeats every 300.0 ¢, or 4 times every octave. 16L 4s is a great-grandchild scale of 4L 4s, expanding it by 12 tones. Generators that produce this scale range from 60 ¢ to 75 ¢, or from 225 ¢ to 240 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

↖ 15L 3s	↑ 16L 3s	17L 3s ↗
← 15L 4s	16L 4s	17L 4s →
↙ 15L 5s	↓ 16L 5s	17L 5s ↘

Scale structure
Step pattern	LLLLsLLLLsLLLLsLLLLs sLLLLsLLLLsLLLLsLLLL
Equave	2/1 (1200.0 ¢)
Period	1\4 (300.0 ¢)
Generator size
Bright	1\20 to 1\16 (60.0 ¢ to 75.0 ¢)
Dark	3\16 to 4\20 (225.0 ¢ to 240.0 ¢)
TAMNAMS information
Related to	4L 4s (tetrawood)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	4L 12s
Sister	4L 16s
Daughters	20L 16s, 16L 20s
Neutralized	12L 8s
2-Flought	36L 4s, 16L 24s
Equal tunings
Equalized (L:s = 1:1)	1\20 (60.0 ¢)
Supersoft (L:s = 4:3)	4\76 (63.2 ¢)
Soft (L:s = 3:2)	3\56 (64.3 ¢)
Semisoft (L:s = 5:3)	5\92 (65.2 ¢)
Basic (L:s = 2:1)	2\36 (66.7 ¢)
Semihard (L:s = 5:2)	5\88 (68.2 ¢)
Hard (L:s = 3:1)	3\52 (69.2 ¢)
Superhard (L:s = 4:1)	4\68 (70.6 ¢)
Collapsed (L:s = 1:0)	1\16 (75.0 ¢)
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Modes

Modes of 16L 4s

UDP	Cyclic order	Step pattern
16|0(4)	1	LLLLsLLLLsLLLLsLLLLs
12|4(4)	2	LLLsLLLLsLLLLsLLLLsL
8|8(4)	3	LLsLLLLsLLLLsLLLLsLL
4|12(4)	4	LsLLLLsLLLLsLLLLsLLL
0|16(4)	5	sLLLLsLLLLsLLLLsLLLL

Intervals

Intervals of 16L 4s

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 60.0 ¢
	Perfect 1-mosstep	P1ms	L	60.0 ¢ to 75.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	75.0 ¢ to 120.0 ¢
	Major 2-mosstep	M2ms	2L	120.0 ¢ to 150.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	150.0 ¢ to 180.0 ¢
	Major 3-mosstep	M3ms	3L	180.0 ¢ to 225.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	225.0 ¢ to 240.0 ¢
	Augmented 4-mosstep	A4ms	4L	240.0 ¢ to 300.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	4L + s	300.0 ¢
6-mosstep	Diminished 6-mosstep	d6ms	4L + 2s	300.0 ¢ to 360.0 ¢
	Perfect 6-mosstep	P6ms	5L + s	360.0 ¢ to 375.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	375.0 ¢ to 420.0 ¢
	Major 7-mosstep	M7ms	6L + s	420.0 ¢ to 450.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	450.0 ¢ to 480.0 ¢
	Major 8-mosstep	M8ms	7L + s	480.0 ¢ to 525.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	7L + 2s	525.0 ¢ to 540.0 ¢
	Augmented 9-mosstep	A9ms	8L + s	540.0 ¢ to 600.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	8L + 2s	600.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	8L + 3s	600.0 ¢ to 660.0 ¢
	Perfect 11-mosstep	P11ms	9L + 2s	660.0 ¢ to 675.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	675.0 ¢ to 720.0 ¢
	Major 12-mosstep	M12ms	10L + 2s	720.0 ¢ to 750.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	10L + 3s	750.0 ¢ to 780.0 ¢
	Major 13-mosstep	M13ms	11L + 2s	780.0 ¢ to 825.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	11L + 3s	825.0 ¢ to 840.0 ¢
	Augmented 14-mosstep	A14ms	12L + 2s	840.0 ¢ to 900.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	12L + 3s	900.0 ¢
16-mosstep	Diminished 16-mosstep	d16ms	12L + 4s	900.0 ¢ to 960.0 ¢
	Perfect 16-mosstep	P16ms	13L + 3s	960.0 ¢ to 975.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	13L + 4s	975.0 ¢ to 1020.0 ¢
	Major 17-mosstep	M17ms	14L + 3s	1020.0 ¢ to 1050.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	14L + 4s	1050.0 ¢ to 1080.0 ¢
	Major 18-mosstep	M18ms	15L + 3s	1080.0 ¢ to 1125.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	15L + 4s	1125.0 ¢ to 1140.0 ¢
	Augmented 19-mosstep	A19ms	16L + 3s	1140.0 ¢ to 1200.0 ¢
20-mosstep	Perfect 20-mosstep	P20ms	16L + 4s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 16L 4s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\20						60.000	240.000	1:1	1.000	Equalized 16L 4s
					6\116	62.069	237.931	6:5	1.200
				5\96		62.500	237.500	5:4	1.250
					9\172	62.791	237.209	9:7	1.286
			4\76			63.158	236.842	4:3	1.333	Supersoft 16L 4s
					11\208	63.462	236.538	11:8	1.375
				7\132		63.636	236.364	7:5	1.400
					10\188	63.830	236.170	10:7	1.429
		3\56				64.286	235.714	3:2	1.500	Soft 16L 4s
					11\204	64.706	235.294	11:7	1.571
				8\148		64.865	235.135	8:5	1.600
					13\240	65.000	235.000	13:8	1.625
			5\92			65.217	234.783	5:3	1.667	Semisoft 16L 4s
					12\220	65.455	234.545	12:7	1.714
				7\128		65.625	234.375	7:4	1.750
					9\164	65.854	234.146	9:5	1.800
	2\36					66.667	233.333	2:1	2.000	Basic 16L 4s
					9\160	67.500	232.500	9:4	2.250
				7\124		67.742	232.258	7:3	2.333
					12\212	67.925	232.075	12:5	2.400
			5\88			68.182	231.818	5:2	2.500	Semihard 16L 4s
					13\228	68.421	231.579	13:5	2.600
				8\140		68.571	231.429	8:3	2.667
					11\192	68.750	231.250	11:4	2.750
		3\52				69.231	230.769	3:1	3.000	Hard 16L 4s
					10\172	69.767	230.233	10:3	3.333
				7\120		70.000	230.000	7:2	3.500
					11\188	70.213	229.787	11:3	3.667
			4\68			70.588	229.412	4:1	4.000	Superhard 16L 4s
					9\152	71.053	228.947	9:2	4.500
				5\84		71.429	228.571	5:1	5.000
					6\100	72.000	228.000	6:1	6.000
1\16						75.000	225.000	1:0	→ ∞	Collapsed 16L 4s

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