4L 16s

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

┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┐ │║││││║││││║││││║│││││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssLssssLssssLssss ssssLssssLssssLssssL
Equave	2/1 (1200.0¢)
Period	1\4 (300.0¢)
Generator size
Bright	4\20 to 1\4 (240.0¢ to 300.0¢)
Dark	0\4 to 1\20 (0.0¢ to 60.0¢)
TAMNAMS information
Descends from	4L 4s (tetrawood)
Ancestor's step ratio range	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	4L 12s
Sister	16L 4s
Daughters	20L 4s, 4L 20s
Neutralized	8L 12s
2-Flought	24L 16s, 4L 36s
Equal tunings
Equalized (L:s = 1:1)	4\20 (240.0¢)
Supersoft (L:s = 4:3)	13\64 (243.8¢)
Soft (L:s = 3:2)	9\44 (245.5¢)
Semisoft (L:s = 5:3)	14\68 (247.1¢)
Basic (L:s = 2:1)	5\24 (250.0¢)
Semihard (L:s = 5:2)	11\52 (253.8¢)
Hard (L:s = 3:1)	6\28 (257.1¢)
Superhard (L:s = 4:1)	7\32 (262.5¢)
Collapsed (L:s = 1:0)	1\4 (300.0¢)

4L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 16 small steps, with a period of 1 large step and 4 small steps that repeats every 300.0¢, or 4 times every octave. 4L 16s is a great-grandchild scale of 4L 4s, expanding it by 12 tones. Generators that produce this scale range from 240¢ to 300¢, or from 0¢ to 60¢.

Modes

Modes of 4L 16s

UDP	Cyclic order	Step pattern
16|0(4)	1	LssssLssssLssssLssss
12|4(4)	5	sLssssLssssLssssLsss
8|8(4)	4	ssLssssLssssLssssLss
4|12(4)	3	sssLssssLssssLssssLs
0|16(4)	2	ssssLssssLssssLssssL

Intervals

Intervals of 4L 16s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0¢ to 60.0¢
	Augmented 1-mosstep	A1ms	L	60.0¢ to 300.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 120.0¢
	Major 2-mosstep	M2ms	L + s	120.0¢ to 300.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 180.0¢
	Major 3-mosstep	M3ms	L + 2s	180.0¢ to 300.0¢
4-mosstep	Diminished 4-mosstep	d4ms	4s	0.0¢ to 240.0¢
	Perfect 4-mosstep	P4ms	L + 3s	240.0¢ to 300.0¢
5-mosstep	Perfect 5-mosstep	P5ms	L + 4s	300.0¢
6-mosstep	Perfect 6-mosstep	P6ms	L + 5s	300.0¢ to 360.0¢
	Augmented 6-mosstep	A6ms	2L + 4s	360.0¢ to 600.0¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	300.0¢ to 420.0¢
	Major 7-mosstep	M7ms	2L + 5s	420.0¢ to 600.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	300.0¢ to 480.0¢
	Major 8-mosstep	M8ms	2L + 6s	480.0¢ to 600.0¢
9-mosstep	Diminished 9-mosstep	d9ms	L + 8s	300.0¢ to 540.0¢
	Perfect 9-mosstep	P9ms	2L + 7s	540.0¢ to 600.0¢
10-mosstep	Perfect 10-mosstep	P10ms	2L + 8s	600.0¢
11-mosstep	Perfect 11-mosstep	P11ms	2L + 9s	600.0¢ to 660.0¢
	Augmented 11-mosstep	A11ms	3L + 8s	660.0¢ to 900.0¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	600.0¢ to 720.0¢
	Major 12-mosstep	M12ms	3L + 9s	720.0¢ to 900.0¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	600.0¢ to 780.0¢
	Major 13-mosstep	M13ms	3L + 10s	780.0¢ to 900.0¢
14-mosstep	Diminished 14-mosstep	d14ms	2L + 12s	600.0¢ to 840.0¢
	Perfect 14-mosstep	P14ms	3L + 11s	840.0¢ to 900.0¢
15-mosstep	Perfect 15-mosstep	P15ms	3L + 12s	900.0¢
16-mosstep	Perfect 16-mosstep	P16ms	3L + 13s	900.0¢ to 960.0¢
	Augmented 16-mosstep	A16ms	4L + 12s	960.0¢ to 1200.0¢
17-mosstep	Minor 17-mosstep	m17ms	3L + 14s	900.0¢ to 1020.0¢
	Major 17-mosstep	M17ms	4L + 13s	1020.0¢ to 1200.0¢
18-mosstep	Minor 18-mosstep	m18ms	3L + 15s	900.0¢ to 1080.0¢
	Major 18-mosstep	M18ms	4L + 14s	1080.0¢ to 1200.0¢
19-mosstep	Diminished 19-mosstep	d19ms	3L + 16s	900.0¢ to 1140.0¢
	Perfect 19-mosstep	P19ms	4L + 15s	1140.0¢ to 1200.0¢
20-mosstep	Perfect 20-mosstep	P20ms	4L + 16s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 4L 16s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\20						240.000	60.000	1:1	1.000	Equalized 4L 16s
					21\104	242.308	57.692	6:5	1.200
				17\84		242.857	57.143	5:4	1.250
					30\148	243.243	56.757	9:7	1.286
			13\64			243.750	56.250	4:3	1.333	Supersoft 4L 16s
					35\172	244.186	55.814	11:8	1.375
				22\108		244.444	55.556	7:5	1.400
					31\152	244.737	55.263	10:7	1.429
		9\44				245.455	54.545	3:2	1.500	Soft 4L 16s
					32\156	246.154	53.846	11:7	1.571
				23\112		246.429	53.571	8:5	1.600
					37\180	246.667	53.333	13:8	1.625
			14\68			247.059	52.941	5:3	1.667	Semisoft 4L 16s
					33\160	247.500	52.500	12:7	1.714
				19\92		247.826	52.174	7:4	1.750
					24\116	248.276	51.724	9:5	1.800
	5\24					250.000	50.000	2:1	2.000	Basic 4L 16s Scales with tunings softer than this are proper
					21\100	252.000	48.000	9:4	2.250
				16\76		252.632	47.368	7:3	2.333
					27\128	253.125	46.875	12:5	2.400
			11\52			253.846	46.154	5:2	2.500	Semihard 4L 16s
					28\132	254.545	45.455	13:5	2.600
				17\80		255.000	45.000	8:3	2.667
					23\108	255.556	44.444	11:4	2.750
		6\28				257.143	42.857	3:1	3.000	Hard 4L 16s
					19\88	259.091	40.909	10:3	3.333
				13\60		260.000	40.000	7:2	3.500
					20\92	260.870	39.130	11:3	3.667
			7\32			262.500	37.500	4:1	4.000	Superhard 4L 16s
					15\68	264.706	35.294	9:2	4.500
				8\36		266.667	33.333	5:1	5.000
					9\40	270.000	30.000	6:1	6.000
1\4						300.000	0.000	1:0	→ ∞	Collapsed 4L 16s

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