9L 12s

↖ 8L 11s	↑ 9L 11s	10L 11s ↗
← 8L 12s	9L 12s	10L 12s →
↙ 8L 13s	↓ 9L 13s	10L 13s ↘

┌╥┬╥┬╥┬┬╥┬╥┬╥┬┬╥┬╥┬╥┬┬┐ │║│║│║││║│║│║││║│║│║│││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLsLssLsLsLssLsLsLss ssLsLsLssLsLsLssLsLsL
Equave	2/1 (1200.0¢)
Period	1\3 (400.0¢)
Generator size
Bright	2\21 to 1\9 (114.3¢ to 133.3¢)
Dark	2\9 to 5\21 (266.7¢ to 285.7¢)
TAMNAMS information
Descends from	3L 6s (tcherepnin)
Ancestor's step ratio range	1:1 to 3:2 (soft)
Related MOS scales
Parent	9L 3s
Sister	12L 9s
Daughters	21L 9s, 9L 21s
Neutralized	18L 3s
2-Flought	30L 12s, 9L 33s
Equal tunings
Equalized (L:s = 1:1)	2\21 (114.3¢)
Supersoft (L:s = 4:3)	7\72 (116.7¢)
Soft (L:s = 3:2)	5\51 (117.6¢)
Semisoft (L:s = 5:3)	8\81 (118.5¢)
Basic (L:s = 2:1)	3\30 (120.0¢)
Semihard (L:s = 5:2)	7\69 (121.7¢)
Hard (L:s = 3:1)	4\39 (123.1¢)
Superhard (L:s = 4:1)	5\48 (125.0¢)
Collapsed (L:s = 1:0)	1\9 (133.3¢)

9L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 12 small steps, with a period of 3 large steps and 4 small steps that repeats every 400.0¢, or 3 times every octave. 9L 12s is a grandchild scale of 3L 6s, expanding it by 12 tones. Generators that produce this scale range from 114.3¢ to 133.3¢, or from 266.7¢ to 285.7¢.

Modes

Modes of 9L 12s

UDP	Cyclic order	Step pattern
18|0(3)	1	LsLsLssLsLsLssLsLsLss
15|3(3)	3	LsLssLsLsLssLsLsLssLs
12|6(3)	5	LssLsLsLssLsLsLssLsLs
9|9(3)	7	sLsLsLssLsLsLssLsLsLs
6|12(3)	2	sLsLssLsLsLssLsLsLssL
3|15(3)	4	sLssLsLsLssLsLsLssLsL
0|18(3)	6	ssLsLsLssLsLsLssLsLsL

