12L 12s

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Scale structure
Step pattern	LsLsLsLsLsLsLsLsLsLsLsLs sLsLsLsLsLsLsLsLsLsLsLsL
Equave	2/1 (1200.0 ¢)
Period	1\12 (100.0 ¢)
Generator size
Bright	1\24 to 1\12 (50.0 ¢ to 100.0 ¢)
Dark	0\12 to 1\24 (0.0 ¢ to 50.0 ¢)
Related MOS scales
Parent	none
Sister	12L 12s (self)
Daughters	24L 12s, 12L 24s
Neutralized	24edo
2-Flought	36L 12s, 12L 36s
Equal tunings
Equalized (L:s = 1:1)	1\24 (50.0 ¢)
Supersoft (L:s = 4:3)	4\84 (57.1 ¢)
Soft (L:s = 3:2)	3\60 (60.0 ¢)
Semisoft (L:s = 5:3)	5\96 (62.5 ¢)
Basic (L:s = 2:1)	2\36 (66.7 ¢)
Semihard (L:s = 5:2)	5\84 (71.4 ¢)
Hard (L:s = 3:1)	3\48 (75.0 ¢)
Superhard (L:s = 4:1)	4\60 (80.0 ¢)
Collapsed (L:s = 1:0)	1\12 (100.0 ¢)
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12L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 12 small steps, with a period of 1 large step and 1 small step that repeats every 100.0 ¢, or 12 times every octave. Generators that produce this scale range from 50 ¢ to 100 ¢, or from 0 ¢ to 50 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

It is the 24-note mos scale of the compton, catler, and duodecim temperaments of the compton family, which divide the octave into 12 parts. As such, this mos scale can be considered to be 2 rings of 12edo, and can be replicated with two 12edo instruments detuned from each other by a fixed amount. All of these temperaments map 3/2 to 7 steps of 12edo, thus tempering out the Pythagorean comma. Compton uses the 3-limit of 12edo, and adds an independent generator for 5/4 to improve the accuracy of 5-limit harmony. Catler additionally maps 5/4 to 4\12, thus preserving the 5-limit of 12edo, and adds 7/4 as an independent generator. Duodecim is a low-accuracy temperament that further maps 7/4 to 10\12, thus keeping the full 7-limit of 12edo, and uses 11/8 as an independent generator.

Using the TAMNAMS extension, it can be named dodecawood, since it has 12 periods per octave, each with one large step and one small step.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 12L 12s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 50.0 ¢
	Major 1-mosstep	M1ms	L	50.0 ¢ to 100.0 ¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	100.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	100.0 ¢ to 150.0 ¢
	Major 3-mosstep	M3ms	2L + s	150.0 ¢ to 200.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	2L + 2s	200.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	200.0 ¢ to 250.0 ¢
	Major 5-mosstep	M5ms	3L + 2s	250.0 ¢ to 300.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	3L + 3s	300.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	3L + 4s	300.0 ¢ to 350.0 ¢
	Major 7-mosstep	M7ms	4L + 3s	350.0 ¢ to 400.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	4L + 4s	400.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	4L + 5s	400.0 ¢ to 450.0 ¢
	Major 9-mosstep	M9ms	5L + 4s	450.0 ¢ to 500.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	5L + 5s	500.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	5L + 6s	500.0 ¢ to 550.0 ¢
	Major 11-mosstep	M11ms	6L + 5s	550.0 ¢ to 600.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	6L + 6s	600.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	6L + 7s	600.0 ¢ to 650.0 ¢
	Major 13-mosstep	M13ms	7L + 6s	650.0 ¢ to 700.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	7L + 7s	700.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	7L + 8s	700.0 ¢ to 750.0 ¢
	Major 15-mosstep	M15ms	8L + 7s	750.0 ¢ to 800.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	8L + 8s	800.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	8L + 9s	800.0 ¢ to 850.0 ¢
	Major 17-mosstep	M17ms	9L + 8s	850.0 ¢ to 900.0 ¢
18-mosstep	Perfect 18-mosstep	P18ms	9L + 9s	900.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	9L + 10s	900.0 ¢ to 950.0 ¢
	Major 19-mosstep	M19ms	10L + 9s	950.0 ¢ to 1000.0 ¢
20-mosstep	Perfect 20-mosstep	P20ms	10L + 10s	1000.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	10L + 11s	1000.0 ¢ to 1050.0 ¢
	Major 21-mosstep	M21ms	11L + 10s	1050.0 ¢ to 1100.0 ¢
22-mosstep	Perfect 22-mosstep	P22ms	11L + 11s	1100.0 ¢
23-mosstep	Minor 23-mosstep	m23ms	11L + 12s	1100.0 ¢ to 1150.0 ¢
	Major 23-mosstep	M23ms	12L + 11s	1150.0 ¢ to 1200.0 ¢
24-mosstep	Perfect 24-mosstep	P24ms	12L + 12s	1200.0 ¢

