5L 16s

↖ 4L 15s	↑ 5L 15s	6L 15s ↗
← 4L 16s	5L 16s	6L 16s →
↙ 4L 17s	↓ 5L 17s	6L 17s ↘

┌╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┬┐ │║│││║│││║│││║│││║│││││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsssLsssLsssLsssLssss ssssLsssLsssLsssLsssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	4\21 to 1\5 (228.6 ¢ to 240.0 ¢)
Dark	4\5 to 17\21 (960.0 ¢ to 971.4 ¢)
TAMNAMS information
Related to	5L 1s (machinoid)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	5L 11s
Sister	16L 5s
Daughters	21L 5s, 5L 21s
Neutralized	10L 11s
2-Flought	26L 16s, 5L 37s
Equal tunings
Equalized (L:s = 1:1)	4\21 (228.6 ¢)
Supersoft (L:s = 4:3)	13\68 (229.4 ¢)
Soft (L:s = 3:2)	9\47 (229.8 ¢)
Semisoft (L:s = 5:3)	14\73 (230.1 ¢)
Basic (L:s = 2:1)	5\26 (230.8 ¢)
Semihard (L:s = 5:2)	11\57 (231.6 ¢)
Hard (L:s = 3:1)	6\31 (232.3 ¢)
Superhard (L:s = 4:1)	7\36 (233.3 ¢)
Collapsed (L:s = 1:0)	1\5 (240.0 ¢)

5L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 16 small steps, repeating every octave. 5L 16s is a great-grandchild scale of 5L 1s, expanding it by 15 tones. Generators that produce this scale range from 228.6 ¢ to 240 ¢, or from 960 ¢ to 971.4 ¢.

This is the MOS which splits its small steps 3-3-3-3-4 between its large steps. Its "diatonic" whole tone/supermajor second generator measures no less than 4/21edo (228.571 ¢), meaning 8/7 is less than the boundary of "practicality" for it (which is at 31edo).

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Scale tree

Scale tree and tuning spectrum of 5L 16s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\21						228.571	971.429	1:1	1.000	Equalized 5L 16s
					21\110	229.091	970.909	6:5	1.200
				17\89		229.213	970.787	5:4	1.250
					30\157	229.299	970.701	9:7	1.286
			13\68			229.412	970.588	4:3	1.333	Supersoft 5L 16s
					35\183	229.508	970.492	11:8	1.375
				22\115		229.565	970.435	7:5	1.400
					31\162	229.630	970.370	10:7	1.429
		9\47				229.787	970.213	3:2	1.500	Soft 5L 16s
					32\167	229.940	970.060	11:7	1.571
				23\120		230.000	970.000	8:5	1.600
					37\193	230.052	969.948	13:8	1.625
			14\73			230.137	969.863	5:3	1.667	Semisoft 5L 16s
					33\172	230.233	969.767	12:7	1.714
				19\99		230.303	969.697	7:4	1.750
					24\125	230.400	969.600	9:5	1.800
	5\26					230.769	969.231	2:1	2.000	Basic 5L 16s Scales with tunings softer than this are proper
					21\109	231.193	968.807	9:4	2.250	Nearly pure 8/7; Amaranthine
				16\83		231.325	968.675	7:3	2.333
					27\140	231.429	968.571	12:5	2.400
			11\57			231.579	968.421	5:2	2.500	Semihard 5L 16s
					28\145	231.724	968.276	13:5	2.600
				17\88		231.818	968.182	8:3	2.667
					23\119	231.933	968.067	11:4	2.750	Mothra
		6\31				232.258	967.742	3:1	3.000	Hard 5L 16s
					19\98	232.653	967.347	10:3	3.333	Mosura
				13\67		232.836	967.164	7:2	3.500
					20\103	233.010	966.990	11:3	3.667
			7\36			233.333	966.667	4:1	4.000	Superhard 5L 16s
					15\77	233.766	966.234	9:2	4.500	Guiron
				8\41		234.146	965.854	5:1	5.000	Rodan
					9\46	234.783	965.217	6:1	6.000
1\5						240.000	960.000	1:0	→ ∞	Collapsed 5L 16s