12L 4s

12L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 4 small steps, with a period of 3 large steps and 1 small step that repeats every 300.0 ¢, or 4 times every octave. 12L 4s is a grandchild scale of 4L 4s, expanding it by 8 tones. Generators that produce this scale range from 75 ¢ to 100 ¢, or from 200 ¢ to 225 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

↖ 11L 3s	↑ 12L 3s	13L 3s ↗
← 11L 4s	12L 4s	13L 4s →
↙ 11L 5s	↓ 12L 5s	13L 5s ↘

Scale structure
Step pattern	LLLsLLLsLLLsLLLs sLLLsLLLsLLLsLLL
Equave	2/1 (1200.0 ¢)
Period	1\4 (300.0 ¢)
Generator size
Bright	1\16 to 1\12 (75.0 ¢ to 100.0 ¢)
Dark	2\12 to 3\16 (200.0 ¢ to 225.0 ¢)
TAMNAMS information
Related to	4L 4s (tetrawood)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	4L 8s
Sister	4L 12s
Daughters	16L 12s, 12L 16s
Neutralized	8L 8s
2-Flought	28L 4s, 12L 20s
Equal tunings
Equalized (L:s = 1:1)	1\16 (75.0 ¢)
Supersoft (L:s = 4:3)	4\60 (80.0 ¢)
Soft (L:s = 3:2)	3\44 (81.8 ¢)
Semisoft (L:s = 5:3)	5\72 (83.3 ¢)
Basic (L:s = 2:1)	2\28 (85.7 ¢)
Semihard (L:s = 5:2)	5\68 (88.2 ¢)
Hard (L:s = 3:1)	3\40 (90.0 ¢)
Superhard (L:s = 4:1)	4\52 (92.3 ¢)
Collapsed (L:s = 1:0)	1\12 (100.0 ¢)
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Modes

Modes of 12L 4s

UDP	Cyclic order	Step pattern
12|0(4)	1	LLLsLLLsLLLsLLLs
8|4(4)	2	LLsLLLsLLLsLLLsL
4|8(4)	3	LsLLLsLLLsLLLsLL
0|12(4)	4	sLLLsLLLsLLLsLLL

Intervals

Intervals of 12L 4s

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 75.0 ¢
	Perfect 1-mosstep	P1ms	L	75.0 ¢ to 100.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	100.0 ¢ to 150.0 ¢
	Major 2-mosstep	M2ms	2L	150.0 ¢ to 200.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	200.0 ¢ to 225.0 ¢
	Augmented 3-mosstep	A3ms	3L	225.0 ¢ to 300.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	300.0 ¢
5-mosstep	Diminished 5-mosstep	d5ms	3L + 2s	300.0 ¢ to 375.0 ¢
	Perfect 5-mosstep	P5ms	4L + s	375.0 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	400.0 ¢ to 450.0 ¢
	Major 6-mosstep	M6ms	5L + s	450.0 ¢ to 500.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	500.0 ¢ to 525.0 ¢
	Augmented 7-mosstep	A7ms	6L + s	525.0 ¢ to 600.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	6L + 2s	600.0 ¢
9-mosstep	Diminished 9-mosstep	d9ms	6L + 3s	600.0 ¢ to 675.0 ¢
	Perfect 9-mosstep	P9ms	7L + 2s	675.0 ¢ to 700.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	700.0 ¢ to 750.0 ¢
	Major 10-mosstep	M10ms	8L + 2s	750.0 ¢ to 800.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	8L + 3s	800.0 ¢ to 825.0 ¢
	Augmented 11-mosstep	A11ms	9L + 2s	825.0 ¢ to 900.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	9L + 3s	900.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	9L + 4s	900.0 ¢ to 975.0 ¢
	Perfect 13-mosstep	P13ms	10L + 3s	975.0 ¢ to 1000.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	1000.0 ¢ to 1050.0 ¢
	Major 14-mosstep	M14ms	11L + 3s	1050.0 ¢ to 1100.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	11L + 4s	1100.0 ¢ to 1125.0 ¢
	Augmented 15-mosstep	A15ms	12L + 3s	1125.0 ¢ to 1200.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	12L + 4s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 12L 4s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\16						75.000	225.000	1:1	1.000	Equalized 12L 4s
					6\92	78.261	221.739	6:5	1.200
				5\76		78.947	221.053	5:4	1.250
					9\136	79.412	220.588	9:7	1.286
			4\60			80.000	220.000	4:3	1.333	Supersoft 12L 4s
					11\164	80.488	219.512	11:8	1.375
				7\104		80.769	219.231	7:5	1.400
					10\148	81.081	218.919	10:7	1.429
		3\44				81.818	218.182	3:2	1.500	Soft 12L 4s
					11\160	82.500	217.500	11:7	1.571
				8\116		82.759	217.241	8:5	1.600
					13\188	82.979	217.021	13:8	1.625
			5\72			83.333	216.667	5:3	1.667	Semisoft 12L 4s
					12\172	83.721	216.279	12:7	1.714
				7\100		84.000	216.000	7:4	1.750
					9\128	84.375	215.625	9:5	1.800
	2\28					85.714	214.286	2:1	2.000	Basic 12L 4s
					9\124	87.097	212.903	9:4	2.250
				7\96		87.500	212.500	7:3	2.333
					12\164	87.805	212.195	12:5	2.400
			5\68			88.235	211.765	5:2	2.500	Semihard 12L 4s
					13\176	88.636	211.364	13:5	2.600
				8\108		88.889	211.111	8:3	2.667
					11\148	89.189	210.811	11:4	2.750
		3\40				90.000	210.000	3:1	3.000	Hard 12L 4s
					10\132	90.909	209.091	10:3	3.333
				7\92		91.304	208.696	7:2	3.500
					11\144	91.667	208.333	11:3	3.667
			4\52			92.308	207.692	4:1	4.000	Superhard 12L 4s
					9\116	93.103	206.897	9:2	4.500
				5\64		93.750	206.250	5:1	5.000
					6\76	94.737	205.263	6:1	6.000
1\12						100.000	200.000	1:0	→ ∞	Collapsed 12L 4s

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