6L 7s

Todo: cleanup Clean up intro

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

Scale structure
Step pattern	LsLsLsLsLsLss ssLsLsLsLsLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	2\13 to 1\6 (184.6 ¢ to 200.0 ¢)
Dark	5\6 to 11\13 (1000.0 ¢ to 1015.4 ¢)
TAMNAMS information
Related to	6L 1s (archaeotonic)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	6L 1s
Sister	7L 6s
Daughters	13L 6s, 6L 13s
Neutralized	12L 1s
2-Flought	19L 7s, 6L 20s
Equal tunings
Equalized (L:s = 1:1)	2\13 (184.6 ¢)
Supersoft (L:s = 4:3)	7\45 (186.7 ¢)
Soft (L:s = 3:2)	5\32 (187.5 ¢)
Semisoft (L:s = 5:3)	8\51 (188.2 ¢)
Basic (L:s = 2:1)	3\19 (189.5 ¢)
Semihard (L:s = 5:2)	7\44 (190.9 ¢)
Hard (L:s = 3:1)	4\25 (192.0 ¢)
Superhard (L:s = 4:1)	5\31 (193.5 ¢)
Collapsed (L:s = 1:0)	1\6 (200.0 ¢)
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6L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 7 small steps, repeating every octave. 6L 7s is a child scale of 6L 1s, expanding it by 6 tones. Generators that produce this scale range from 184.6 ¢ to 200 ¢, or from 1000 ¢ to 1015.4 ¢. This MOS is the chromatic scale of a family of temperaments which are index 2 subtemperaments of various meantone temperaments. It is a great early step into un-syntonic temperaments by virtue of this property, though admittedly Neutral thirds/Mohajira is greater in this respect if you don't mind essentially giving up major and minor seconds/sevenths and thirds/sixths (syntonic temperaments are index 2 subtemperaments of them) because it at least has an albitonic sized MOS which feels like a division of the octave, which cannot be said for the temperaments which this scale belongs to (Happy and Grumpy scales have a very strong period dysphoric feeling due to the common practice use of the equally divided chromatic scale, and Grumpy scales have it stronger because their small step is the the odd step out).

Modes

Modes of 6L 7s

UDP	Cyclic order	Step pattern
12|0	1	LsLsLsLsLsLss
11|1	3	LsLsLsLsLssLs
10|2	5	LsLsLsLssLsLs
9|3	7	LsLsLssLsLsLs
8|4	9	LsLssLsLsLsLs
7|5	11	LssLsLsLsLsLs
6|6	13	sLsLsLsLsLsLs
5|7	2	sLsLsLsLsLssL
4|8	4	sLsLsLsLssLsL
3|9	6	sLsLsLssLsLsL
2|10	8	sLsLssLsLsLsL
1|11	10	sLssLsLsLsLsL
0|12	12	ssLsLsLsLsLsL

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 7s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\13						184.615	1015.385	1:1	1.000	Equalized 6L 7s
					11\71	185.915	1014.085	6:5	1.200
				9\58		186.207	1013.793	5:4	1.250
					16\103	186.408	1013.592	9:7	1.286
			7\45			186.667	1013.333	4:3	1.333	Supersoft 6L 7s
					19\122	186.885	1013.115	11:8	1.375
				12\77		187.013	1012.987	7:5	1.400
					17\109	187.156	1012.844	10:7	1.429
		5\32				187.500	1012.500	3:2	1.500	Soft 6L 7s
					18\115	187.826	1012.174	11:7	1.571
				13\83		187.952	1012.048	8:5	1.600
					21\134	188.060	1011.940	13:8	1.625
			8\51			188.235	1011.765	5:3	1.667	Semisoft 6L 7s
					19\121	188.430	1011.570	12:7	1.714
				11\70		188.571	1011.429	7:4	1.750
					14\89	188.764	1011.236	9:5	1.800
	3\19					189.474	1010.526	2:1	2.000	Basic 6L 7s Scales with tunings softer than this are proper
					13\82	190.244	1009.756	9:4	2.250
				10\63		190.476	1009.524	7:3	2.333
					17\107	190.654	1009.346	12:5	2.400
			7\44			190.909	1009.091	5:2	2.500	Semihard 6L 7s
					18\113	191.150	1008.850	13:5	2.600
				11\69		191.304	1008.696	8:3	2.667
					15\94	191.489	1008.511	11:4	2.750
		4\25				192.000	1008.000	3:1	3.000	Hard 6L 7s
					13\81	192.593	1007.407	10:3	3.333
				9\56		192.857	1007.143	7:2	3.500
					14\87	193.103	1006.897	11:3	3.667
			5\31			193.548	1006.452	4:1	4.000	Superhard 6L 7s
					11\68	194.118	1005.882	9:2	4.500
				6\37		194.595	1005.405	5:1	5.000
					7\43	195.349	1004.651	6:1	6.000
1\6						200.000	1000.000	1:0	→ ∞	Collapsed 6L 7s