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
Descends from	6L 1s (archaeotonic)
Required step ratio range	3:1 to 1:0 (hard)
Related MOS scales
Parent	6L 7s
Sister	13L 6s
Daughters	19L 6s 6L 19s
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¢)

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 13edo hexatonic scale. Its generator is a "neutral" whole tone between 3/19edo (189.474) and 1/6edo (200 cents), making it index 2 in meantone.

Modes

Modes of 6L 13s

UDP	Rotational 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

Scale tree

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