12L 9s

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↙ 11L 10s	↓ 12L 10s	13L 10s ↘

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Scale structure
Step pattern	LLsLsLsLLsLsLsLLsLsLs sLsLsLLsLsLsLLsLsLsLL
Equave	2/1 (1200.0¢)
Period	1\3 (400.0¢)
Generator size
Bright	5\21 to 3\12 (285.7¢ to 300.0¢)
Dark	1\12 to 2\21 (100.0¢ to 114.3¢)
TAMNAMS information
Descends from	3L 6s
Ancestor's step ratio range	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	9L 3s
Sister	9L 12s
Daughters	21L 12s, 12L 21s
Neutralized	3L 18s
2-Flought	33L 9s, 12L 30s
Equal tunings
Equalized (L:s = 1:1)	5\21 (285.7¢)
Supersoft (L:s = 4:3)	18\75 (288.0¢)
Soft (L:s = 3:2)	13\54 (288.9¢)
Semisoft (L:s = 5:3)	21\87 (289.7¢)
Basic (L:s = 2:1)	8\33 (290.9¢)
Semihard (L:s = 5:2)	19\78 (292.3¢)
Hard (L:s = 3:1)	11\45 (293.3¢)
Superhard (L:s = 4:1)	14\57 (294.7¢)
Collapsed (L:s = 1:0)	3\12 (300.0¢)

12L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 9 small steps, with a period of 4 large steps and 3 small steps that repeats every 400.0¢, or 3 times every octave. 12L 9s is a grandchild scale of 3L 6s, expanding it by 12 tones. Generators that produce this scale range from 285.7¢ to 300¢, or from 100¢ to 114.3¢.

Modes

Modes of 12L 9s

UDP	Cyclic order	Step pattern
18|0(3)	1	LLsLsLsLLsLsLsLLsLsLs
15|3(3)	6	LsLLsLsLsLLsLsLsLLsLs
12|6(3)	4	LsLsLLsLsLsLLsLsLsLLs
9|9(3)	2	LsLsLsLLsLsLsLLsLsLsL
6|12(3)	7	sLLsLsLsLLsLsLsLLsLsL
3|15(3)	5	sLsLLsLsLsLLsLsLsLLsL
0|18(3)	3	sLsLsLLsLsLsLLsLsLsLL

