1L 12s

	↑ 1L 11s	2L 11s ↗
	1L 12s	2L 12s →
	↓ 1L 13s	2L 13s ↘

Scale structure
Step pattern	Lssssssssssss ssssssssssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	12\13 to 1\1 (1107.7 ¢ to 1200.0 ¢)
Dark	0\1 to 1\13 (0.0 ¢ to 92.3 ¢)
TAMNAMS information
Related to	1L 9s (antisinatonic)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	1L 11s
Sister	12L 1s
Daughters	13L 1s, 1L 13s
Neutralized	2L 11s
2-Flought	14L 12s, 1L 25s
Equal tunings
Equalized (L:s = 1:1)	12\13 (1107.7 ¢)
Supersoft (L:s = 4:3)	37\40 (1110.0 ¢)
Soft (L:s = 3:2)	25\27 (1111.1 ¢)
Semisoft (L:s = 5:3)	38\41 (1112.2 ¢)
Basic (L:s = 2:1)	13\14 (1114.3 ¢)
Semihard (L:s = 5:2)	27\29 (1117.2 ¢)
Hard (L:s = 3:1)	14\15 (1120.0 ¢)
Superhard (L:s = 4:1)	15\16 (1125.0 ¢)
Collapsed (L:s = 1:0)	1\1 (1200.0 ¢)
View • Talk • Edit

1L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 12 small steps, repeating every octave. 1L 12s is a great-grandchild scale of 1L 9s, expanding it by 3 tones. Generators that produce this scale range from 1107.7 ¢ to 1200 ¢, or from 0 ¢ to 92.3 ¢. This MOS, also called the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.

Modes

Modes of 1L 12s

UDP	Cyclic order	Step pattern
12|0	1	Lssssssssssss
11|1	13	sLsssssssssss
10|2	12	ssLssssssssss
9|3	11	sssLsssssssss
8|4	10	ssssLssssssss
7|5	9	sssssLsssssss
6|6	8	ssssssLssssss
5|7	7	sssssssLsssss
4|8	6	ssssssssLssss
3|9	5	sssssssssLsss
2|10	4	ssssssssssLss
1|11	3	sssssssssssLs
0|12	2	ssssssssssssL

Scale tree

		Cents
0/1		0
1/17		70.588
	4/67	71.641
	3/50	72
	2/33	72.727
	3/49	73.469
	4/65	73.846
	5/81	74.074
1/16		75
	3/47	76.596
	2/31	77.419
	3/46	78.261
	4/61	78.6885
	5/76	78.947
	6/91	79.121
		1200/(12+pi)
1/15		80
		1200/(12+e)
	3/44	81.818
		1200/(13+phi)
	2/29	82.759
	3/43	83.721
	4/57	84.2105
1/14		85.714
	4/55	86.364
		1200/(12+sqrt(3))
	3/41	87.805
		1200/(12+phi)
	5/68	88.235
		1200/(12+pi/2)
2/27		88.889
	5/67	89.552
3/40		90
4/53		90.556
1/13		92.308