16L 5s

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

┌╥╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║║│║║║│║║║│║║║│║║║││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLsLLLsLLLsLLLsLLLs sLLLsLLLsLLLsLLLsLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	17\21 to 13\16 (971.4¢ to 975.0¢)
Dark	3\16 to 4\21 (225.0¢ to 228.6¢)
TAMNAMS information
Descends from	5L 1s (machinoid)
Ancestor's step ratio range	3:1 to 4:1 (parahard)
Related MOS scales
Parent	5L 11s
Sister	5L 16s
Daughters	21L 16s, 16L 21s
Neutralized	11L 10s
2-Flought	37L 5s, 16L 26s
Equal tunings
Equalized (L:s = 1:1)	17\21 (971.4¢)
Supersoft (L:s = 4:3)	64\79 (972.2¢)
Soft (L:s = 3:2)	47\58 (972.4¢)
Semisoft (L:s = 5:3)	77\95 (972.6¢)
Basic (L:s = 2:1)	30\37 (973.0¢)
Semihard (L:s = 5:2)	73\90 (973.3¢)
Hard (L:s = 3:1)	43\53 (973.6¢)
Superhard (L:s = 4:1)	56\69 (973.9¢)
Collapsed (L:s = 1:0)	13\16 (975.0¢)

16L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 5 small steps, repeating every octave. 16L 5s is a great-grandchild scale of 5L 1s, expanding it by 15 tones. Generators that produce this scale range from 971.4¢ to 975¢, or from 225¢ to 228.6¢.

Modes

Modes of 16L 5s

UDP	Cyclic order	Step pattern
20|0	1	LLLLsLLLsLLLsLLLsLLLs
19|1	18	LLLsLLLLsLLLsLLLsLLLs
18|2	14	LLLsLLLsLLLLsLLLsLLLs
17|3	10	LLLsLLLsLLLsLLLLsLLLs
16|4	6	LLLsLLLsLLLsLLLsLLLLs
15|5	2	LLLsLLLsLLLsLLLsLLLsL
14|6	19	LLsLLLLsLLLsLLLsLLLsL
13|7	15	LLsLLLsLLLLsLLLsLLLsL
12|8	11	LLsLLLsLLLsLLLLsLLLsL
11|9	7	LLsLLLsLLLsLLLsLLLLsL
10|10	3	LLsLLLsLLLsLLLsLLLsLL
9|11	20	LsLLLLsLLLsLLLsLLLsLL
8|12	16	LsLLLsLLLLsLLLsLLLsLL
7|13	12	LsLLLsLLLsLLLLsLLLsLL
6|14	8	LsLLLsLLLsLLLsLLLLsLL
5|15	4	LsLLLsLLLsLLLsLLLsLLL
4|16	21	sLLLLsLLLsLLLsLLLsLLL
3|17	17	sLLLsLLLLsLLLsLLLsLLL
2|18	13	sLLLsLLLsLLLLsLLLsLLL
1|19	9	sLLLsLLLsLLLsLLLLsLLL
0|20	5	sLLLsLLLsLLLsLLLsLLLL

Scale tree

Scale Tree and Tuning Spectrum of 16L 5s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
17\21						971.429	228.571	1:1	1.000	Equalized 16L 5s
					98\121	971.901	228.099	6:5	1.200
				81\100		972.000	228.000	5:4	1.250
					145\179	972.067	227.933	9:7	1.286
			64\79			972.152	227.848	4:3	1.333	Supersoft 16L 5s
					175\216	972.222	227.778	11:8	1.375
				111\137		972.263	227.737	7:5	1.400
					158\195	972.308	227.692	10:7	1.429
		47\58				972.414	227.586	3:2	1.500	Soft 16L 5s
					171\211	972.512	227.488	11:7	1.571
				124\153		972.549	227.451	8:5	1.600
					201\248	972.581	227.419	13:8	1.625
			77\95			972.632	227.368	5:3	1.667	Semisoft 16L 5s
					184\227	972.687	227.313	12:7	1.714
				107\132		972.727	227.273	7:4	1.750
					137\169	972.781	227.219	9:5	1.800
	30\37					972.973	227.027	2:1	2.000	Basic 16L 5s Scales with tunings softer than this are proper
					133\164	973.171	226.829	9:4	2.250
				103\127		973.228	226.772	7:3	2.333
					176\217	973.272	226.728	12:5	2.400
			73\90			973.333	226.667	5:2	2.500	Semihard 16L 5s
					189\233	973.391	226.609	13:5	2.600
				116\143		973.427	226.573	8:3	2.667
					159\196	973.469	226.531	11:4	2.750
		43\53				973.585	226.415	3:1	3.000	Hard 16L 5s
					142\175	973.714	226.286	10:3	3.333
				99\122		973.770	226.230	7:2	3.500
					155\191	973.822	226.178	11:3	3.667
			56\69			973.913	226.087	4:1	4.000	Superhard 16L 5s
					125\154	974.026	225.974	9:2	4.500
				69\85		974.118	225.882	5:1	5.000
					82\101	974.257	225.743	6:1	6.000
13\16						975.000	225.000	1:0	→ ∞	Collapsed 16L 5s

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