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 ¢. 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).

↖ 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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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

Tuning spectrum

1/5					240
				8/41	234.146
			7/36		233.333
				13/67	232.836
					232.431
		6/31			232.258
					231.8895
				17/88	231.818
					231.75
			11/57		231.578
				16/83	231.325
	5/26				230.769
				19/99	230.303
					230.268
			14/73		230.137
					230.037
				23/120	230
					229.939
		9/47			229.787
				22/115	229.565
			13/68		229.412
				17/89	229.2135
4/21					228.571