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
Descends from	5L 1s (machinoid)
Required step ratio range	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	5L 11s
Sister	16L 5s
Daughters	21L 5s 5L 21s
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 cents), meaning 8/7 is less than the boundary of "practicality" for it (which is at 31edo).

Modes

Modes of 5L 16s

UDP	Rotational order	Step pattern
20|0	1	LsssLsssLsssLsssLssss
19|1	5	LsssLsssLsssLssssLsss
18|2	9	LsssLsssLssssLsssLsss
17|3	13	LsssLssssLsssLsssLsss
16|4	17	LssssLsssLsssLsssLsss
15|5	21	sLsssLsssLsssLsssLsss
14|6	4	sLsssLsssLsssLssssLss
13|7	8	sLsssLsssLssssLsssLss
12|8	12	sLsssLssssLsssLsssLss
11|9	16	sLssssLsssLsssLsssLss
10|10	20	ssLsssLsssLsssLsssLss
9|11	3	ssLsssLsssLsssLssssLs
8|12	7	ssLsssLsssLssssLsssLs
7|13	11	ssLsssLssssLsssLsssLs
6|14	15	ssLssssLsssLsssLsssLs
5|15	19	sssLsssLsssLsssLsssLs
4|16	2	sssLsssLsssLsssLssssL
3|17	6	sssLsssLsssLssssLsssL
2|18	10	sssLsssLssssLsssLsssL
1|19	14	sssLssssLsssLsssLsssL
0|20	18	ssssLsssLsssLsssLsssL

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
				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
		6\31				232.258	967.742	3:1	3.000	Hard 5L 16s
					19\98	232.653	967.347	10:3	3.333
				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
				8\41		234.146	965.854	5:1	5.000
					9\46	234.783	965.217	6:1	6.000
1\5						240.000	960.000	1:0	→ ∞	Collapsed 5L 16s