5L 16s

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 ¢.

↖ 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 ¢)
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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	Cyclic 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

Intervals

Intervals of 5L 16s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 57.1 ¢
	Major 1-mosstep	M1ms	L	57.1 ¢ to 240.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 114.3 ¢
	Major 2-mosstep	M2ms	L + s	114.3 ¢ to 240.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 171.4 ¢
	Major 3-mosstep	M3ms	L + 2s	171.4 ¢ to 240.0 ¢
4-mosstep	Diminished 4-mosstep	d4ms	4s	0.0 ¢ to 228.6 ¢
	Perfect 4-mosstep	P4ms	L + 3s	228.6 ¢ to 240.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	240.0 ¢ to 285.7 ¢
	Major 5-mosstep	M5ms	2L + 3s	285.7 ¢ to 480.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	240.0 ¢ to 342.9 ¢
	Major 6-mosstep	M6ms	2L + 4s	342.9 ¢ to 480.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	240.0 ¢ to 400.0 ¢
	Major 7-mosstep	M7ms	2L + 5s	400.0 ¢ to 480.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	240.0 ¢ to 457.1 ¢
	Major 8-mosstep	M8ms	2L + 6s	457.1 ¢ to 480.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	480.0 ¢ to 514.3 ¢
	Major 9-mosstep	M9ms	3L + 6s	514.3 ¢ to 720.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	480.0 ¢ to 571.4 ¢
	Major 10-mosstep	M10ms	3L + 7s	571.4 ¢ to 720.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	2L + 9s	480.0 ¢ to 628.6 ¢
	Major 11-mosstep	M11ms	3L + 8s	628.6 ¢ to 720.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	480.0 ¢ to 685.7 ¢
	Major 12-mosstep	M12ms	3L + 9s	685.7 ¢ to 720.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	3L + 10s	720.0 ¢ to 742.9 ¢
	Major 13-mosstep	M13ms	4L + 9s	742.9 ¢ to 960.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	3L + 11s	720.0 ¢ to 800.0 ¢
	Major 14-mosstep	M14ms	4L + 10s	800.0 ¢ to 960.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	3L + 12s	720.0 ¢ to 857.1 ¢
	Major 15-mosstep	M15ms	4L + 11s	857.1 ¢ to 960.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	3L + 13s	720.0 ¢ to 914.3 ¢
	Major 16-mosstep	M16ms	4L + 12s	914.3 ¢ to 960.0 ¢
17-mosstep	Perfect 17-mosstep	P17ms	4L + 13s	960.0 ¢ to 971.4 ¢
	Augmented 17-mosstep	A17ms	5L + 12s	971.4 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	4L + 14s	960.0 ¢ to 1028.6 ¢
	Major 18-mosstep	M18ms	5L + 13s	1028.6 ¢ to 1200.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	4L + 15s	960.0 ¢ to 1085.7 ¢
	Major 19-mosstep	M19ms	5L + 14s	1085.7 ¢ to 1200.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	4L + 16s	960.0 ¢ to 1142.9 ¢
	Major 20-mosstep	M20ms	5L + 15s	1142.9 ¢ to 1200.0 ¢
21-mosstep	Perfect 21-mosstep	P21ms	5L + 16s	1200.0 ¢

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 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