12L 8s

↖ 11L 7s	↑ 12L 7s	13L 7s ↗
← 11L 8s	12L 8s	13L 8s →
↙ 11L 9s	↓ 12L 9s	13L 9s ↘

┌╥╥┬╥┬╥╥┬╥┬╥╥┬╥┬╥╥┬╥┬┐ │║║│║│║║│║│║║│║│║║│║││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLsLLsLsLLsLsLLsLs sLsLLsLsLLsLsLLsLsLL
Equave	2/1 (1200.0¢)
Period	1\4 (300.0¢)
Generator size
Bright	3\20 to 2\12 (180.0¢ to 200.0¢)
Dark	1\12 to 2\20 (100.0¢ to 120.0¢)
TAMNAMS information
Descends from	4L 4s (tetrawood)
Ancestor's step ratio range	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	8L 4s
Sister	8L 12s
Daughters	20L 12s, 12L 20s
Neutralized	4L 16s
2-Flought	32L 8s, 12L 28s
Equal tunings
Equalized (L:s = 1:1)	3\20 (180.0¢)
Supersoft (L:s = 4:3)	11\72 (183.3¢)
Soft (L:s = 3:2)	8\52 (184.6¢)
Semisoft (L:s = 5:3)	13\84 (185.7¢)
Basic (L:s = 2:1)	5\32 (187.5¢)
Semihard (L:s = 5:2)	12\76 (189.5¢)
Hard (L:s = 3:1)	7\44 (190.9¢)
Superhard (L:s = 4:1)	9\56 (192.9¢)
Collapsed (L:s = 1:0)	2\12 (200.0¢)

12L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 8 small steps, with a period of 3 large steps and 2 small steps that repeats every 300.0¢, or 4 times every octave. 12L 8s is a grandchild scale of 4L 4s, expanding it by 12 tones. Generators that produce this scale range from 180¢ to 200¢, or from 100¢ to 120¢.

Modes

Modes of 12L 8s

UDP	Cyclic order	Step pattern
16|0(4)	1	LLsLsLLsLsLLsLsLLsLs
12|4(4)	4	LsLLsLsLLsLsLLsLsLLs
8|8(4)	2	LsLsLLsLsLLsLsLLsLsL
4|12(4)	5	sLLsLsLLsLsLLsLsLLsL
0|16(4)	3	sLsLLsLsLLsLsLLsLsLL

Intervals

Intervals of 12L 8s

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 60.0¢
	Major 1-mosstep	M1ms	L	60.0¢ to 100.0¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	100.0¢ to 120.0¢
	Augmented 2-mosstep	A2ms	2L	120.0¢ to 200.0¢
3-mosstep	Diminished 3-mosstep	d3ms	L + 2s	100.0¢ to 180.0¢
	Perfect 3-mosstep	P3ms	2L + s	180.0¢ to 200.0¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	200.0¢ to 240.0¢
	Major 4-mosstep	M4ms	3L + s	240.0¢ to 300.0¢
5-mosstep	Perfect 5-mosstep	P5ms	3L + 2s	300.0¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	300.0¢ to 360.0¢
	Major 6-mosstep	M6ms	4L + 2s	360.0¢ to 400.0¢
7-mosstep	Perfect 7-mosstep	P7ms	4L + 3s	400.0¢ to 420.0¢
	Augmented 7-mosstep	A7ms	5L + 2s	420.0¢ to 500.0¢
8-mosstep	Diminished 8-mosstep	d8ms	4L + 4s	400.0¢ to 480.0¢
	Perfect 8-mosstep	P8ms	5L + 3s	480.0¢ to 500.0¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	500.0¢ to 540.0¢
	Major 9-mosstep	M9ms	6L + 3s	540.0¢ to 600.0¢
10-mosstep	Perfect 10-mosstep	P10ms	6L + 4s	600.0¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	600.0¢ to 660.0¢
	Major 11-mosstep	M11ms	7L + 4s	660.0¢ to 700.0¢
12-mosstep	Perfect 12-mosstep	P12ms	7L + 5s	700.0¢ to 720.0¢
	Augmented 12-mosstep	A12ms	8L + 4s	720.0¢ to 800.0¢
13-mosstep	Diminished 13-mosstep	d13ms	7L + 6s	700.0¢ to 780.0¢
	Perfect 13-mosstep	P13ms	8L + 5s	780.0¢ to 800.0¢
14-mosstep	Minor 14-mosstep	m14ms	8L + 6s	800.0¢ to 840.0¢
	Major 14-mosstep	M14ms	9L + 5s	840.0¢ to 900.0¢
15-mosstep	Perfect 15-mosstep	P15ms	9L + 6s	900.0¢
16-mosstep	Minor 16-mosstep	m16ms	9L + 7s	900.0¢ to 960.0¢
	Major 16-mosstep	M16ms	10L + 6s	960.0¢ to 1000.0¢
17-mosstep	Perfect 17-mosstep	P17ms	10L + 7s	1000.0¢ to 1020.0¢
	Augmented 17-mosstep	A17ms	11L + 6s	1020.0¢ to 1100.0¢
18-mosstep	Diminished 18-mosstep	d18ms	10L + 8s	1000.0¢ to 1080.0¢
	Perfect 18-mosstep	P18ms	11L + 7s	1080.0¢ to 1100.0¢
19-mosstep	Minor 19-mosstep	m19ms	11L + 8s	1100.0¢ to 1140.0¢
	Major 19-mosstep	M19ms	12L + 7s	1140.0¢ to 1200.0¢
20-mosstep	Perfect 20-mosstep	P20ms	12L + 8s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 12L 8s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\20						180.000	120.000	1:1	1.000	Equalized 12L 8s
					17\112	182.143	117.857	6:5	1.200
				14\92		182.609	117.391	5:4	1.250
					25\164	182.927	117.073	9:7	1.286
			11\72			183.333	116.667	4:3	1.333	Supersoft 12L 8s
					30\196	183.673	116.327	11:8	1.375
				19\124		183.871	116.129	7:5	1.400
					27\176	184.091	115.909	10:7	1.429
		8\52				184.615	115.385	3:2	1.500	Soft 12L 8s
					29\188	185.106	114.894	11:7	1.571
				21\136		185.294	114.706	8:5	1.600
					34\220	185.455	114.545	13:8	1.625
			13\84			185.714	114.286	5:3	1.667	Semisoft 12L 8s
					31\200	186.000	114.000	12:7	1.714
				18\116		186.207	113.793	7:4	1.750
					23\148	186.486	113.514	9:5	1.800
	5\32					187.500	112.500	2:1	2.000	Basic 12L 8s Scales with tunings softer than this are proper
					22\140	188.571	111.429	9:4	2.250
				17\108		188.889	111.111	7:3	2.333
					29\184	189.130	110.870	12:5	2.400
			12\76			189.474	110.526	5:2	2.500	Semihard 12L 8s
					31\196	189.796	110.204	13:5	2.600
				19\120		190.000	110.000	8:3	2.667
					26\164	190.244	109.756	11:4	2.750
		7\44				190.909	109.091	3:1	3.000	Hard 12L 8s
					23\144	191.667	108.333	10:3	3.333
				16\100		192.000	108.000	7:2	3.500
					25\156	192.308	107.692	11:3	3.667
			9\56			192.857	107.143	4:1	4.000	Superhard 12L 8s
					20\124	193.548	106.452	9:2	4.500
				11\68		194.118	105.882	5:1	5.000
					13\80	195.000	105.000	6:1	6.000
2\12						200.000	100.000	1:0	→ ∞	Collapsed 12L 8s

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