User:MisterShafXen/18L 12s

18L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 18 large steps and 12 small steps, with a period of 3 large steps and 2 small steps that repeats every 200.0 ¢, or 6 times every octave. 18L 12s is a grandchild scale of 6L 6s, expanding it by 18 tones. Generators that produce this scale range from 120 ¢ to 133.3 ¢, or from 66.7 ¢ to 80 ¢.

↖ 17L 11s	↑ 18L 11s	19L 11s ↗
← 17L 12s	18L 12s	19L 12s →
↙ 17L 13s	↓ 18L 13s	19L 13s ↘

Scale structure
Step pattern	LLsLsLLsLsLLsLsLLsLsLLsLsLLsLs sLsLLsLsLLsLsLLsLsLLsLsLLsLsLL
Equave	2/1 (1200.0 ¢)
Period	1\6 (200.0 ¢)
Generator size
Bright	3\30 to 2\18 (120.0 ¢ to 133.3 ¢)
Dark	1\18 to 2\30 (66.7 ¢ to 80.0 ¢)
TAMNAMS information
Related to	6L 6s
With tunings	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	12L 6s
Sister	12L 18s
Daughters	30L 18s, 18L 30s
Neutralized	6L 24s
2-Flought	48L 12s, 18L 42s
Equal tunings
Equalized (L:s = 1:1)	3\30 (120.0 ¢)
Supersoft (L:s = 4:3)	11\108 (122.2 ¢)
Soft (L:s = 3:2)	8\78 (123.1 ¢)
Semisoft (L:s = 5:3)	13\126 (123.8 ¢)
Basic (L:s = 2:1)	5\48 (125.0 ¢)
Semihard (L:s = 5:2)	12\114 (126.3 ¢)
Hard (L:s = 3:1)	7\66 (127.3 ¢)
Superhard (L:s = 4:1)	9\84 (128.6 ¢)
Collapsed (L:s = 1:0)	2\18 (133.3 ¢)
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Scale properties

Intervals of 18L 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 40.0 ¢
	Major 1-mosstep	M1ms	L	40.0 ¢ to 66.7 ¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	66.7 ¢ to 80.0 ¢
	Augmented 2-mosstep	A2ms	2L	80.0 ¢ to 133.3 ¢
3-mosstep	Diminished 3-mosstep	d3ms	L + 2s	66.7 ¢ to 120.0 ¢
	Perfect 3-mosstep	P3ms	2L + s	120.0 ¢ to 133.3 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	133.3 ¢ to 160.0 ¢
	Major 4-mosstep	M4ms	3L + s	160.0 ¢ to 200.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	3L + 2s	200.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	200.0 ¢ to 240.0 ¢
	Major 6-mosstep	M6ms	4L + 2s	240.0 ¢ to 266.7 ¢
7-mosstep	Perfect 7-mosstep	P7ms	4L + 3s	266.7 ¢ to 280.0 ¢
	Augmented 7-mosstep	A7ms	5L + 2s	280.0 ¢ to 333.3 ¢
8-mosstep	Diminished 8-mosstep	d8ms	4L + 4s	266.7 ¢ to 320.0 ¢
	Perfect 8-mosstep	P8ms	5L + 3s	320.0 ¢ to 333.3 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	333.3 ¢ to 360.0 ¢
	Major 9-mosstep	M9ms	6L + 3s	360.0 ¢ to 400.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	6L + 4s	400.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	400.0 ¢ to 440.0 ¢
	Major 11-mosstep	M11ms	7L + 4s	440.0 ¢ to 466.7 ¢
12-mosstep	Perfect 12-mosstep	P12ms	7L + 5s	466.7 ¢ to 480.0 ¢
	Augmented 12-mosstep	A12ms	8L + 4s	480.0 ¢ to 533.3 ¢
13-mosstep	Diminished 13-mosstep	d13ms	7L + 6s	466.7 ¢ to 520.0 ¢
	Perfect 13-mosstep	P13ms	8L + 5s	520.0 ¢ to 533.3 ¢
14-mosstep	Minor 14-mosstep	m14ms	8L + 6s	533.3 ¢ to 560.0 ¢
	Major 14-mosstep	M14ms	9L + 5s	560.0 ¢ to 600.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	9L + 6s	600.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	9L + 7s	600.0 ¢ to 640.0 ¢
	Major 16-mosstep	M16ms	10L + 6s	640.0 ¢ to 666.7 ¢
17-mosstep	Perfect 17-mosstep	P17ms	10L + 7s	666.7 ¢ to 680.0 ¢
	Augmented 17-mosstep	A17ms	11L + 6s	680.0 ¢ to 733.3 ¢
18-mosstep	Diminished 18-mosstep	d18ms	10L + 8s	666.7 ¢ to 720.0 ¢
	Perfect 18-mosstep	P18ms	11L + 7s	720.0 ¢ to 733.3 ¢
19-mosstep	Minor 19-mosstep	m19ms	11L + 8s	733.3 ¢ to 760.0 ¢
	Major 19-mosstep	M19ms	12L + 7s	760.0 ¢ to 800.0 ¢
20-mosstep	Perfect 20-mosstep	P20ms	12L + 8s	800.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	12L + 9s	800.0 ¢ to 840.0 ¢
	Major 21-mosstep	M21ms	13L + 8s	840.0 ¢ to 866.7 ¢
22-mosstep	Perfect 22-mosstep	P22ms	13L + 9s	866.7 ¢ to 880.0 ¢
	Augmented 22-mosstep	A22ms	14L + 8s	880.0 ¢ to 933.3 ¢
23-mosstep	Diminished 23-mosstep	d23ms	13L + 10s	866.7 ¢ to 920.0 ¢
	Perfect 23-mosstep	P23ms	14L + 9s	920.0 ¢ to 933.3 ¢
24-mosstep	Minor 24-mosstep	m24ms	14L + 10s	933.3 ¢ to 960.0 ¢
	Major 24-mosstep	M24ms	15L + 9s	960.0 ¢ to 1000.0 ¢
25-mosstep	Perfect 25-mosstep	P25ms	15L + 10s	1000.0 ¢
26-mosstep	Minor 26-mosstep	m26ms	15L + 11s	1000.0 ¢ to 1040.0 ¢
	Major 26-mosstep	M26ms	16L + 10s	1040.0 ¢ to 1066.7 ¢
27-mosstep	Perfect 27-mosstep	P27ms	16L + 11s	1066.7 ¢ to 1080.0 ¢
	Augmented 27-mosstep	A27ms	17L + 10s	1080.0 ¢ to 1133.3 ¢
28-mosstep	Diminished 28-mosstep	d28ms	16L + 12s	1066.7 ¢ to 1120.0 ¢
	Perfect 28-mosstep	P28ms	17L + 11s	1120.0 ¢ to 1133.3 ¢
29-mosstep	Minor 29-mosstep	m29ms	17L + 12s	1133.3 ¢ to 1160.0 ¢
	Major 29-mosstep	M29ms	18L + 11s	1160.0 ¢ to 1200.0 ¢
30-mosstep	Perfect 30-mosstep	P30ms	18L + 12s	1200.0 ¢