Intervals

Intervals of 9L 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 57.1¢
	Major 1-mosstep	M1ms	L	57.1¢ to 133.3¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0¢ to 114.3¢
	Perfect 2-mosstep	P2ms	L + s	114.3¢ to 133.3¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	133.3¢ to 171.4¢
	Major 3-mosstep	M3ms	2L + s	171.4¢ to 266.7¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	133.3¢ to 228.6¢
	Major 4-mosstep	M4ms	2L + 2s	228.6¢ to 266.7¢
5-mosstep	Perfect 5-mosstep	P5ms	2L + 3s	266.7¢ to 285.7¢
	Augmented 5-mosstep	A5ms	3L + 2s	285.7¢ to 400.0¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	266.7¢ to 342.9¢
	Major 6-mosstep	M6ms	3L + 3s	342.9¢ to 400.0¢
7-mosstep	Perfect 7-mosstep	P7ms	3L + 4s	400.0¢
8-mosstep	Minor 8-mosstep	m8ms	3L + 5s	400.0¢ to 457.1¢
	Major 8-mosstep	M8ms	4L + 4s	457.1¢ to 533.3¢
9-mosstep	Diminished 9-mosstep	d9ms	3L + 6s	400.0¢ to 514.3¢
	Perfect 9-mosstep	P9ms	4L + 5s	514.3¢ to 533.3¢
10-mosstep	Minor 10-mosstep	m10ms	4L + 6s	533.3¢ to 571.4¢
	Major 10-mosstep	M10ms	5L + 5s	571.4¢ to 666.7¢
11-mosstep	Minor 11-mosstep	m11ms	4L + 7s	533.3¢ to 628.6¢
	Major 11-mosstep	M11ms	5L + 6s	628.6¢ to 666.7¢
12-mosstep	Perfect 12-mosstep	P12ms	5L + 7s	666.7¢ to 685.7¢
	Augmented 12-mosstep	A12ms	6L + 6s	685.7¢ to 800.0¢
13-mosstep	Minor 13-mosstep	m13ms	5L + 8s	666.7¢ to 742.9¢
	Major 13-mosstep	M13ms	6L + 7s	742.9¢ to 800.0¢
14-mosstep	Perfect 14-mosstep	P14ms	6L + 8s	800.0¢
15-mosstep	Minor 15-mosstep	m15ms	6L + 9s	800.0¢ to 857.1¢
	Major 15-mosstep	M15ms	7L + 8s	857.1¢ to 933.3¢
16-mosstep	Diminished 16-mosstep	d16ms	6L + 10s	800.0¢ to 914.3¢
	Perfect 16-mosstep	P16ms	7L + 9s	914.3¢ to 933.3¢
17-mosstep	Minor 17-mosstep	m17ms	7L + 10s	933.3¢ to 971.4¢
	Major 17-mosstep	M17ms	8L + 9s	971.4¢ to 1066.7¢
18-mosstep	Minor 18-mosstep	m18ms	7L + 11s	933.3¢ to 1028.6¢
	Major 18-mosstep	M18ms	8L + 10s	1028.6¢ to 1066.7¢
19-mosstep	Perfect 19-mosstep	P19ms	8L + 11s	1066.7¢ to 1085.7¢
	Augmented 19-mosstep	A19ms	9L + 10s	1085.7¢ to 1200.0¢
20-mosstep	Minor 20-mosstep	m20ms	8L + 12s	1066.7¢ to 1142.9¢
	Major 20-mosstep	M20ms	9L + 11s	1142.9¢ to 1200.0¢
21-mosstep	Perfect 21-mosstep	P21ms	9L + 12s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 9L 12s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\21						114.286	285.714	1:1	1.000	Equalized 9L 12s
					11\114	115.789	284.211	6:5	1.200
				9\93		116.129	283.871	5:4	1.250
					16\165	116.364	283.636	9:7	1.286
			7\72			116.667	283.333	4:3	1.333	Supersoft 9L 12s
					19\195	116.923	283.077	11:8	1.375
				12\123		117.073	282.927	7:5	1.400
					17\174	117.241	282.759	10:7	1.429
		5\51				117.647	282.353	3:2	1.500	Soft 9L 12s
					18\183	118.033	281.967	11:7	1.571
				13\132		118.182	281.818	8:5	1.600
					21\213	118.310	281.690	13:8	1.625
			8\81			118.519	281.481	5:3	1.667	Semisoft 9L 12s
					19\192	118.750	281.250	12:7	1.714
				11\111		118.919	281.081	7:4	1.750
					14\141	119.149	280.851	9:5	1.800
	3\30					120.000	280.000	2:1	2.000	Basic 9L 12s Scales with tunings softer than this are proper
					13\129	120.930	279.070	9:4	2.250
				10\99		121.212	278.788	7:3	2.333
					17\168	121.429	278.571	12:5	2.400
			7\69			121.739	278.261	5:2	2.500	Semihard 9L 12s
					18\177	122.034	277.966	13:5	2.600
				11\108		122.222	277.778	8:3	2.667
					15\147	122.449	277.551	11:4	2.750
		4\39				123.077	276.923	3:1	3.000	Hard 9L 12s
					13\126	123.810	276.190	10:3	3.333
				9\87		124.138	275.862	7:2	3.500
					14\135	124.444	275.556	11:3	3.667
			5\48			125.000	275.000	4:1	4.000	Superhard 9L 12s
					11\105	125.714	274.286	9:2	4.500
				6\57		126.316	273.684	5:1	5.000
					7\66	127.273	272.727	6:1	6.000
1\9						133.333	266.667	1:0	→ ∞	Collapsed 9L 12s

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