6L 13s

↖ 5L 12s	↑ 6L 12s	7L 12s ↗
← 5L 13s	6L 13s	7L 13s →
↙ 5L 14s	↓ 6L 14s	7L 14s ↘

Scale structure
Step pattern	LssLssLssLssLssLsss sssLssLssLssLssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\19 to 1\6 (189.5 ¢ to 200.0 ¢)
Dark	5\6 to 16\19 (1000.0 ¢ to 1010.5 ¢)
TAMNAMS information
Related to	6L 1s (archaeotonic)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	6L 7s
Sister	13L 6s
Daughters	19L 6s, 6L 19s
Neutralized	12L 7s
2-Flought	25L 13s, 6L 32s
Equal tunings
Equalized (L:s = 1:1)	3\19 (189.5 ¢)
Supersoft (L:s = 4:3)	10\63 (190.5 ¢)
Soft (L:s = 3:2)	7\44 (190.9 ¢)
Semisoft (L:s = 5:3)	11\69 (191.3 ¢)
Basic (L:s = 2:1)	4\25 (192.0 ¢)
Semihard (L:s = 5:2)	9\56 (192.9 ¢)
Hard (L:s = 3:1)	5\31 (193.5 ¢)
Superhard (L:s = 4:1)	6\37 (194.6 ¢)
Collapsed (L:s = 1:0)	1\6 (200.0 ¢)
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6L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 13 small steps, repeating every octave. 6L 13s is a grandchild scale of 6L 1s, expanding it by 12 tones. Generators that produce this scale range from 189.5 ¢ to 200 ¢, or from 1000 ¢ to 1010.5 ¢.

This MOS divides its small steps 2-2-2-2-2-3, like the hexatonic scale from 13edo. Its generator is a "neutral" whole tone between 3/19edo (189.474 cents) and 1/6edo (200 cents), making it index 2 in meantone. ("Neutral" as in neutrality between 10/9 and 9/8.)

Modes

Modes of 6L 13s

UDP	Cyclic order	Step pattern
18|0	1	LssLssLssLssLssLsss
17|1	4	LssLssLssLssLsssLss
16|2	7	LssLssLssLsssLssLss
15|3	10	LssLssLsssLssLssLss
14|4	13	LssLsssLssLssLssLss
13|5	16	LsssLssLssLssLssLss
12|6	19	sLssLssLssLssLssLss
11|7	3	sLssLssLssLssLsssLs
10|8	6	sLssLssLssLsssLssLs
9|9	9	sLssLssLsssLssLssLs
8|10	12	sLssLsssLssLssLssLs
7|11	15	sLsssLssLssLssLssLs
6|12	18	ssLssLssLssLssLssLs
5|13	2	ssLssLssLssLssLsssL
4|14	5	ssLssLssLssLsssLssL
3|15	8	ssLssLssLsssLssLssL
2|16	11	ssLssLsssLssLssLssL
1|17	14	ssLsssLssLssLssLssL
0|18	17	sssLssLssLssLssLssL

Intervals

Intervals of 6L 13s

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 63.2 ¢
	Major 1-mosstep	M1ms	L	63.2 ¢ to 200.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 126.3 ¢
	Major 2-mosstep	M2ms	L + s	126.3 ¢ to 200.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 189.5 ¢
	Perfect 3-mosstep	P3ms	L + 2s	189.5 ¢ to 200.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	200.0 ¢ to 252.6 ¢
	Major 4-mosstep	M4ms	2L + 2s	252.6 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	200.0 ¢ to 315.8 ¢
	Major 5-mosstep	M5ms	2L + 3s	315.8 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	200.0 ¢ to 378.9 ¢
	Major 6-mosstep	M6ms	2L + 4s	378.9 ¢ to 400.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	400.0 ¢ to 442.1 ¢
	Major 7-mosstep	M7ms	3L + 4s	442.1 ¢ to 600.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	400.0 ¢ to 505.3 ¢
	Major 8-mosstep	M8ms	3L + 5s	505.3 ¢ to 600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	400.0 ¢ to 568.4 ¢
	Major 9-mosstep	M9ms	3L + 6s	568.4 ¢ to 600.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	600.0 ¢ to 631.6 ¢
	Major 10-mosstep	M10ms	4L + 6s	631.6 ¢ to 800.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	3L + 8s	600.0 ¢ to 694.7 ¢
	Major 11-mosstep	M11ms	4L + 7s	694.7 ¢ to 800.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	600.0 ¢ to 757.9 ¢
	Major 12-mosstep	M12ms	4L + 8s	757.9 ¢ to 800.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	4L + 9s	800.0 ¢ to 821.1 ¢
	Major 13-mosstep	M13ms	5L + 8s	821.1 ¢ to 1000.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	4L + 10s	800.0 ¢ to 884.2 ¢
	Major 14-mosstep	M14ms	5L + 9s	884.2 ¢ to 1000.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	4L + 11s	800.0 ¢ to 947.4 ¢
	Major 15-mosstep	M15ms	5L + 10s	947.4 ¢ to 1000.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	5L + 11s	1000.0 ¢ to 1010.5 ¢
	Augmented 16-mosstep	A16ms	6L + 10s	1010.5 ¢ to 1200.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	5L + 12s	1000.0 ¢ to 1073.7 ¢
	Major 17-mosstep	M17ms	6L + 11s	1073.7 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	5L + 13s	1000.0 ¢ to 1136.8 ¢
	Major 18-mosstep	M18ms	6L + 12s	1136.8 ¢ to 1200.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	6L + 13s	1200.0 ¢

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 13s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\19						189.474	1010.526	1:1	1.000	Equalized 6L 13s
					16\101	190.099	1009.901	6:5	1.200
				13\82		190.244	1009.756	5:4	1.250
					23\145	190.345	1009.655	9:7	1.286
			10\63			190.476	1009.524	4:3	1.333	Supersoft 6L 13s
					27\170	190.588	1009.412	11:8	1.375
				17\107		190.654	1009.346	7:5	1.400
					24\151	190.728	1009.272	10:7	1.429
		7\44				190.909	1009.091	3:2	1.500	Soft 6L 13s
					25\157	191.083	1008.917	11:7	1.571
				18\113		191.150	1008.850	8:5	1.600
					29\182	191.209	1008.791	13:8	1.625
			11\69			191.304	1008.696	5:3	1.667	Semisoft 6L 13s
					26\163	191.411	1008.589	12:7	1.714
				15\94		191.489	1008.511	7:4	1.750
					19\119	191.597	1008.403	9:5	1.800
	4\25					192.000	1008.000	2:1	2.000	Basic 6L 13s Scales with tunings softer than this are proper
					17\106	192.453	1007.547	9:4	2.250
				13\81		192.593	1007.407	7:3	2.333
					22\137	192.701	1007.299	12:5	2.400
			9\56			192.857	1007.143	5:2	2.500	Semihard 6L 13s
					23\143	193.007	1006.993	13:5	2.600
				14\87		193.103	1006.897	8:3	2.667
					19\118	193.220	1006.780	11:4	2.750
		5\31				193.548	1006.452	3:1	3.000	Hard 6L 13s
					16\99	193.939	1006.061	10:3	3.333
				11\68		194.118	1005.882	7:2	3.500
					17\105	194.286	1005.714	11:3	3.667
			6\37			194.595	1005.405	4:1	4.000	Superhard 6L 13s
					13\80	195.000	1005.000	9:2	4.500
				7\43		195.349	1004.651	5:1	5.000
					8\49	195.918	1004.082	6:1	6.000
1\6						200.000	1000.000	1:0	→ ∞	Collapsed 6L 13s