6L 9s

6L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 9 small steps, with a period of 2 large steps and 3 small steps that repeats every 400.0 ¢, or 3 times every octave. 6L 9s is a child scale of 6L 3s, expanding it by 6 tones. Generators that produce this scale range from 160 ¢ to 200 ¢, or from 200 ¢ to 240 ¢.

↖ 5L 8s	↑ 6L 8s	7L 8s ↗
← 5L 9s	6L 9s	7L 9s →
↙ 5L 10s	↓ 6L 10s	7L 10s ↘

Scale structure
Step pattern	LsLssLsLssLsLss ssLsLssLsLssLsL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	2\15 to 1\6 (160.0 ¢ to 200.0 ¢)
Dark	1\6 to 3\15 (200.0 ¢ to 240.0 ¢)
TAMNAMS information
Related to	6L 3s (hyrulic)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	6L 3s
Sister	9L 6s
Daughters	15L 6s, 6L 15s
Neutralized	12L 3s
2-Flought	21L 9s, 6L 24s
Equal tunings
Equalized (L:s = 1:1)	2\15 (160.0 ¢)
Supersoft (L:s = 4:3)	7\51 (164.7 ¢)
Soft (L:s = 3:2)	5\36 (166.7 ¢)
Semisoft (L:s = 5:3)	8\57 (168.4 ¢)
Basic (L:s = 2:1)	3\21 (171.4 ¢)
Semihard (L:s = 5:2)	7\48 (175.0 ¢)
Hard (L:s = 3:1)	4\27 (177.8 ¢)
Superhard (L:s = 4:1)	5\33 (181.8 ¢)
Collapsed (L:s = 1:0)	1\6 (200.0 ¢)
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Modes

Modes of 6L 9s

UDP	Cyclic order	Step pattern
12|0(3)	1	LsLssLsLssLsLss
9|3(3)	3	LssLsLssLsLssLs
6|6(3)	5	sLsLssLsLssLsLs
3|9(3)	2	sLssLsLssLsLssL
0|12(3)	4	ssLsLssLsLssLsL

Intervals

Intervals of 6L 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 80.0 ¢
	Major 1-mosstep	M1ms	L	80.0 ¢ to 200.0 ¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0 ¢ to 160.0 ¢
	Perfect 2-mosstep	P2ms	L + s	160.0 ¢ to 200.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	200.0 ¢ to 240.0 ¢
	Augmented 3-mosstep	A3ms	2L + s	240.0 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	200.0 ¢ to 320.0 ¢
	Major 4-mosstep	M4ms	2L + 2s	320.0 ¢ to 400.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	2L + 3s	400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	400.0 ¢ to 480.0 ¢
	Major 6-mosstep	M6ms	3L + 3s	480.0 ¢ to 600.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	2L + 5s	400.0 ¢ to 560.0 ¢
	Perfect 7-mosstep	P7ms	3L + 4s	560.0 ¢ to 600.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	3L + 5s	600.0 ¢ to 640.0 ¢
	Augmented 8-mosstep	A8ms	4L + 4s	640.0 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	600.0 ¢ to 720.0 ¢
	Major 9-mosstep	M9ms	4L + 5s	720.0 ¢ to 800.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	4L + 6s	800.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	4L + 7s	800.0 ¢ to 880.0 ¢
	Major 11-mosstep	M11ms	5L + 6s	880.0 ¢ to 1000.0 ¢
12-mosstep	Diminished 12-mosstep	d12ms	4L + 8s	800.0 ¢ to 960.0 ¢
	Perfect 12-mosstep	P12ms	5L + 7s	960.0 ¢ to 1000.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	5L + 8s	1000.0 ¢ to 1040.0 ¢
	Augmented 13-mosstep	A13ms	6L + 7s	1040.0 ¢ to 1200.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	5L + 9s	1000.0 ¢ to 1120.0 ¢
	Major 14-mosstep	M14ms	6L + 8s	1120.0 ¢ to 1200.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	6L + 9s	1200.0 ¢

Tuning spectrum

Todo: review Review entries from past page revision and enter them into the scale tree.

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 6L 9s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\15						160.000	240.000	1:1	1.000	Equalized 6L 9s
					11\81	162.963	237.037	6:5	1.200
				9\66		163.636	236.364	5:4	1.250
					16\117	164.103	235.897	9:7	1.286
			7\51			164.706	235.294	4:3	1.333	Supersoft 6L 9s
					19\138	165.217	234.783	11:8	1.375
				12\87		165.517	234.483	7:5	1.400
					17\123	165.854	234.146	10:7	1.429
		5\36				166.667	233.333	3:2	1.500	Soft 6L 9s
					18\129	167.442	232.558	11:7	1.571
				13\93		167.742	232.258	8:5	1.600
					21\150	168.000	232.000	13:8	1.625
			8\57			168.421	231.579	5:3	1.667	Semisoft 6L 9s
					19\135	168.889	231.111	12:7	1.714
				11\78		169.231	230.769	7:4	1.750
					14\99	169.697	230.303	9:5	1.800
	3\21					171.429	228.571	2:1	2.000	Basic 6L 9s Scales with tunings softer than this are proper
					13\90	173.333	226.667	9:4	2.250
				10\69		173.913	226.087	7:3	2.333
					17\117	174.359	225.641	12:5	2.400
			7\48			175.000	225.000	5:2	2.500	Semihard 6L 9s
					18\123	175.610	224.390	13:5	2.600
				11\75		176.000	224.000	8:3	2.667
					15\102	176.471	223.529	11:4	2.750
		4\27				177.778	222.222	3:1	3.000	Hard 6L 9s
					13\87	179.310	220.690	10:3	3.333
				9\60		180.000	220.000	7:2	3.500
					14\93	180.645	219.355	11:3	3.667
			5\33			181.818	218.182	4:1	4.000	Superhard 6L 9s
					11\72	183.333	216.667	9:2	4.500
				6\39		184.615	215.385	5:1	5.000
					7\45	186.667	213.333	6:1	6.000
1\6						200.000	200.000	1:0	→ ∞	Collapsed 6L 9s

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