Generator chain

Generator chain of 12L 12s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.
2	Augmented 0-mosdegree	A0md	Augmented 2-mosdegree	A2md	Augmented 4-mosdegree	A4md	Augmented 6-mosdegree	A6md	Augmented 8-mosdegree	A8md	Augmented 10-mosdegree	A10md	Augmented 12-mosdegree	A12md	Augmented 14-mosdegree	A14md	Augmented 16-mosdegree	A16md	Augmented 18-mosdegree	A18md	Augmented 20-mosdegree	A20md	Augmented 22-mosdegree	A22md
1	Major 1-mosdegree	M1md	Major 3-mosdegree	M3md	Major 5-mosdegree	M5md	Major 7-mosdegree	M7md	Major 9-mosdegree	M9md	Major 11-mosdegree	M11md	Major 13-mosdegree	M13md	Major 15-mosdegree	M15md	Major 17-mosdegree	M17md	Major 19-mosdegree	M19md	Major 21-mosdegree	M21md	Major 23-mosdegree	M23md
0	Perfect 0-mosdegree Perfect 2-mosdegree	P0md P2md	Perfect 2-mosdegree Perfect 4-mosdegree	P2md P4md	Perfect 4-mosdegree Perfect 6-mosdegree	P4md P6md	Perfect 6-mosdegree Perfect 8-mosdegree	P6md P8md	Perfect 8-mosdegree Perfect 10-mosdegree	P8md P10md	Perfect 10-mosdegree Perfect 12-mosdegree	P10md P12md	Perfect 12-mosdegree Perfect 14-mosdegree	P12md P14md	Perfect 14-mosdegree Perfect 16-mosdegree	P14md P16md	Perfect 16-mosdegree Perfect 18-mosdegree	P16md P18md	Perfect 18-mosdegree Perfect 20-mosdegree	P18md P20md	Perfect 20-mosdegree Perfect 22-mosdegree	P20md P22md	Perfect 22-mosdegree Perfect 24-mosdegree	P22md P24md
−1	Minor 1-mosdegree	m1md	Minor 3-mosdegree	m3md	Minor 5-mosdegree	m5md	Minor 7-mosdegree	m7md	Minor 9-mosdegree	m9md	Minor 11-mosdegree	m11md	Minor 13-mosdegree	m13md	Minor 15-mosdegree	m15md	Minor 17-mosdegree	m17md	Minor 19-mosdegree	m19md	Minor 21-mosdegree	m21md	Minor 23-mosdegree	m23md
−2	Diminished 2-mosdegree	d2md	Diminished 4-mosdegree	d4md	Diminished 6-mosdegree	d6md	Diminished 8-mosdegree	d8md	Diminished 10-mosdegree	d10md	Diminished 12-mosdegree	d12md	Diminished 14-mosdegree	d14md	Diminished 16-mosdegree	d16md	Diminished 18-mosdegree	d18md	Diminished 20-mosdegree	d20md	Diminished 22-mosdegree	d22md	Diminished 24-mosdegree	d24md

Modes

Scale degrees of the modes of 12L 12s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
12|0(12)	1	LsLsLsLsLsLsLsLsLsLsLsLs	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.
0|12(12)	2	sLsLsLsLsLsLsLsLsLsLsLsL	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 12L 12s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\24						50.000	50.000	1:1	1.000	Equalized 12L 12s
					6\132	54.545	45.455	6:5	1.200
				5\108		55.556	44.444	5:4	1.250
					9\192	56.250	43.750	9:7	1.286
			4\84			57.143	42.857	4:3	1.333	Supersoft 12L 12s
					11\228	57.895	42.105	11:8	1.375
				7\144		58.333	41.667	7:5	1.400
					10\204	58.824	41.176	10:7	1.429
		3\60				60.000	40.000	3:2	1.500	Soft 12L 12s Duodecim
					11\216	61.111	38.889	11:7	1.571
				8\156		61.538	38.462	8:5	1.600
					13\252	61.905	38.095	13:8	1.625
			5\96			62.500	37.500	5:3	1.667	Semisoft 12L 12s
					12\228	63.158	36.842	12:7	1.714
				7\132		63.636	36.364	7:4	1.750
					9\168	64.286	35.714	9:5	1.800
	2\36					66.667	33.333	2:1	2.000	Basic 12L 12s
					9\156	69.231	30.769	9:4	2.250
				7\120		70.000	30.000	7:3	2.333
					12\204	70.588	29.412	12:5	2.400
			5\84			71.429	28.571	5:2	2.500	Semihard 12L 12s
					13\216	72.222	27.778	13:5	2.600
				8\132		72.727	27.273	8:3	2.667
					11\180	73.333	26.667	11:4	2.750
		3\48				75.000	25.000	3:1	3.000	Hard 12L 12s Catler
					10\156	76.923	23.077	10:3	3.333
				7\108		77.778	22.222	7:2	3.500
					11\168	78.571	21.429	11:3	3.667
			4\60			80.000	20.000	4:1	4.000	Superhard 12L 12s
					9\132	81.818	18.182	9:2	4.500
				5\72		83.333	16.667	5:1	5.000	Compton
					6\84	85.714	14.286	6:1	6.000
1\12						100.000	0.000	1:0	→ ∞	Collapsed 12L 12s