12L 1s

← 11L 1s	12L 1s	13L 1s →
↙ 11L 2s	↓ 12L 2s	13L 2s ↘

Scale structure
Step pattern	LLLLLLLLLLLLs sLLLLLLLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	1\13 to 1\12 (92.3 ¢ to 100.0 ¢)
Dark	11\12 to 12\13 (1100.0 ¢ to 1107.7 ¢)
TAMNAMS information
Related to	1L 9s (antisinatonic)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	1L 11s
Sister	1L 12s
Daughters	13L 12s, 12L 13s
Neutralized	11L 2s
2-Flought	25L 1s, 12L 14s
Equal tunings
Equalized (L:s = 1:1)	1\13 (92.3 ¢)
Supersoft (L:s = 4:3)	4\51 (94.1 ¢)
Soft (L:s = 3:2)	3\38 (94.7 ¢)
Semisoft (L:s = 5:3)	5\63 (95.2 ¢)
Basic (L:s = 2:1)	2\25 (96.0 ¢)
Semihard (L:s = 5:2)	5\62 (96.8 ¢)
Hard (L:s = 3:1)	3\37 (97.3 ¢)
Superhard (L:s = 4:1)	4\49 (98.0 ¢)
Collapsed (L:s = 1:0)	1\12 (100.0 ¢)
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12L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 1 small step, repeating every octave. 12L 1s is a great-grandchild scale of 1L 9s, expanding it by 3 tones. Generators that produce this scale range from 92.3 ¢ to 100 ¢, or from 1100 ¢ to 1107.7 ¢. Scales of this form are always proper because there is only one small step.

Quasidozenal does not have many regular temperament applications.

However, it becomes a compressed 12edo scale when you ignore the octave (this obviously does not work when the generator is very near 12edo (within -7/24 ¢ of it), for the 13th degree of the scale registers as identical to the octave for human listeners.

And it becomes indistinct from 13edo or 1L 11s in the 1.75 ¢ above 1\13 because the large and small steps register as identical to one another for human listeners).

Modes

Modes of 12L 1s

UDP	Cyclic order	Step pattern
12|0	1	LLLLLLLLLLLLs
11|1	2	LLLLLLLLLLLsL
10|2	3	LLLLLLLLLLsLL
9|3	4	LLLLLLLLLsLLL
8|4	5	LLLLLLLLsLLLL
7|5	6	LLLLLLLsLLLLL
6|6	7	LLLLLLsLLLLLL
5|7	8	LLLLLsLLLLLLL
4|8	9	LLLLsLLLLLLLL
3|9	10	LLLsLLLLLLLLL
2|10	11	LLsLLLLLLLLLL
1|11	12	LsLLLLLLLLLLL
0|12	13	sLLLLLLLLLLLL

Intervals

Intervals of 12L 1s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 92.3 ¢
	Perfect 1-mosstep	P1ms	L	92.3 ¢ to 100.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	100.0 ¢ to 184.6 ¢
	Major 2-mosstep	M2ms	2L	184.6 ¢ to 200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	200.0 ¢ to 276.9 ¢
	Major 3-mosstep	M3ms	3L	276.9 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	300.0 ¢ to 369.2 ¢
	Major 4-mosstep	M4ms	4L	369.2 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	400.0 ¢ to 461.5 ¢
	Major 5-mosstep	M5ms	5L	461.5 ¢ to 500.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	500.0 ¢ to 553.8 ¢
	Major 6-mosstep	M6ms	6L	553.8 ¢ to 600.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	600.0 ¢ to 646.2 ¢
	Major 7-mosstep	M7ms	7L	646.2 ¢ to 700.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	700.0 ¢ to 738.5 ¢
	Major 8-mosstep	M8ms	8L	738.5 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	8L + s	800.0 ¢ to 830.8 ¢
	Major 9-mosstep	M9ms	9L	830.8 ¢ to 900.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	9L + s	900.0 ¢ to 923.1 ¢
	Major 10-mosstep	M10ms	10L	923.1 ¢ to 1000.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	10L + s	1000.0 ¢ to 1015.4 ¢
	Major 11-mosstep	M11ms	11L	1015.4 ¢ to 1100.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	11L + s	1100.0 ¢ to 1107.7 ¢
	Augmented 12-mosstep	A12ms	12L	1107.7 ¢ to 1200.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	12L + s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 12L 1s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\13						92.308	1107.692	1:1	1.000	Equalized 12L 1s
					6\77	93.506	1106.494	6:5	1.200
				5\64		93.750	1106.250	5:4	1.250
					9\115	93.913	1106.087	9:7	1.286
			4\51			94.118	1105.882	4:3	1.333	Supersoft 12L 1s
					11\140	94.286	1105.714	11:8	1.375
				7\89		94.382	1105.618	7:5	1.400
					10\127	94.488	1105.512	10:7	1.429
		3\38				94.737	1105.263	3:2	1.500	Soft 12L 1s
					11\139	94.964	1105.036	11:7	1.571
				8\101		95.050	1104.950	8:5	1.600
					13\164	95.122	1104.878	13:8	1.625
			5\63			95.238	1104.762	5:3	1.667	Semisoft 12L 1s
					12\151	95.364	1104.636	12:7	1.714
				7\88		95.455	1104.545	7:4	1.750
					9\113	95.575	1104.425	9:5	1.800
	2\25					96.000	1104.000	2:1	2.000	Basic 12L 1s
					9\112	96.429	1103.571	9:4	2.250
				7\87		96.552	1103.448	7:3	2.333
					12\149	96.644	1103.356	12:5	2.400
			5\62			96.774	1103.226	5:2	2.500	Semihard 12L 1s
					13\161	96.894	1103.106	13:5	2.600
				8\99		96.970	1103.030	8:3	2.667
					11\136	97.059	1102.941	11:4	2.750
		3\37				97.297	1102.703	3:1	3.000	Hard 12L 1s
					10\123	97.561	1102.439	10:3	3.333
				7\86		97.674	1102.326	7:2	3.500
					11\135	97.778	1102.222	11:3	3.667
			4\49			97.959	1102.041	4:1	4.000	Superhard 12L 1s
					9\110	98.182	1101.818	9:2	4.500
				5\61		98.361	1101.639	5:1	5.000
					6\73	98.630	1101.370	6:1	6.000
1\12						100.000	1100.000	1:0	→ ∞	Collapsed 12L 1s

Todo: cleanup, add etymology Clean up lead section, find out who first proposed the name quasidozenal