12L 2s

↖ 11L 1s	↑ 12L 1s	13L 1s ↗
← 11L 2s	12L 2s	13L 2s →
↙ 11L 3s	↓ 12L 3s	13L 3s ↘

┌╥╥╥╥╥╥┬╥╥╥╥╥╥┬┐ │║║║║║║│║║║║║║││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLsLLLLLLs sLLLLLLsLLLLLL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	1\14 to 1\12 (85.7 ¢ to 100.0 ¢)
Dark	5\12 to 6\14 (500.0 ¢ to 514.3 ¢)
TAMNAMS information
Related to	2L 8s (jaric)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	2L 10s
Sister	2L 12s
Daughters	14L 12s, 12L 14s
Neutralized	10L 4s
2-Flought	26L 2s, 12L 16s
Equal tunings
Equalized (L:s = 1:1)	1\14 (85.7 ¢)
Supersoft (L:s = 4:3)	4\54 (88.9 ¢)
Soft (L:s = 3:2)	3\40 (90.0 ¢)
Semisoft (L:s = 5:3)	5\66 (90.9 ¢)
Basic (L:s = 2:1)	2\26 (92.3 ¢)
Semihard (L:s = 5:2)	5\64 (93.8 ¢)
Hard (L:s = 3:1)	3\38 (94.7 ¢)
Superhard (L:s = 4:1)	4\50 (96.0 ¢)
Collapsed (L:s = 1:0)	1\12 (100.0 ¢)

12L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 2 small steps, with a period of 6 large steps and 1 small step that repeats every 600.0 ¢, or twice every octave. 12L 2s is a grandchild scale of 2L 8s, expanding it by 4 tones. Generators that produce this scale range from 85.7 ¢ to 100 ¢, or from 500 ¢ to 514.3 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

It appears as the mega chromatic scale of injera temperament, meaning that its harmonic entropy is where +4 generators equals 5/4 (simple) or +10 generators equals 5/3 (complex).

Modes

Modes of 12L 2s

UDP	Cyclic order	Step pattern
12|0(2)	1	LLLLLLsLLLLLLs
10|2(2)	2	LLLLLsLLLLLLsL
8|4(2)	3	LLLLsLLLLLLsLL
6|6(2)	4	LLLsLLLLLLsLLL
4|8(2)	5	LLsLLLLLLsLLLL
2|10(2)	6	LsLLLLLLsLLLLL
0|12(2)	7	sLLLLLLsLLLLLL

Intervals

Intervals of 12L 2s

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 85.7 ¢
	Perfect 1-mosstep	P1ms	L	85.7 ¢ to 100.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	100.0 ¢ to 171.4 ¢
	Major 2-mosstep	M2ms	2L	171.4 ¢ to 200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	200.0 ¢ to 257.1 ¢
	Major 3-mosstep	M3ms	3L	257.1 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	300.0 ¢ to 342.9 ¢
	Major 4-mosstep	M4ms	4L	342.9 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	400.0 ¢ to 428.6 ¢
	Major 5-mosstep	M5ms	5L	428.6 ¢ to 500.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	5L + s	500.0 ¢ to 514.3 ¢
	Augmented 6-mosstep	A6ms	6L	514.3 ¢ to 600.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	6L + s	600.0 ¢
8-mosstep	Diminished 8-mosstep	d8ms	6L + 2s	600.0 ¢ to 685.7 ¢
	Perfect 8-mosstep	P8ms	7L + s	685.7 ¢ to 700.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	700.0 ¢ to 771.4 ¢
	Major 9-mosstep	M9ms	8L + s	771.4 ¢ to 800.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	800.0 ¢ to 857.1 ¢
	Major 10-mosstep	M10ms	9L + s	857.1 ¢ to 900.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	900.0 ¢ to 942.9 ¢
	Major 11-mosstep	M11ms	10L + s	942.9 ¢ to 1000.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	1000.0 ¢ to 1028.6 ¢
	Major 12-mosstep	M12ms	11L + s	1028.6 ¢ to 1100.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	11L + 2s	1100.0 ¢ to 1114.3 ¢
	Augmented 13-mosstep	A13ms	12L + s	1114.3 ¢ to 1200.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	12L + 2s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 12L 2s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\14						85.714	514.286	1:1	1.000	Equalized 12L 2s
					6\82	87.805	512.195	6:5	1.200
				5\68		88.235	511.765	5:4	1.250
					9\122	88.525	511.475	9:7	1.286
			4\54			88.889	511.111	4:3	1.333	Supersoft 12L 2s
					11\148	89.189	510.811	11:8	1.375
				7\94		89.362	510.638	7:5	1.400
					10\134	89.552	510.448	10:7	1.429
		3\40				90.000	510.000	3:2	1.500	Soft 12L 2s
					11\146	90.411	509.589	11:7	1.571
				8\106		90.566	509.434	8:5	1.600
					13\172	90.698	509.302	13:8	1.625
			5\66			90.909	509.091	5:3	1.667	Semisoft 12L 2s
					12\158	91.139	508.861	12:7	1.714
				7\92		91.304	508.696	7:4	1.750
					9\118	91.525	508.475	9:5	1.800
	2\26					92.308	507.692	2:1	2.000	Basic 12L 2s
					9\116	93.103	506.897	9:4	2.250
				7\90		93.333	506.667	7:3	2.333
					12\154	93.506	506.494	12:5	2.400
			5\64			93.750	506.250	5:2	2.500	Semihard 12L 2s
					13\166	93.976	506.024	13:5	2.600
				8\102		94.118	505.882	8:3	2.667
					11\140	94.286	505.714	11:4	2.750
		3\38				94.737	505.263	3:1	3.000	Hard 12L 2s Injera
					10\126	95.238	504.762	10:3	3.333
				7\88		95.455	504.545	7:2	3.500
					11\138	95.652	504.348	11:3	3.667
			4\50			96.000	504.000	4:1	4.000	Superhard 12L 2s
					9\112	96.429	503.571	9:2	4.500
				5\62		96.774	503.226	5:1	5.000
					6\74	97.297	502.703	6:1	6.000
1\12						100.000	500.000	1:0	→ ∞	Collapsed 12L 2s