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¢)
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)
Ancestor's step ratio range	1:1 to 3:2 (soft)
Related MOS scales
Parent	10L 3s
Sister	13L 10s
Daughters	23L 10s, 10L 23s
Neutralized	20L 3s
2-Flought	33L 13s, 10L 36s
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¢.

Intervals

Intervals of 10L 13s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0¢ to 52.2¢
	Major 1-mosstep	M1ms	L	52.2¢ to 120.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 104.3¢
	Major 2-mosstep	M2ms	L + s	104.3¢ to 120.0¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	120.0¢ to 156.5¢
	Major 3-mosstep	M3ms	2L + s	156.5¢ to 240.0¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	120.0¢ to 208.7¢
	Major 4-mosstep	M4ms	2L + 2s	208.7¢ to 240.0¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	240.0¢ to 260.9¢
	Major 5-mosstep	M5ms	3L + 2s	260.9¢ to 360.0¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	240.0¢ to 313.0¢
	Major 6-mosstep	M6ms	3L + 3s	313.0¢ to 360.0¢
7-mosstep	Perfect 7-mosstep	P7ms	3L + 4s	360.0¢ to 365.2¢
	Augmented 7-mosstep	A7ms	4L + 3s	365.2¢ to 480.0¢
8-mosstep	Minor 8-mosstep	m8ms	3L + 5s	360.0¢ to 417.4¢
	Major 8-mosstep	M8ms	4L + 4s	417.4¢ to 480.0¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	360.0¢ to 469.6¢
	Major 9-mosstep	M9ms	4L + 5s	469.6¢ to 480.0¢
10-mosstep	Minor 10-mosstep	m10ms	4L + 6s	480.0¢ to 521.7¢
	Major 10-mosstep	M10ms	5L + 5s	521.7¢ to 600.0¢
11-mosstep	Minor 11-mosstep	m11ms	4L + 7s	480.0¢ to 573.9¢
	Major 11-mosstep	M11ms	5L + 6s	573.9¢ to 600.0¢
12-mosstep	Minor 12-mosstep	m12ms	5L + 7s	600.0¢ to 626.1¢
	Major 12-mosstep	M12ms	6L + 6s	626.1¢ to 720.0¢
13-mosstep	Minor 13-mosstep	m13ms	5L + 8s	600.0¢ to 678.3¢
	Major 13-mosstep	M13ms	6L + 7s	678.3¢ to 720.0¢
14-mosstep	Minor 14-mosstep	m14ms	6L + 8s	720.0¢ to 730.4¢
	Major 14-mosstep	M14ms	7L + 7s	730.4¢ to 840.0¢
15-mosstep	Minor 15-mosstep	m15ms	6L + 9s	720.0¢ to 782.6¢
	Major 15-mosstep	M15ms	7L + 8s	782.6¢ to 840.0¢
16-mosstep	Diminished 16-mosstep	d16ms	6L + 10s	720.0¢ to 834.8¢
	Perfect 16-mosstep	P16ms	7L + 9s	834.8¢ to 840.0¢
17-mosstep	Minor 17-mosstep	m17ms	7L + 10s	840.0¢ to 887.0¢
	Major 17-mosstep	M17ms	8L + 9s	887.0¢ to 960.0¢
18-mosstep	Minor 18-mosstep	m18ms	7L + 11s	840.0¢ to 939.1¢
	Major 18-mosstep	M18ms	8L + 10s	939.1¢ to 960.0¢
19-mosstep	Minor 19-mosstep	m19ms	8L + 11s	960.0¢ to 991.3¢
	Major 19-mosstep	M19ms	9L + 10s	991.3¢ to 1080.0¢
20-mosstep	Minor 20-mosstep	m20ms	8L + 12s	960.0¢ to 1043.5¢
	Major 20-mosstep	M20ms	9L + 11s	1043.5¢ to 1080.0¢
21-mosstep	Minor 21-mosstep	m21ms	9L + 12s	1080.0¢ to 1095.7¢
	Major 21-mosstep	M21ms	10L + 11s	1095.7¢ to 1200.0¢
22-mosstep	Minor 22-mosstep	m22ms	9L + 13s	1080.0¢ to 1147.8¢
	Major 22-mosstep	M22ms	10L + 12s	1147.8¢ to 1200.0¢
23-mosstep	Perfect 23-mosstep	P23ms	10L + 13s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 10L 13s

Generator(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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