10L 13s

↖9L 12s	↑10L 12s	11L 12s↗
←9L 13s	10L 13s	11L 13s→
↙9L 14s	↓10L 14s	11L 14s↘

┌╥┬╥┬╥┬╥┬┬╥┬╥┬╥┬┬╥┬╥┬╥┬┬┐ │║│║│║│║││║│║│║││║│║│║│││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLsLsLssLsLsLssLsLsLss ssLsLsLssLsLsLssLsLsLsL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Step size
Large	1\23 to 1\10 (52.2¢ to 120.0¢)
Small	0\10 to 1\23 (0.0¢ to 52.2¢)
Generator size
Bright	16\23 to 7\10 (834.8¢ to 840.0¢)
Dark	3\10 to 7\23 (360.0¢ to 365.2¢)
TAMNAMS information
Descends from	3L 7s (sephiroid)
Related MOS scales
Parent	10L 3s
Sister	13L 10s
Daughters	23L 10s 10L 23s
Equal tunings
Equalized (L:s = 1:1)	16\23 (834.8¢)
Supersoft (L:s = 4:3)	55\79 (835.4¢)
Soft (L:s = 3:2)	39\56 (835.7¢)
Semisoft (L:s = 5:3)	62\89 (836.0¢)
Basic (L:s = 2:1)	23\33 (836.4¢)
Semihard (L:s = 5:2)	53\76 (836.8¢)
Hard (L:s = 3:1)	30\43 (837.2¢)
Superhard (L:s = 4:1)	37\53 (837.7¢)
Collapsed (L:s = 1:0)	7\10 (840.0¢)

10L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 13 small steps, repeating every octave. 10L 13s is a grandchild scale of 3L 7s, expanding it by 13 tones. Generators that produce this scale range from 834.8¢ to 840¢, or from 360¢ to 365.2¢.

Modes

Modes of 10L 13s

UDP	Rotational order	Step pattern
22|0	1	LsLsLsLssLsLsLssLsLsLss
21|1	17	LsLsLssLsLsLsLssLsLsLss
20|2	10	LsLsLssLsLsLssLsLsLsLss
19|3	3	LsLsLssLsLsLssLsLsLssLs
18|4	19	LsLssLsLsLsLssLsLsLssLs
17|5	12	LsLssLsLsLssLsLsLsLssLs
16|6	5	LsLssLsLsLssLsLsLssLsLs
15|7	21	LssLsLsLsLssLsLsLssLsLs
14|8	14	LssLsLsLssLsLsLsLssLsLs
13|9	7	LssLsLsLssLsLsLssLsLsLs
12|10	23	sLsLsLsLssLsLsLssLsLsLs
11|11	16	sLsLsLssLsLsLsLssLsLsLs
10|12	9	sLsLsLssLsLsLssLsLsLsLs
9|13	2	sLsLsLssLsLsLssLsLsLssL
8|14	18	sLsLssLsLsLsLssLsLsLssL
7|15	11	sLsLssLsLsLssLsLsLsLssL
6|16	4	sLsLssLsLsLssLsLsLssLsL
5|17	20	sLssLsLsLsLssLsLsLssLsL
4|18	13	sLssLsLsLssLsLsLsLssLsL
3|19	6	sLssLsLsLssLsLsLssLsLsL
2|20	22	ssLsLsLsLssLsLsLssLsLsL
1|21	15	ssLsLsLssLsLsLsLssLsLsL
0|22	8	ssLsLsLssLsLsLssLsLsLsL

Scale tree

Scale tree and tuning spectrum of 10L 13s

Generator (in steps of edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
16\23						834.783	365.217	1:1	1.000	Equalized 10L 13s
					87\125	835.200	364.800	6:5	1.200
				71\102		835.294	364.706	5:4	1.250
					126\181	835.359	364.641	9:7	1.286
			55\79			835.443	364.557	4:3	1.333	Supersoft 10L 13s
					149\214	835.514	364.486	11:8	1.375
				94\135		835.556	364.444	7:5	1.400
					133\191	835.602	364.398	10:7	1.429
		39\56				835.714	364.286	3:2	1.500	Soft 10L 13s
					140\201	835.821	364.179	11:7	1.571
				101\145		835.862	364.138	8:5	1.600
					163\234	835.897	364.103	13:8	1.625
			62\89			835.955	364.045	5:3	1.667	Semisoft 10L 13s
					147\211	836.019	363.981	12:7	1.714
				85\122		836.066	363.934	7:4	1.750
					108\155	836.129	363.871	9:5	1.800
	23\33					836.364	363.636	2:1	2.000	Basic 10L 13s Scales with tunings softer than this are proper
					99\142	836.620	363.380	9:4	2.250
				76\109		836.697	363.303	7:3	2.333
					129\185	836.757	363.243	12:5	2.400
			53\76			836.842	363.158	5:2	2.500	Semihard 10L 13s
					136\195	836.923	363.077	13:5	2.600
				83\119		836.975	363.025	8:3	2.667
					113\162	837.037	362.963	11:4	2.750
		30\43				837.209	362.791	3:1	3.000	Hard 10L 13s
					97\139	837.410	362.590	10:3	3.333
				67\96		837.500	362.500	7:2	3.500
					104\149	837.584	362.416	11:3	3.667
			37\53			837.736	362.264	4:1	4.000	Superhard 10L 13s
					81\116	837.931	362.069	9:2	4.500
				44\63		838.095	361.905	5:1	5.000
					51\73	838.356	361.644	6:1	6.000
7\10						840.000	360.000	1:0	→ ∞	Collapsed 10L 13s

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