Intervals

Intervals of 12L 9s

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 57.1¢
	Major 1-mosstep	M1ms	L	57.1¢ to 100.0¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	100.0¢ to 114.3¢
	Augmented 2-mosstep	A2ms	2L	114.3¢ to 200.0¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	100.0¢ to 171.4¢
	Major 3-mosstep	M3ms	2L + s	171.4¢ to 200.0¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	200.0¢ to 228.6¢
	Major 4-mosstep	M4ms	3L + s	228.6¢ to 300.0¢
5-mosstep	Diminished 5-mosstep	d5ms	2L + 3s	200.0¢ to 285.7¢
	Perfect 5-mosstep	P5ms	3L + 2s	285.7¢ to 300.0¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	300.0¢ to 342.9¢
	Major 6-mosstep	M6ms	4L + 2s	342.9¢ to 400.0¢
7-mosstep	Perfect 7-mosstep	P7ms	4L + 3s	400.0¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	400.0¢ to 457.1¢
	Major 8-mosstep	M8ms	5L + 3s	457.1¢ to 500.0¢
9-mosstep	Perfect 9-mosstep	P9ms	5L + 4s	500.0¢ to 514.3¢
	Augmented 9-mosstep	A9ms	6L + 3s	514.3¢ to 600.0¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	500.0¢ to 571.4¢
	Major 10-mosstep	M10ms	6L + 4s	571.4¢ to 600.0¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	600.0¢ to 628.6¢
	Major 11-mosstep	M11ms	7L + 4s	628.6¢ to 700.0¢
12-mosstep	Diminished 12-mosstep	d12ms	6L + 6s	600.0¢ to 685.7¢
	Perfect 12-mosstep	P12ms	7L + 5s	685.7¢ to 700.0¢
13-mosstep	Minor 13-mosstep	m13ms	7L + 6s	700.0¢ to 742.9¢
	Major 13-mosstep	M13ms	8L + 5s	742.9¢ to 800.0¢
14-mosstep	Perfect 14-mosstep	P14ms	8L + 6s	800.0¢
15-mosstep	Minor 15-mosstep	m15ms	8L + 7s	800.0¢ to 857.1¢
	Major 15-mosstep	M15ms	9L + 6s	857.1¢ to 900.0¢
16-mosstep	Perfect 16-mosstep	P16ms	9L + 7s	900.0¢ to 914.3¢
	Augmented 16-mosstep	A16ms	10L + 6s	914.3¢ to 1000.0¢
17-mosstep	Minor 17-mosstep	m17ms	9L + 8s	900.0¢ to 971.4¢
	Major 17-mosstep	M17ms	10L + 7s	971.4¢ to 1000.0¢
18-mosstep	Minor 18-mosstep	m18ms	10L + 8s	1000.0¢ to 1028.6¢
	Major 18-mosstep	M18ms	11L + 7s	1028.6¢ to 1100.0¢
19-mosstep	Diminished 19-mosstep	d19ms	10L + 9s	1000.0¢ to 1085.7¢
	Perfect 19-mosstep	P19ms	11L + 8s	1085.7¢ to 1100.0¢
20-mosstep	Minor 20-mosstep	m20ms	11L + 9s	1100.0¢ to 1142.9¢
	Major 20-mosstep	M20ms	12L + 8s	1142.9¢ to 1200.0¢
21-mosstep	Perfect 21-mosstep	P21ms	12L + 9s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 12L 9s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\21						285.714	114.286	1:1	1.000	Equalized 12L 9s
					28\117	287.179	112.821	6:5	1.200
				23\96		287.500	112.500	5:4	1.250
					41\171	287.719	112.281	9:7	1.286
			18\75			288.000	112.000	4:3	1.333	Supersoft 12L 9s
					49\204	288.235	111.765	11:8	1.375
				31\129		288.372	111.628	7:5	1.400
					44\183	288.525	111.475	10:7	1.429
		13\54				288.889	111.111	3:2	1.500	Soft 12L 9s
					47\195	289.231	110.769	11:7	1.571
				34\141		289.362	110.638	8:5	1.600
					55\228	289.474	110.526	13:8	1.625
			21\87			289.655	110.345	5:3	1.667	Semisoft 12L 9s
					50\207	289.855	110.145	12:7	1.714
				29\120		290.000	110.000	7:4	1.750
					37\153	290.196	109.804	9:5	1.800
	8\33					290.909	109.091	2:1	2.000	Basic 12L 9s Scales with tunings softer than this are proper
					35\144	291.667	108.333	9:4	2.250
				27\111		291.892	108.108	7:3	2.333
					46\189	292.063	107.937	12:5	2.400
			19\78			292.308	107.692	5:2	2.500	Semihard 12L 9s
					49\201	292.537	107.463	13:5	2.600
				30\123		292.683	107.317	8:3	2.667
					41\168	292.857	107.143	11:4	2.750
		11\45				293.333	106.667	3:1	3.000	Hard 12L 9s
					36\147	293.878	106.122	10:3	3.333
				25\102		294.118	105.882	7:2	3.500
					39\159	294.340	105.660	11:3	3.667
			14\57			294.737	105.263	4:1	4.000	Superhard 12L 9s
					31\126	295.238	104.762	9:2	4.500
				17\69		295.652	104.348	5:1	5.000
					20\81	296.296	103.704	6:1	6.000
3\12						300.000	100.000	1:0	→ ∞	Collapsed 12L 9s

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