5L 12s

↖ 4L 11s	↑ 5L 11s	6L 11s ↗
← 4L 12s	5L 12s	6L 12s →
↙ 4L 13s	↓ 5L 13s	6L 13s ↘

┌╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐ │║││║││║│││║││║││││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssLssLsssLssLsss sssLssLsssLssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	10\17 to 3\5 (705.9 ¢ to 720.0 ¢)
Dark	2\5 to 7\17 (480.0 ¢ to 494.1 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	5L 7s
Sister	12L 5s
Daughters	17L 5s, 5L 17s
Neutralized	10L 7s
2-Flought	22L 12s, 5L 29s
Equal tunings
Equalized (L:s = 1:1)	10\17 (705.9 ¢)
Supersoft (L:s = 4:3)	33\56 (707.1 ¢)
Soft (L:s = 3:2)	23\39 (707.7 ¢)
Semisoft (L:s = 5:3)	36\61 (708.2 ¢)
Basic (L:s = 2:1)	13\22 (709.1 ¢)
Semihard (L:s = 5:2)	29\49 (710.2 ¢)
Hard (L:s = 3:1)	16\27 (711.1 ¢)
Superhard (L:s = 4:1)	19\32 (712.5 ¢)
Collapsed (L:s = 1:0)	3\5 (720.0 ¢)

5L 12s, also called s-enharmonic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 12 small steps, repeating every octave. 5L 12s is a grandchild scale of 5L 2s, expanding it by 10 tones. Generators that produce this scale range from 705.9 ¢ to 720 ¢, or from 480 ¢ to 494.1 ¢.

This scale is characterized by having a diesis (the difference between a large step and two small steps) that is larger than the chroma.

The supra/quasisuper version is proper, but the superpyth/ultrapyth version is improper (it does not become proper until you add 5 more notes to form the superpyth 22-note scale).

Modes

Modes of 5L 12s

UDP	Cyclic order	Step pattern
16|0	1	LssLssLsssLssLsss
15|1	11	LssLsssLssLssLsss
14|2	4	LssLsssLssLsssLss
13|3	14	LsssLssLssLsssLss
12|4	7	LsssLssLsssLssLss
11|5	17	sLssLssLsssLssLss
10|6	10	sLssLsssLssLssLss
9|7	3	sLssLsssLssLsssLs
8|8	13	sLsssLssLssLsssLs
7|9	6	sLsssLssLsssLssLs
6|10	16	ssLssLssLsssLssLs
5|11	9	ssLssLsssLssLssLs
4|12	2	ssLssLsssLssLsssL
3|13	12	ssLsssLssLssLsssL
2|14	5	ssLsssLssLsssLssL
1|15	15	sssLssLssLsssLssL
0|16	8	sssLssLsssLssLssL

Intervals

Intervals of 5L 12s

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 70.6 ¢
	Major 1-mosstep	M1ms	L	70.6 ¢ to 240.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 141.2 ¢
	Major 2-mosstep	M2ms	L + s	141.2 ¢ to 240.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 211.8 ¢
	Major 3-mosstep	M3ms	L + 2s	211.8 ¢ to 240.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	240.0 ¢ to 282.4 ¢
	Major 4-mosstep	M4ms	2L + 2s	282.4 ¢ to 480.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	240.0 ¢ to 352.9 ¢
	Major 5-mosstep	M5ms	2L + 3s	352.9 ¢ to 480.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	240.0 ¢ to 423.5 ¢
	Major 6-mosstep	M6ms	2L + 4s	423.5 ¢ to 480.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	2L + 5s	480.0 ¢ to 494.1 ¢
	Augmented 7-mosstep	A7ms	3L + 4s	494.1 ¢ to 720.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	480.0 ¢ to 564.7 ¢
	Major 8-mosstep	M8ms	3L + 5s	564.7 ¢ to 720.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	480.0 ¢ to 635.3 ¢
	Major 9-mosstep	M9ms	3L + 6s	635.3 ¢ to 720.0 ¢
10-mosstep	Diminished 10-mosstep	d10ms	2L + 8s	480.0 ¢ to 705.9 ¢
	Perfect 10-mosstep	P10ms	3L + 7s	705.9 ¢ to 720.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	3L + 8s	720.0 ¢ to 776.5 ¢
	Major 11-mosstep	M11ms	4L + 7s	776.5 ¢ to 960.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	720.0 ¢ to 847.1 ¢
	Major 12-mosstep	M12ms	4L + 8s	847.1 ¢ to 960.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	3L + 10s	720.0 ¢ to 917.6 ¢
	Major 13-mosstep	M13ms	4L + 9s	917.6 ¢ to 960.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	4L + 10s	960.0 ¢ to 988.2 ¢
	Major 14-mosstep	M14ms	5L + 9s	988.2 ¢ to 1200.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	4L + 11s	960.0 ¢ to 1058.8 ¢
	Major 15-mosstep	M15ms	5L + 10s	1058.8 ¢ to 1200.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	4L + 12s	960.0 ¢ to 1129.4 ¢
	Major 16-mosstep	M16ms	5L + 11s	1129.4 ¢ to 1200.0 ¢
17-mosstep	Perfect 17-mosstep	P17ms	5L + 12s	1200.0 ¢