9L 11s

↖ 8L 10s	↑ 9L 10s	10L 10s ↗
← 8L 11s	9L 11s	10L 11s →
↙ 8L 12s	↓ 9L 12s	10L 12s ↘

┌╥┬╥┬╥┬╥┬╥┬┬╥┬╥┬╥┬╥┬┬┐ │║│║│║│║│║││║│║│║│║│││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLsLsLsLssLsLsLsLss ssLsLsLsLssLsLsLsLsL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	11\20 to 5\9 (660.0¢ to 666.7¢)
Dark	4\9 to 9\20 (533.3¢ to 540.0¢)
TAMNAMS information
Descends from	2L 7s (balzano)
Ancestor's step ratio range	1:1 to 3:2 (soft)
Related MOS scales
Parent	9L 2s
Sister	11L 9s
Daughters	20L 9s, 9L 20s
Neutralized	18L 2s
2-Flought	29L 11s, 9L 31s
Equal tunings
Equalized (L:s = 1:1)	11\20 (660.0¢)
Supersoft (L:s = 4:3)	38\69 (660.9¢)
Soft (L:s = 3:2)	27\49 (661.2¢)
Semisoft (L:s = 5:3)	43\78 (661.5¢)
Basic (L:s = 2:1)	16\29 (662.1¢)
Semihard (L:s = 5:2)	37\67 (662.7¢)
Hard (L:s = 3:1)	21\38 (663.2¢)
Superhard (L:s = 4:1)	26\47 (663.8¢)
Collapsed (L:s = 1:0)	5\9 (666.7¢)

9L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 11 small steps, repeating every octave. 9L 11s is a grandchild scale of 2L 7s, expanding it by 11 tones. Generators that produce this scale range from 660¢ to 666.7¢, or from 533.3¢ to 540¢.

Modes

Modes of 9L 11s

UDP	Cyclic Order	Step Pattern
19|0	1	LsLsLsLsLssLsLsLsLss
18|1	12	LsLsLsLssLsLsLsLsLss
17|2	3	LsLsLsLssLsLsLsLssLs
16|3	14	LsLsLssLsLsLsLsLssLs
15|4	5	LsLsLssLsLsLsLssLsLs
14|5	16	LsLssLsLsLsLsLssLsLs
13|6	7	LsLssLsLsLsLssLsLsLs
12|7	18	LssLsLsLsLsLssLsLsLs
11|8	9	LssLsLsLsLssLsLsLsLs
10|9	20	sLsLsLsLsLssLsLsLsLs
9|10	11	sLsLsLsLssLsLsLsLsLs
8|11	2	sLsLsLsLssLsLsLsLssL
7|12	13	sLsLsLssLsLsLsLsLssL
6|13	4	sLsLsLssLsLsLsLssLsL
5|14	15	sLsLssLsLsLsLsLssLsL
4|15	6	sLsLssLsLsLsLssLsLsL
3|16	17	sLssLsLsLsLsLssLsLsL
2|17	8	sLssLsLsLsLssLsLsLsL
1|18	19	ssLsLsLsLsLssLsLsLsL
0|19	10	ssLsLsLsLssLsLsLsLsL

Scale tree

Scale Tree and Tuning Spectrum of 9L 11s

Generator(edo)						Cents		Step Ratio		Comments
						Bright	Dark	L:s	Hardness
11\20						660.000	540.000	1:1	1.000	Equalized 9L 11s
					60\109	660.550	539.450	6:5	1.200
				49\89		660.674	539.326	5:4	1.250
					87\158	660.759	539.241	9:7	1.286
			38\69			660.870	539.130	4:3	1.333	Supersoft 9L 11s
					103\187	660.963	539.037	11:8	1.375
				65\118		661.017	538.983	7:5	1.400
					92\167	661.078	538.922	10:7	1.429
		27\49				661.224	538.776	3:2	1.500	Soft 9L 11s
					97\176	661.364	538.636	11:7	1.571
				70\127		661.417	538.583	8:5	1.600
					113\205	661.463	538.537	13:8	1.625
			43\78			661.538	538.462	5:3	1.667	Semisoft 9L 11s
					102\185	661.622	538.378	12:7	1.714
				59\107		661.682	538.318	7:4	1.750
					75\136	661.765	538.235	9:5	1.800
	16\29					662.069	537.931	2:1	2.000	Basic 9L 11s Scales with tunings softer than this are proper
					69\125	662.400	537.600	9:4	2.250
				53\96		662.500	537.500	7:3	2.333
					90\163	662.577	537.423	12:5	2.400
			37\67			662.687	537.313	5:2	2.500	Semihard 9L 11s
					95\172	662.791	537.209	13:5	2.600
				58\105		662.857	537.143	8:3	2.667
					79\143	662.937	537.063	11:4	2.750
		21\38				663.158	536.842	3:1	3.000	Hard 9L 11s
					68\123	663.415	536.585	10:3	3.333
				47\85		663.529	536.471	7:2	3.500
					73\132	663.636	536.364	11:3	3.667
			26\47			663.830	536.170	4:1	4.000	Superhard 9L 11s
					57\103	664.078	535.922	9:2	4.500
				31\56		664.286	535.714	5:1	5.000
					36\65	664.615	535.385	6:1	6.000
5\9						666.667	533.333	1:0	→ ∞	Collapsed 9L 11s

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