3L 16s

3L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 16 small steps, repeating every octave. 3L 16s is a great-grandchild scale of 3L 7s, expanding it by 9 tones. Generators that produce this scale range from 378.9 ¢ to 400 ¢, or from 800 ¢ to 821.1 ¢.

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

Scale structure
Step pattern	LsssssLsssssLssssss ssssssLsssssLsssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	6\19 to 1\3 (378.9 ¢ to 400.0 ¢)
Dark	2\3 to 13\19 (800.0 ¢ to 821.1 ¢)
TAMNAMS information
Related to	3L 7s (sephiroid)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	3L 13s
Sister	16L 3s
Daughters	19L 3s, 3L 19s
Neutralized	6L 13s
2-Flought	22L 16s, 3L 35s
Equal tunings
Equalized (L:s = 1:1)	6\19 (378.9 ¢)
Supersoft (L:s = 4:3)	19\60 (380.0 ¢)
Soft (L:s = 3:2)	13\41 (380.5 ¢)
Semisoft (L:s = 5:3)	20\63 (381.0 ¢)
Basic (L:s = 2:1)	7\22 (381.8 ¢)
Semihard (L:s = 5:2)	15\47 (383.0 ¢)
Hard (L:s = 3:1)	8\25 (384.0 ¢)
Superhard (L:s = 4:1)	9\28 (385.7 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)
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This scale is associated with magic temperament, where 5 bright generators maps to 3/1 and the generator is a flat 5/4, and würschmidt temperament, where 8 bright generators map to 6/1 and the generator is a slightly sharp 5/4.

Modes

Modes of 3L 16s

UDP	Cyclic order	Step pattern
18|0	1	LsssssLsssssLssssss
17|1	7	LsssssLssssssLsssss
16|2	13	LssssssLsssssLsssss
15|3	19	sLsssssLsssssLsssss
14|4	6	sLsssssLssssssLssss
13|5	12	sLssssssLsssssLssss
12|6	18	ssLsssssLsssssLssss
11|7	5	ssLsssssLssssssLsss
10|8	11	ssLssssssLsssssLsss
9|9	17	sssLsssssLsssssLsss
8|10	4	sssLsssssLssssssLss
7|11	10	sssLssssssLsssssLss
6|12	16	ssssLsssssLsssssLss
5|13	3	ssssLsssssLssssssLs
4|14	9	ssssLssssssLsssssLs
3|15	15	sssssLsssssLsssssLs
2|16	2	sssssLsssssLssssssL
1|17	8	sssssLssssssLsssssL
0|18	14	ssssssLsssssLsssssL

Intervals

Intervals of 3L 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 63.2 ¢
	Major 1-mosstep	M1ms	L	63.2 ¢ to 400.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 126.3 ¢
	Major 2-mosstep	M2ms	L + s	126.3 ¢ to 400.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 189.5 ¢
	Major 3-mosstep	M3ms	L + 2s	189.5 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 252.6 ¢
	Major 4-mosstep	M4ms	L + 3s	252.6 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 315.8 ¢
	Major 5-mosstep	M5ms	L + 4s	315.8 ¢ to 400.0 ¢
6-mosstep	Diminished 6-mosstep	d6ms	6s	0.0 ¢ to 378.9 ¢
	Perfect 6-mosstep	P6ms	L + 5s	378.9 ¢ to 400.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	400.0 ¢ to 442.1 ¢
	Major 7-mosstep	M7ms	2L + 5s	442.1 ¢ to 800.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	400.0 ¢ to 505.3 ¢
	Major 8-mosstep	M8ms	2L + 6s	505.3 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	400.0 ¢ to 568.4 ¢
	Major 9-mosstep	M9ms	2L + 7s	568.4 ¢ to 800.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	400.0 ¢ to 631.6 ¢
	Major 10-mosstep	M10ms	2L + 8s	631.6 ¢ to 800.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	400.0 ¢ to 694.7 ¢
	Major 11-mosstep	M11ms	2L + 9s	694.7 ¢ to 800.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	400.0 ¢ to 757.9 ¢
	Major 12-mosstep	M12ms	2L + 10s	757.9 ¢ to 800.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	2L + 11s	800.0 ¢ to 821.1 ¢
	Augmented 13-mosstep	A13ms	3L + 10s	821.1 ¢ to 1200.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	800.0 ¢ to 884.2 ¢
	Major 14-mosstep	M14ms	3L + 11s	884.2 ¢ to 1200.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	800.0 ¢ to 947.4 ¢
	Major 15-mosstep	M15ms	3L + 12s	947.4 ¢ to 1200.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	2L + 14s	800.0 ¢ to 1010.5 ¢
	Major 16-mosstep	M16ms	3L + 13s	1010.5 ¢ to 1200.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	2L + 15s	800.0 ¢ to 1073.7 ¢
	Major 17-mosstep	M17ms	3L + 14s	1073.7 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	2L + 16s	800.0 ¢ to 1136.8 ¢
	Major 18-mosstep	M18ms	3L + 15s	1136.8 ¢ to 1200.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	3L + 16s	1200.0 ¢

Scale tree

{{MOS tuning spectrum | depth = 5 | 11/8 = Witchcraft | 3/2 = Magic is around here | 13/8 = Necromancy
Golden magic (380.8191 ¢) | 12/5 = Marveltri is around here | 13/5 = Unnamed golden tuning (383.2314 ¢) | 9/2 = Sulis | 5/1 = Grendel/Würschmidt }