16L 4s

↖ 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
Descends from	4L 4s (tetrawood)
Ancestor's step ratio range	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¢)

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.

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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