16L 3s

↖ 15L 2s	↑ 16L 2s	17L 2s ↗
← 15L 3s	16L 3s	17L 3s →
↙ 15L 4s	↓ 16L 4s	17L 4s ↘

┌╥╥╥╥╥╥┬╥╥╥╥╥┬╥╥╥╥╥┬┐ │║║║║║║│║║║║║│║║║║║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLsLLLLLsLLLLLs sLLLLLsLLLLLsLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	13\19 to 11\16 (821.1 ¢ to 825.0 ¢)
Dark	5\16 to 6\19 (375.0 ¢ to 378.9 ¢)
TAMNAMS information
Related to	3L 7s (sephiroid)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	3L 13s
Sister	3L 16s
Daughters	19L 16s, 16L 19s
Neutralized	13L 6s
2-Flought	35L 3s, 16L 22s
Equal tunings
Equalized (L:s = 1:1)	13\19 (821.1 ¢)
Supersoft (L:s = 4:3)	50\73 (821.9 ¢)
Soft (L:s = 3:2)	37\54 (822.2 ¢)
Semisoft (L:s = 5:3)	61\89 (822.5 ¢)
Basic (L:s = 2:1)	24\35 (822.9 ¢)
Semihard (L:s = 5:2)	59\86 (823.3 ¢)
Hard (L:s = 3:1)	35\51 (823.5 ¢)
Superhard (L:s = 4:1)	46\67 (823.9 ¢)
Collapsed (L:s = 1:0)	11\16 (825.0 ¢)

16L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 3 small steps, repeating every octave. 16L 3s is a great-grandchild scale of 3L 7s, expanding it by 9 tones. Generators that produce this scale range from 821.1 ¢ to 825 ¢, or from 375 ¢ to 378.9 ¢.

Modes

Modes of 16L 3s

UDP	Cyclic order	Step pattern
18|0	1	LLLLLLsLLLLLsLLLLLs
17|1	14	LLLLLsLLLLLLsLLLLLs
16|2	8	LLLLLsLLLLLsLLLLLLs
15|3	2	LLLLLsLLLLLsLLLLLsL
14|4	15	LLLLsLLLLLLsLLLLLsL
13|5	9	LLLLsLLLLLsLLLLLLsL
12|6	3	LLLLsLLLLLsLLLLLsLL
11|7	16	LLLsLLLLLLsLLLLLsLL
10|8	10	LLLsLLLLLsLLLLLLsLL
9|9	4	LLLsLLLLLsLLLLLsLLL
8|10	17	LLsLLLLLLsLLLLLsLLL
7|11	11	LLsLLLLLsLLLLLLsLLL
6|12	5	LLsLLLLLsLLLLLsLLLL
5|13	18	LsLLLLLLsLLLLLsLLLL
4|14	12	LsLLLLLsLLLLLLsLLLL
3|15	6	LsLLLLLsLLLLLsLLLLL
2|16	19	sLLLLLLsLLLLLsLLLLL
1|17	13	sLLLLLsLLLLLLsLLLLL
0|18	7	sLLLLLsLLLLLsLLLLLL

Intervals

Intervals of 16L 3s

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 63.2 ¢
	Major 1-mosstep	M1ms	L	63.2 ¢ to 75.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	75.0 ¢ to 126.3 ¢
	Major 2-mosstep	M2ms	2L	126.3 ¢ to 150.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	150.0 ¢ to 189.5 ¢
	Major 3-mosstep	M3ms	3L	189.5 ¢ to 225.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	225.0 ¢ to 252.6 ¢
	Major 4-mosstep	M4ms	4L	252.6 ¢ to 300.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	300.0 ¢ to 315.8 ¢
	Major 5-mosstep	M5ms	5L	315.8 ¢ to 375.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	5L + s	375.0 ¢ to 378.9 ¢
	Augmented 6-mosstep	A6ms	6L	378.9 ¢ to 450.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	375.0 ¢ to 442.1 ¢
	Major 7-mosstep	M7ms	6L + s	442.1 ¢ to 450.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	450.0 ¢ to 505.3 ¢
	Major 8-mosstep	M8ms	7L + s	505.3 ¢ to 525.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	525.0 ¢ to 568.4 ¢
	Major 9-mosstep	M9ms	8L + s	568.4 ¢ to 600.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	600.0 ¢ to 631.6 ¢
	Major 10-mosstep	M10ms	9L + s	631.6 ¢ to 675.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	675.0 ¢ to 694.7 ¢
	Major 11-mosstep	M11ms	10L + s	694.7 ¢ to 750.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	750.0 ¢ to 757.9 ¢
	Major 12-mosstep	M12ms	11L + s	757.9 ¢ to 825.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	10L + 3s	750.0 ¢ to 821.1 ¢
	Perfect 13-mosstep	P13ms	11L + 2s	821.1 ¢ to 825.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	11L + 3s	825.0 ¢ to 884.2 ¢
	Major 14-mosstep	M14ms	12L + 2s	884.2 ¢ to 900.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	12L + 3s	900.0 ¢ to 947.4 ¢
	Major 15-mosstep	M15ms	13L + 2s	947.4 ¢ to 975.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	13L + 3s	975.0 ¢ to 1010.5 ¢
	Major 16-mosstep	M16ms	14L + 2s	1010.5 ¢ to 1050.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	14L + 3s	1050.0 ¢ to 1073.7 ¢
	Major 17-mosstep	M17ms	15L + 2s	1073.7 ¢ to 1125.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	15L + 3s	1125.0 ¢ to 1136.8 ¢
	Major 18-mosstep	M18ms	16L + 2s	1136.8 ¢ to 1200.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	16L + 3s	1200.0 ¢

Scale tree

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