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
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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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

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

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