13L 10s

Todo: expand, confirm Confirm temperaments that correspond with this mos

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

Scale structure
Step pattern	LLsLsLsLLsLsLsLLsLsLsLs sLsLsLsLLsLsLsLLsLsLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	7\23 to 4\13 (365.2 ¢ to 369.2 ¢)
Dark	9\13 to 16\23 (830.8 ¢ to 834.8 ¢)
TAMNAMS information
Related to	3L 7s (sephiroid)
With tunings	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	10L 3s
Sister	10L 13s
Daughters	23L 13s, 13L 23s
Neutralized	3L 20s
2-Flought	36L 10s, 13L 33s
Equal tunings
Equalized (L:s = 1:1)	7\23 (365.2 ¢)
Supersoft (L:s = 4:3)	25\82 (365.9 ¢)
Soft (L:s = 3:2)	18\59 (366.1 ¢)
Semisoft (L:s = 5:3)	29\95 (366.3 ¢)
Basic (L:s = 2:1)	11\36 (366.7 ¢)
Semihard (L:s = 5:2)	26\85 (367.1 ¢)
Hard (L:s = 3:1)	15\49 (367.3 ¢)
Superhard (L:s = 4:1)	19\62 (367.7 ¢)
Collapsed (L:s = 1:0)	4\13 (369.2 ¢)
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13L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 10 small steps, repeating every octave. 13L 10s is a grandchild scale of 3L 7s, expanding it by 13 tones. Generators that produce this scale range from 365.2 ¢ to 369.2 ¢, or from 830.8 ¢ to 834.8 ¢.

This scale is the quartertone scale of unidec temperament.

Modes

Modes of 13L 10s

UDP	Cyclic order	Step pattern
22|0	1	LLsLsLsLLsLsLsLLsLsLsLs
21|1	8	LLsLsLsLLsLsLsLsLLsLsLs
20|2	15	LLsLsLsLsLLsLsLsLLsLsLs
19|3	22	LsLLsLsLsLLsLsLsLLsLsLs
18|4	6	LsLLsLsLsLLsLsLsLsLLsLs
17|5	13	LsLLsLsLsLsLLsLsLsLLsLs
16|6	20	LsLsLLsLsLsLLsLsLsLLsLs
15|7	4	LsLsLLsLsLsLLsLsLsLsLLs
14|8	11	LsLsLLsLsLsLsLLsLsLsLLs
13|9	18	LsLsLsLLsLsLsLLsLsLsLLs
12|10	2	LsLsLsLLsLsLsLLsLsLsLsL
11|11	9	LsLsLsLLsLsLsLsLLsLsLsL
10|12	16	LsLsLsLsLLsLsLsLLsLsLsL
9|13	23	sLLsLsLsLLsLsLsLLsLsLsL
8|14	7	sLLsLsLsLLsLsLsLsLLsLsL
7|15	14	sLLsLsLsLsLLsLsLsLLsLsL
6|16	21	sLsLLsLsLsLLsLsLsLLsLsL
5|17	5	sLsLLsLsLsLLsLsLsLsLLsL
4|18	12	sLsLLsLsLsLsLLsLsLsLLsL
3|19	19	sLsLsLLsLsLsLLsLsLsLLsL
2|20	3	sLsLsLLsLsLsLLsLsLsLsLL
1|21	10	sLsLsLLsLsLsLsLLsLsLsLL
0|22	17	sLsLsLsLLsLsLsLLsLsLsLL