Generator chain of 18L 12s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.
7	Augmented 1-mosdegree	A1md	Augmented 6-mosdegree	A6md	Augmented 11-mosdegree	A11md	Augmented 16-mosdegree	A16md	Augmented 21-mosdegree	A21md	Augmented 26-mosdegree	A26md
6	Augmented 3-mosdegree	A3md	Augmented 8-mosdegree	A8md	Augmented 13-mosdegree	A13md	Augmented 18-mosdegree	A18md	Augmented 23-mosdegree	A23md	Augmented 28-mosdegree	A28md
5	Augmented 0-mosdegree	A0md	Augmented 5-mosdegree	A5md	Augmented 10-mosdegree	A10md	Augmented 15-mosdegree	A15md	Augmented 20-mosdegree	A20md	Augmented 25-mosdegree	A25md
4	Augmented 2-mosdegree	A2md	Augmented 7-mosdegree	A7md	Augmented 12-mosdegree	A12md	Augmented 17-mosdegree	A17md	Augmented 22-mosdegree	A22md	Augmented 27-mosdegree	A27md
3	Major 4-mosdegree	M4md	Major 9-mosdegree	M9md	Major 14-mosdegree	M14md	Major 19-mosdegree	M19md	Major 24-mosdegree	M24md	Major 29-mosdegree	M29md
2	Major 1-mosdegree	M1md	Major 6-mosdegree	M6md	Major 11-mosdegree	M11md	Major 16-mosdegree	M16md	Major 21-mosdegree	M21md	Major 26-mosdegree	M26md
1	Perfect 3-mosdegree	P3md	Perfect 8-mosdegree	P8md	Perfect 13-mosdegree	P13md	Perfect 18-mosdegree	P18md	Perfect 23-mosdegree	P23md	Perfect 28-mosdegree	P28md
0	Perfect 0-mosdegree Perfect 5-mosdegree	P0md P5md	Perfect 5-mosdegree Perfect 10-mosdegree	P5md P10md	Perfect 10-mosdegree Perfect 15-mosdegree	P10md P15md	Perfect 15-mosdegree Perfect 20-mosdegree	P15md P20md	Perfect 20-mosdegree Perfect 25-mosdegree	P20md P25md	Perfect 25-mosdegree Perfect 30-mosdegree	P25md P30md
−1	Perfect 2-mosdegree	P2md	Perfect 7-mosdegree	P7md	Perfect 12-mosdegree	P12md	Perfect 17-mosdegree	P17md	Perfect 22-mosdegree	P22md	Perfect 27-mosdegree	P27md
−2	Minor 4-mosdegree	m4md	Minor 9-mosdegree	m9md	Minor 14-mosdegree	m14md	Minor 19-mosdegree	m19md	Minor 24-mosdegree	m24md	Minor 29-mosdegree	m29md
−3	Minor 1-mosdegree	m1md	Minor 6-mosdegree	m6md	Minor 11-mosdegree	m11md	Minor 16-mosdegree	m16md	Minor 21-mosdegree	m21md	Minor 26-mosdegree	m26md
−4	Diminished 3-mosdegree	d3md	Diminished 8-mosdegree	d8md	Diminished 13-mosdegree	d13md	Diminished 18-mosdegree	d18md	Diminished 23-mosdegree	d23md	Diminished 28-mosdegree	d28md
−5	Diminished 5-mosdegree	d5md	Diminished 10-mosdegree	d10md	Diminished 15-mosdegree	d15md	Diminished 20-mosdegree	d20md	Diminished 25-mosdegree	d25md	Diminished 30-mosdegree	d30md
−6	Diminished 2-mosdegree	d2md	Diminished 7-mosdegree	d7md	Diminished 12-mosdegree	d12md	Diminished 17-mosdegree	d17md	Diminished 22-mosdegree	d22md	Diminished 27-mosdegree	d27md
−7	Diminished 4-mosdegree	d4md	Diminished 9-mosdegree	d9md	Diminished 14-mosdegree	d14md	Diminished 19-mosdegree	d19md	Diminished 24-mosdegree	d24md	Diminished 29-mosdegree	d29md

