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

Intervals

Intervals of 16L 5s

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 75.0¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	75.0¢ to 114.3¢
	Major 2-mosstep	M2ms	2L	114.3¢ to 150.0¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	150.0¢ to 171.4¢
	Major 3-mosstep	M3ms	3L	171.4¢ to 225.0¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	225.0¢ to 228.6¢
	Augmented 4-mosstep	A4ms	4L	228.6¢ to 300.0¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	225.0¢ to 285.7¢
	Major 5-mosstep	M5ms	4L + s	285.7¢ to 300.0¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	300.0¢ to 342.9¢
	Major 6-mosstep	M6ms	5L + s	342.9¢ to 375.0¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	375.0¢ to 400.0¢
	Major 7-mosstep	M7ms	6L + s	400.0¢ to 450.0¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	450.0¢ to 457.1¢
	Major 8-mosstep	M8ms	7L + s	457.1¢ to 525.0¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	450.0¢ to 514.3¢
	Major 9-mosstep	M9ms	7L + 2s	514.3¢ to 525.0¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	525.0¢ to 571.4¢
	Major 10-mosstep	M10ms	8L + 2s	571.4¢ to 600.0¢
11-mosstep	Minor 11-mosstep	m11ms	8L + 3s	600.0¢ to 628.6¢
	Major 11-mosstep	M11ms	9L + 2s	628.6¢ to 675.0¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	675.0¢ to 685.7¢
	Major 12-mosstep	M12ms	10L + 2s	685.7¢ to 750.0¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	675.0¢ to 742.9¢
	Major 13-mosstep	M13ms	10L + 3s	742.9¢ to 750.0¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	750.0¢ to 800.0¢
	Major 14-mosstep	M14ms	11L + 3s	800.0¢ to 825.0¢
15-mosstep	Minor 15-mosstep	m15ms	11L + 4s	825.0¢ to 857.1¢
	Major 15-mosstep	M15ms	12L + 3s	857.1¢ to 900.0¢
16-mosstep	Minor 16-mosstep	m16ms	12L + 4s	900.0¢ to 914.3¢
	Major 16-mosstep	M16ms	13L + 3s	914.3¢ to 975.0¢
17-mosstep	Diminished 17-mosstep	d17ms	12L + 5s	900.0¢ to 971.4¢
	Perfect 17-mosstep	P17ms	13L + 4s	971.4¢ to 975.0¢
18-mosstep	Minor 18-mosstep	m18ms	13L + 5s	975.0¢ to 1028.6¢
	Major 18-mosstep	M18ms	14L + 4s	1028.6¢ to 1050.0¢
19-mosstep	Minor 19-mosstep	m19ms	14L + 5s	1050.0¢ to 1085.7¢
	Major 19-mosstep	M19ms	15L + 4s	1085.7¢ to 1125.0¢
20-mosstep	Minor 20-mosstep	m20ms	15L + 5s	1125.0¢ to 1142.9¢
	Major 20-mosstep	M20ms	16L + 4s	1142.9¢ to 1200.0¢
21-mosstep	Perfect 21-mosstep	P21ms	16L + 5s	1200.0¢

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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