5L 16s

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← 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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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.

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 ¢

Generator chain

Generator chain of 5L 16s

Bright gens	Scale degree	Abbrev.
25	Augmented 16-mosdegree	A16md
24	Augmented 12-mosdegree	A12md
23	Augmented 8-mosdegree	A8md
22	Augmented 4-mosdegree	A4md
21	Augmented 0-mosdegree	A0md
20	Augmented 17-mosdegree	A17md
19	Major 13-mosdegree	M13md
18	Major 9-mosdegree	M9md
17	Major 5-mosdegree	M5md
16	Major 1-mosdegree	M1md
15	Major 18-mosdegree	M18md
14	Major 14-mosdegree	M14md
13	Major 10-mosdegree	M10md
12	Major 6-mosdegree	M6md
11	Major 2-mosdegree	M2md
10	Major 19-mosdegree	M19md
9	Major 15-mosdegree	M15md
8	Major 11-mosdegree	M11md
7	Major 7-mosdegree	M7md
6	Major 3-mosdegree	M3md
5	Major 20-mosdegree	M20md
4	Major 16-mosdegree	M16md
3	Major 12-mosdegree	M12md
2	Major 8-mosdegree	M8md
1	Perfect 4-mosdegree	P4md
0	Perfect 0-mosdegree Perfect 21-mosdegree	P0md P21md
−1	Perfect 17-mosdegree	P17md
−2	Minor 13-mosdegree	m13md
−3	Minor 9-mosdegree	m9md
−4	Minor 5-mosdegree	m5md
−5	Minor 1-mosdegree	m1md
−6	Minor 18-mosdegree	m18md
−7	Minor 14-mosdegree	m14md
−8	Minor 10-mosdegree	m10md
−9	Minor 6-mosdegree	m6md
−10	Minor 2-mosdegree	m2md
−11	Minor 19-mosdegree	m19md
−12	Minor 15-mosdegree	m15md
−13	Minor 11-mosdegree	m11md
−14	Minor 7-mosdegree	m7md
−15	Minor 3-mosdegree	m3md
−16	Minor 20-mosdegree	m20md
−17	Minor 16-mosdegree	m16md
−18	Minor 12-mosdegree	m12md
−19	Minor 8-mosdegree	m8md
−20	Diminished 4-mosdegree	d4md
−21	Diminished 21-mosdegree	d21md
−22	Diminished 17-mosdegree	d17md
−23	Diminished 13-mosdegree	d13md
−24	Diminished 9-mosdegree	d9md
−25	Diminished 5-mosdegree	d5md

Modes

Scale degrees of the modes of 5L 16s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
20|0	1	LsssLsssLsssLsssLssss	Perf.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Perf.
19|1	5	LsssLsssLsssLssssLsss	Perf.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Perf.
18|2	9	LsssLsssLssssLsssLsss	Perf.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Perf.
17|3	13	LsssLssssLsssLsssLsss	Perf.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Perf.
16|4	17	LssssLsssLsssLsssLsss	Perf.	Maj.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Perf.
15|5	21	sLsssLsssLsssLsssLsss	Perf.	Min.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Perf.
14|6	4	sLsssLsssLsssLssssLss	Perf.	Min.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Perf.
13|7	8	sLsssLsssLssssLsssLss	Perf.	Min.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Perf.
12|8	12	sLsssLssssLsssLsssLss	Perf.	Min.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Perf.
11|9	16	sLssssLsssLsssLsssLss	Perf.	Min.	Maj.	Maj.	Perf.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Perf.
10|10	20	ssLsssLsssLsssLsssLss	Perf.	Min.	Min.	Maj.	Perf.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Perf.
9|11	3	ssLsssLsssLsssLssssLs	Perf.	Min.	Min.	Maj.	Perf.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Perf.	Min.	Min.	Maj.	Perf.
8|12	7	ssLsssLsssLssssLsssLs	Perf.	Min.	Min.	Maj.	Perf.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Min.	Maj.	Perf.	Min.	Min.	Maj.	Perf.
7|13	11	ssLsssLssssLsssLsssLs	Perf.	Min.	Min.	Maj.	Perf.	Min.	Min.	Maj.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Perf.	Min.	Min.	Maj.	Perf.
6|14	15	ssLssssLsssLsssLsssLs	Perf.	Min.	Min.	Maj.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Perf.	Min.	Min.	Maj.	Perf.
5|15	19	sssLsssLsssLsssLsssLs	Perf.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Perf.	Min.	Min.	Maj.	Perf.
4|16	2	sssLsssLsssLsssLssssL	Perf.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Perf.	Min.	Min.	Min.	Perf.
3|17	6	sssLsssLsssLssssLsssL	Perf.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Perf.
2|18	10	sssLsssLssssLsssLsssL	Perf.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Perf.
1|19	14	sssLssssLsssLsssLsssL	Perf.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Perf.
0|20	18	ssssLsssLsssLsssLsssL	Perf.	Min.	Min.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Perf.

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