Modes of 18L 12s

UDP	Cyclic order	Step pattern
24|0(6)	1	LLsLsLLsLsLLsLsLLsLsLLsLsLLsLs
18|6(6)	4	LsLLsLsLLsLsLLsLsLLsLsLLsLsLLs
12|12(6)	2	LsLsLLsLsLLsLsLLsLsLLsLsLLsLsL
6|18(6)	5	sLLsLsLLsLsLLsLsLLsLsLLsLsLLsL
0|24(6)	3	sLsLLsLsLLsLsLLsLsLLsLsLLsLsLL

Scale tree

Scale tree and tuning spectrum of 18L 12s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\30						120.000	80.000	1:1	1.000	Equalized 18L 12s
					17\168	121.429	78.571	6:5	1.200
				14\138		121.739	78.261	5:4	1.250
					25\246	121.951	78.049	9:7	1.286
			11\108			122.222	77.778	4:3	1.333	Supersoft 18L 12s
					30\294	122.449	77.551	11:8	1.375
				19\186		122.581	77.419	7:5	1.400
					27\264	122.727	77.273	10:7	1.429
		8\78				123.077	76.923	3:2	1.500	Soft 18L 12s
					29\282	123.404	76.596	11:7	1.571
				21\204		123.529	76.471	8:5	1.600
					34\330	123.636	76.364	13:8	1.625
			13\126			123.810	76.190	5:3	1.667	Semisoft 18L 12s
					31\300	124.000	76.000	12:7	1.714
				18\174		124.138	75.862	7:4	1.750
					23\222	124.324	75.676	9:5	1.800
	5\48					125.000	75.000	2:1	2.000	Basic 18L 12s Scales with tunings softer than this are proper
					22\210	125.714	74.286	9:4	2.250
				17\162		125.926	74.074	7:3	2.333
					29\276	126.087	73.913	12:5	2.400
			12\114			126.316	73.684	5:2	2.500	Semihard 18L 12s
					31\294	126.531	73.469	13:5	2.600
				19\180		126.667	73.333	8:3	2.667
					26\246	126.829	73.171	11:4	2.750
		7\66				127.273	72.727	3:1	3.000	Hard 18L 12s
					23\216	127.778	72.222	10:3	3.333
				16\150		128.000	72.000	7:2	3.500
					25\234	128.205	71.795	11:3	3.667
			9\84			128.571	71.429	4:1	4.000	Superhard 18L 12s
					20\186	129.032	70.968	9:2	4.500
				11\102		129.412	70.588	5:1	5.000
					13\120	130.000	70.000	6:1	6.000
2\18						133.333	66.667	1:0	→ ∞	Collapsed 18L 12s