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 ¢)
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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 (giving Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2 ← −6 generators), and that is not complete until 14 tones.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Template:MOS data is deprecated.

Details: Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Scale tree

Scale tree and tuning spectrum of 1L 12s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
12\13						1107.692	92.308	1:1	1.000	Equalized 1L 12s
					61\66	1109.091	90.909	6:5	1.200
				49\53		1109.434	90.566	5:4	1.250
					86\93	1109.677	90.323	9:7	1.286
			37\40			1110.000	90.000	4:3	1.333	Supersoft 1L 12s
					99\107	1110.280	89.720	11:8	1.375
				62\67		1110.448	89.552	7:5	1.400
					87\94	1110.638	89.362	10:7	1.429	Slithy
		25\27				1111.111	88.889	3:2	1.500	Soft 1L 12s
					88\95	1111.579	88.421	11:7	1.571
				63\68		1111.765	88.235	8:5	1.600
					101\109	1111.927	88.073	13:8	1.625	Golden octacot (88.118¢)
			38\41			1112.195	87.805	5:3	1.667	Semisoft 1L 12s
					89\96	1112.500	87.500	12:7	1.714
				51\55		1112.727	87.273	7:4	1.750
					64\69	1113.043	86.957	9:5	1.800
	13\14					1114.286	85.714	2:1	2.000	Basic 1L 12s Scales with tunings softer than this are proper
					53\57	1115.789	84.211	9:4	2.250
				40\43		1116.279	83.721	7:3	2.333
					67\72	1116.667	83.333	12:5	2.400	Marvolo
			27\29			1117.241	82.759	5:2	2.500	Semihard 1L 12s Nautilus
					68\73	1117.808	82.192	13:5	2.600	Unnamed golden tuning
				41\44		1118.182	81.818	8:3	2.667
					55\59	1118.644	81.356	11:4	2.750
		14\15				1120.000	80.000	3:1	3.000	Hard 1L 12s Nuke
					43\46	1121.739	78.261	10:3	3.333	Valentine
				29\31		1122.581	77.419	7:2	3.500
					44\47	1123.404	76.596	11:3	3.667
			15\16			1125.000	75.000	4:1	4.000	Superhard 1L 12s
					31\33	1127.273	72.727	9:2	4.500	Slurpee
				16\17		1129.412	70.588	5:1	5.000
					17\18	1133.333	66.667	6:1	6.000	↓Unicorn
1\1						1200.000	0.000	1:0	→ ∞	Collapsed 1L 12s

Todo: improve synopsis

Rewrite intro with the same information but worded in a way that’s easier to parse.