Intervals

Intervals of 13L 10s

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 92.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	92.3 ¢ to 104.3 ¢
	Major 2-mosstep	M2ms	2L	104.3 ¢ to 184.6 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	92.3 ¢ to 156.5 ¢
	Major 3-mosstep	M3ms	2L + s	156.5 ¢ to 184.6 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	184.6 ¢ to 208.7 ¢
	Major 4-mosstep	M4ms	3L + s	208.7 ¢ to 276.9 ¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	184.6 ¢ to 260.9 ¢
	Major 5-mosstep	M5ms	3L + 2s	260.9 ¢ to 276.9 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	276.9 ¢ to 313.0 ¢
	Major 6-mosstep	M6ms	4L + 2s	313.0 ¢ to 369.2 ¢
7-mosstep	Diminished 7-mosstep	d7ms	3L + 4s	276.9 ¢ to 365.2 ¢
	Perfect 7-mosstep	P7ms	4L + 3s	365.2 ¢ to 369.2 ¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	369.2 ¢ to 417.4 ¢
	Major 8-mosstep	M8ms	5L + 3s	417.4 ¢ to 461.5 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	461.5 ¢ to 469.6 ¢
	Major 9-mosstep	M9ms	6L + 3s	469.6 ¢ to 553.8 ¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	461.5 ¢ to 521.7 ¢
	Major 10-mosstep	M10ms	6L + 4s	521.7 ¢ to 553.8 ¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	553.8 ¢ to 573.9 ¢
	Major 11-mosstep	M11ms	7L + 4s	573.9 ¢ to 646.2 ¢
12-mosstep	Minor 12-mosstep	m12ms	6L + 6s	553.8 ¢ to 626.1 ¢
	Major 12-mosstep	M12ms	7L + 5s	626.1 ¢ to 646.2 ¢
13-mosstep	Minor 13-mosstep	m13ms	7L + 6s	646.2 ¢ to 678.3 ¢
	Major 13-mosstep	M13ms	8L + 5s	678.3 ¢ to 738.5 ¢
14-mosstep	Minor 14-mosstep	m14ms	7L + 7s	646.2 ¢ to 730.4 ¢
	Major 14-mosstep	M14ms	8L + 6s	730.4 ¢ to 738.5 ¢
15-mosstep	Minor 15-mosstep	m15ms	8L + 7s	738.5 ¢ to 782.6 ¢
	Major 15-mosstep	M15ms	9L + 6s	782.6 ¢ to 830.8 ¢
16-mosstep	Perfect 16-mosstep	P16ms	9L + 7s	830.8 ¢ to 834.8 ¢
	Augmented 16-mosstep	A16ms	10L + 6s	834.8 ¢ to 923.1 ¢
17-mosstep	Minor 17-mosstep	m17ms	9L + 8s	830.8 ¢ to 887.0 ¢
	Major 17-mosstep	M17ms	10L + 7s	887.0 ¢ to 923.1 ¢
18-mosstep	Minor 18-mosstep	m18ms	10L + 8s	923.1 ¢ to 939.1 ¢
	Major 18-mosstep	M18ms	11L + 7s	939.1 ¢ to 1015.4 ¢
19-mosstep	Minor 19-mosstep	m19ms	10L + 9s	923.1 ¢ to 991.3 ¢
	Major 19-mosstep	M19ms	11L + 8s	991.3 ¢ to 1015.4 ¢
20-mosstep	Minor 20-mosstep	m20ms	11L + 9s	1015.4 ¢ to 1043.5 ¢
	Major 20-mosstep	M20ms	12L + 8s	1043.5 ¢ to 1107.7 ¢
21-mosstep	Minor 21-mosstep	m21ms	11L + 10s	1015.4 ¢ to 1095.7 ¢
	Major 21-mosstep	M21ms	12L + 9s	1095.7 ¢ to 1107.7 ¢
22-mosstep	Minor 22-mosstep	m22ms	12L + 10s	1107.7 ¢ to 1147.8 ¢
	Major 22-mosstep	M22ms	13L + 9s	1147.8 ¢ to 1200.0 ¢
23-mosstep	Perfect 23-mosstep	P23ms	13L + 10s	1200.0 ¢

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 13L 10s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\23						365.217	834.783	1:1	1.000	Equalized 13L 10s
					39\128	365.625	834.375	6:5	1.200
				32\105		365.714	834.286	5:4	1.250
					57\187	365.775	834.225	9:7	1.286
			25\82			365.854	834.146	4:3	1.333	Supersoft 13L 10s
					68\223	365.919	834.081	11:8	1.375
				43\141		365.957	834.043	7:5	1.400
					61\200	366.000	834.000	10:7	1.429
		18\59				366.102	833.898	3:2	1.500	Soft 13L 10s
					65\213	366.197	833.803	11:7	1.571
				47\154		366.234	833.766	8:5	1.600
					76\249	366.265	833.735	13:8	1.625
			29\95			366.316	833.684	5:3	1.667	Semisoft 13L 10s
					69\226	366.372	833.628	12:7	1.714
				40\131		366.412	833.588	7:4	1.750
					51\167	366.467	833.533	9:5	1.800
	11\36					366.667	833.333	2:1	2.000	Basic 13L 10s Scales with tunings softer than this are proper
					48\157	366.879	833.121	9:4	2.250
				37\121		366.942	833.058	7:3	2.333
					63\206	366.990	833.010	12:5	2.400
			26\85			367.059	832.941	5:2	2.500	Semihard 13L 10s
					67\219	367.123	832.877	13:5	2.600
				41\134		367.164	832.836	8:3	2.667
					56\183	367.213	832.787	11:4	2.750
		15\49				367.347	832.653	3:1	3.000	Hard 13L 10s
					49\160	367.500	832.500	10:3	3.333
				34\111		367.568	832.432	7:2	3.500
					53\173	367.630	832.370	11:3	3.667
			19\62			367.742	832.258	4:1	4.000	Superhard 13L 10s
					42\137	367.883	832.117	9:2	4.500
				23\75		368.000	832.000	5:1	5.000
					27\88	368.182	831.818	6:1	6.000
4\13						369.231	830.769	1:0	→ ∞	Collapsed 13L 10s