12L 3s

12L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 3 small steps, with a period of 4 large steps and 1 small step that repeats every 400.0 ¢, or 3 times every octave. 12L 3s is a grandchild scale of 3L 6s, expanding it by 6 tones. Generators that produce this scale range from 80 ¢ to 100 ¢, or from 300 ¢ to 320 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

↖ 11L 2s	↑ 12L 2s	13L 2s ↗
← 11L 3s	12L 3s	13L 3s →
↙ 11L 4s	↓ 12L 4s	13L 4s ↘

Scale structure
Step pattern	LLLLsLLLLsLLLLs sLLLLsLLLLsLLLL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	1\15 to 1\12 (80.0 ¢ to 100.0 ¢)
Dark	3\12 to 4\15 (300.0 ¢ to 320.0 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	3L 9s
Sister	3L 12s
Daughters	15L 12s, 12L 15s
Neutralized	9L 6s
2-Flought	27L 3s, 12L 18s
Equal tunings
Equalized (L:s = 1:1)	1\15 (80.0 ¢)
Supersoft (L:s = 4:3)	4\57 (84.2 ¢)
Soft (L:s = 3:2)	3\42 (85.7 ¢)
Semisoft (L:s = 5:3)	5\69 (87.0 ¢)
Basic (L:s = 2:1)	2\27 (88.9 ¢)
Semihard (L:s = 5:2)	5\66 (90.9 ¢)
Hard (L:s = 3:1)	3\39 (92.3 ¢)
Superhard (L:s = 4:1)	4\51 (94.1 ¢)
Collapsed (L:s = 1:0)	1\12 (100.0 ¢)
View • Talk • Edit

Having three periods of 4L 1s, it may be more specifically referred to as the Ternary mode of Augene[15].

Modes

Modes of 12L 3s

UDP	Cyclic order	Step pattern
12|0(3)	1	LLLLsLLLLsLLLLs
9|3(3)	2	LLLsLLLLsLLLLsL
6|6(3)	3	LLsLLLLsLLLLsLL
3|9(3)	4	LsLLLLsLLLLsLLL
0|12(3)	5	sLLLLsLLLLsLLLL

Intervals

Intervals of 12L 3s

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 80.0 ¢
	Perfect 1-mosstep	P1ms	L	80.0 ¢ to 100.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	100.0 ¢ to 160.0 ¢
	Major 2-mosstep	M2ms	2L	160.0 ¢ to 200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	200.0 ¢ to 240.0 ¢
	Major 3-mosstep	M3ms	3L	240.0 ¢ to 300.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	300.0 ¢ to 320.0 ¢
	Augmented 4-mosstep	A4ms	4L	320.0 ¢ to 400.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	4L + s	400.0 ¢
6-mosstep	Diminished 6-mosstep	d6ms	4L + 2s	400.0 ¢ to 480.0 ¢
	Perfect 6-mosstep	P6ms	5L + s	480.0 ¢ to 500.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	500.0 ¢ to 560.0 ¢
	Major 7-mosstep	M7ms	6L + s	560.0 ¢ to 600.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	600.0 ¢ to 640.0 ¢
	Major 8-mosstep	M8ms	7L + s	640.0 ¢ to 700.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	7L + 2s	700.0 ¢ to 720.0 ¢
	Augmented 9-mosstep	A9ms	8L + s	720.0 ¢ to 800.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	8L + 2s	800.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	8L + 3s	800.0 ¢ to 880.0 ¢
	Perfect 11-mosstep	P11ms	9L + 2s	880.0 ¢ to 900.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	900.0 ¢ to 960.0 ¢
	Major 12-mosstep	M12ms	10L + 2s	960.0 ¢ to 1000.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	10L + 3s	1000.0 ¢ to 1040.0 ¢
	Major 13-mosstep	M13ms	11L + 2s	1040.0 ¢ to 1100.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	11L + 3s	1100.0 ¢ to 1120.0 ¢
	Augmented 14-mosstep	A14ms	12L + 2s	1120.0 ¢ to 1200.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	12L + 3s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 12L 3s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\15						80.000	320.000	1:1	1.000	Equalized 12L 3s
					6\87	82.759	317.241	6:5	1.200
				5\72		83.333	316.667	5:4	1.250
					9\129	83.721	316.279	9:7	1.286
			4\57			84.211	315.789	4:3	1.333	Supersoft 12L 3s
					11\156	84.615	315.385	11:8	1.375
				7\99		84.848	315.152	7:5	1.400
					10\141	85.106	314.894	10:7	1.429
		3\42				85.714	314.286	3:2	1.500	Soft 12L 3s
					11\153	86.275	313.725	11:7	1.571
				8\111		86.486	313.514	8:5	1.600
					13\180	86.667	313.333	13:8	1.625
			5\69			86.957	313.043	5:3	1.667	Semisoft 12L 3s
					12\165	87.273	312.727	12:7	1.714
				7\96		87.500	312.500	7:4	1.750
					9\123	87.805	312.195	9:5	1.800
	2\27					88.889	311.111	2:1	2.000	Basic 12L 3s
					9\120	90.000	310.000	9:4	2.250
				7\93		90.323	309.677	7:3	2.333
					12\159	90.566	309.434	12:5	2.400
			5\66			90.909	309.091	5:2	2.500	Semihard 12L 3s
					13\171	91.228	308.772	13:5	2.600
				8\105		91.429	308.571	8:3	2.667
					11\144	91.667	308.333	11:4	2.750
		3\39				92.308	307.692	3:1	3.000	Hard 12L 3s
					10\129	93.023	306.977	10:3	3.333
				7\90		93.333	306.667	7:2	3.500
					11\141	93.617	306.383	11:3	3.667
			4\51			94.118	305.882	4:1	4.000	Superhard 12L 3s
					9\114	94.737	305.263	9:2	4.500
				5\63		95.238	304.762	5:1	5.000
					6\75	96.000	304.000	6:1	6.000
1\12						100.000	300.000	1:0	→ ∞	Collapsed 12L 3s