12L 2s

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.

↖ 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 ¢)
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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