7L 10s

↖6L 9s	↑7L 9s	8L 9s↗
←6L 10s	7L 10s	8L 10s→
↙6L 11s	↓7L 11s	8L 11s↘

┌╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬┐ │║│║│║││║│║││║│║│││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLsLssLsLssLsLss ssLsLssLsLssLsLsL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Step size ranges
Large	1\17 to 1\7 (70.6¢ to 171.4¢)
Small	0\7 to 1\17 (0.0¢ to 70.6¢)
Generator size
Bright	12\17 to 5\7 (847.1¢ to 857.1¢)
Dark	2\7 to 5\17 (342.9¢ to 352.9¢)
TAMNAMS information
Descends from	7L 3s (dicoid)
Related MOS scales
Parent	7L 3s
Sister	10L 7s
Daughters	17L 7s 7L 17s
Equal tunings
Equalized (L:s = 1:1)	12\17 (847.1¢)
Supersoft (L:s = 4:3)	41\58 (848.3¢)
Soft (L:s = 3:2)	29\41 (848.8¢)
Semisoft (L:s = 5:3)	46\65 (849.2¢)
Basic (L:s = 2:1)	17\24 (850.0¢)
Semihard (L:s = 5:2)	39\55 (850.9¢)
Hard (L:s = 3:1)	22\31 (851.6¢)
Superhard (L:s = 4:1)	27\38 (852.6¢)
Collapsed (L:s = 1:0)	5\7 (857.1¢)

7L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 10 small steps, repeating every octave. 7L 10s is a child scale of 7L 3s, expanding it by 7 tones. Generators that produce this scale range from 847.1¢ to 857.1¢, or from 342.9¢ to 352.9¢.

This MOS is a neutral thirds-style meantone scale which spaces its large steps 2s-s-s-2s-s-s-s-2s. It is an improper Mohajira scale when the generator is c. 9/31edo (348.387 cents) and its entire spectrum is 2/7edo (342.857) to 5/17edo (352.941 cents).

Modes

Modes of 7L 10s

UDP	Rotational order	Step pattern
16|0	1	LsLsLssLsLssLsLss
15|1	13	LsLssLsLsLssLsLss
14|2	8	LsLssLsLssLsLsLss
13|3	3	LsLssLsLssLsLssLs
12|4	15	LssLsLsLssLsLssLs
11|5	10	LssLsLssLsLsLssLs
10|6	5	LssLsLssLsLssLsLs
9|7	17	sLsLsLssLsLssLsLs
8|8	12	sLsLssLsLsLssLsLs
7|9	7	sLsLssLsLssLsLsLs
6|10	2	sLsLssLsLssLsLssL
5|11	14	sLssLsLsLssLsLssL
4|12	9	sLssLsLssLsLsLssL
3|13	4	sLssLsLssLsLssLsL
2|14	16	ssLsLsLssLsLssLsL
1|15	11	ssLsLssLsLsLssLsL
0|16	6	ssLsLssLsLssLsLsL

Scale tree

Scale tree and tuning spectrum of 7L 10s

Generator (in steps of edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
12\17						847.059	352.941	1:1	1.000	Equalized 7L 10s
					65\92	847.826	352.174	6:5	1.200
				53\75		848.000	352.000	5:4	1.250
					94\133	848.120	351.880	9:7	1.286
			41\58			848.276	351.724	4:3	1.333	Supersoft 7L 10s
					111\157	848.408	351.592	11:8	1.375
				70\99		848.485	351.515	7:5	1.400
					99\140	848.571	351.429	10:7	1.429
		29\41				848.780	351.220	3:2	1.500	Soft 7L 10s
					104\147	848.980	351.020	11:7	1.571
				75\106		849.057	350.943	8:5	1.600
					121\171	849.123	350.877	13:8	1.625
			46\65			849.231	350.769	5:3	1.667	Semisoft 7L 10s
					109\154	849.351	350.649	12:7	1.714
				63\89		849.438	350.562	7:4	1.750
					80\113	849.558	350.442	9:5	1.800
	17\24					850.000	350.000	2:1	2.000	Basic 7L 10s Scales with tunings softer than this are proper
					73\103	850.485	349.515	9:4	2.250
				56\79		850.633	349.367	7:3	2.333
					95\134	850.746	349.254	12:5	2.400
			39\55			850.909	349.091	5:2	2.500	Semihard 7L 10s
					100\141	851.064	348.936	13:5	2.600
				61\86		851.163	348.837	8:3	2.667
					83\117	851.282	348.718	11:4	2.750
		22\31				851.613	348.387	3:1	3.000	Hard 7L 10s
					71\100	852.000	348.000	10:3	3.333
				49\69		852.174	347.826	7:2	3.500
					76\107	852.336	347.664	11:3	3.667
			27\38			852.632	347.368	4:1	4.000	Superhard 7L 10s
					59\83	853.012	346.988	9:2	4.500
				32\45		853.333	346.667	5:1	5.000
					37\52	853.846	346.154	6:1	6.000
5\7						857.143	342.857	1:0	→ ∞	Collapsed 7L 10s