13L 6s

13L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 6 small steps, repeating every octave. 13L 6s is a grandchild scale of 6L 1s, expanding it by 12 tones. Generators that produce this scale range from 1010.5 ¢ to 1015.4 ¢, or from 184.6 ¢ to 189.5 ¢.

↖ 12L 5s	↑ 13L 5s	14L 5s ↗
← 12L 6s	13L 6s	14L 6s →
↙ 12L 7s	↓ 13L 7s	14L 7s ↘

Scale structure
Step pattern	LLLsLLsLLsLLsLLsLLs sLLsLLsLLsLLsLLsLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	16\19 to 11\13 (1010.5 ¢ to 1015.4 ¢)
Dark	2\13 to 3\19 (184.6 ¢ to 189.5 ¢)
TAMNAMS information
Related to	6L 1s (archaeotonic)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	6L 7s
Sister	6L 13s
Daughters	19L 13s, 13L 19s
Neutralized	7L 12s
2-Flought	32L 6s, 13L 25s
Equal tunings
Equalized (L:s = 1:1)	16\19 (1010.5 ¢)
Supersoft (L:s = 4:3)	59\70 (1011.4 ¢)
Soft (L:s = 3:2)	43\51 (1011.8 ¢)
Semisoft (L:s = 5:3)	70\83 (1012.0 ¢)
Basic (L:s = 2:1)	27\32 (1012.5 ¢)
Semihard (L:s = 5:2)	65\77 (1013.0 ¢)
Hard (L:s = 3:1)	38\45 (1013.3 ¢)
Superhard (L:s = 4:1)	49\58 (1013.8 ¢)
Collapsed (L:s = 1:0)	11\13 (1015.4 ¢)
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Modes

Modes of 13L 6s

UDP	Cyclic order	Step pattern
18|0	1	LLLsLLsLLsLLsLLsLLs
17|1	17	LLsLLLsLLsLLsLLsLLs
16|2	14	LLsLLsLLLsLLsLLsLLs
15|3	11	LLsLLsLLsLLLsLLsLLs
14|4	8	LLsLLsLLsLLsLLLsLLs
13|5	5	LLsLLsLLsLLsLLsLLLs
12|6	2	LLsLLsLLsLLsLLsLLsL
11|7	18	LsLLLsLLsLLsLLsLLsL
10|8	15	LsLLsLLLsLLsLLsLLsL
9|9	12	LsLLsLLsLLLsLLsLLsL
8|10	9	LsLLsLLsLLsLLLsLLsL
7|11	6	LsLLsLLsLLsLLsLLLsL
6|12	3	LsLLsLLsLLsLLsLLsLL
5|13	19	sLLLsLLsLLsLLsLLsLL
4|14	16	sLLsLLLsLLsLLsLLsLL
3|15	13	sLLsLLsLLLsLLsLLsLL
2|16	10	sLLsLLsLLsLLLsLLsLL
1|17	7	sLLsLLsLLsLLsLLLsLL
0|18	4	sLLsLLsLLsLLsLLsLLL

Intervals

Intervals of 13L 6s

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 63.2 ¢
	Major 1-mosstep	M1ms	L	63.2 ¢ to 92.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	92.3 ¢ to 126.3 ¢
	Major 2-mosstep	M2ms	2L	126.3 ¢ to 184.6 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	184.6 ¢ to 189.5 ¢
	Augmented 3-mosstep	A3ms	3L	189.5 ¢ to 276.9 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	184.6 ¢ to 252.6 ¢
	Major 4-mosstep	M4ms	3L + s	252.6 ¢ to 276.9 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	276.9 ¢ to 315.8 ¢
	Major 5-mosstep	M5ms	4L + s	315.8 ¢ to 369.2 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	369.2 ¢ to 378.9 ¢
	Major 6-mosstep	M6ms	5L + s	378.9 ¢ to 461.5 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	369.2 ¢ to 442.1 ¢
	Major 7-mosstep	M7ms	5L + 2s	442.1 ¢ to 461.5 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	461.5 ¢ to 505.3 ¢
	Major 8-mosstep	M8ms	6L + 2s	505.3 ¢ to 553.8 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	553.8 ¢ to 568.4 ¢
	Major 9-mosstep	M9ms	7L + 2s	568.4 ¢ to 646.2 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	553.8 ¢ to 631.6 ¢
	Major 10-mosstep	M10ms	7L + 3s	631.6 ¢ to 646.2 ¢
11-mosstep	Minor 11-mosstep	m11ms	7L + 4s	646.2 ¢ to 694.7 ¢
	Major 11-mosstep	M11ms	8L + 3s	694.7 ¢ to 738.5 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	738.5 ¢ to 757.9 ¢
	Major 12-mosstep	M12ms	9L + 3s	757.9 ¢ to 830.8 ¢
13-mosstep	Minor 13-mosstep	m13ms	8L + 5s	738.5 ¢ to 821.1 ¢
	Major 13-mosstep	M13ms	9L + 4s	821.1 ¢ to 830.8 ¢
14-mosstep	Minor 14-mosstep	m14ms	9L + 5s	830.8 ¢ to 884.2 ¢
	Major 14-mosstep	M14ms	10L + 4s	884.2 ¢ to 923.1 ¢
15-mosstep	Minor 15-mosstep	m15ms	10L + 5s	923.1 ¢ to 947.4 ¢
	Major 15-mosstep	M15ms	11L + 4s	947.4 ¢ to 1015.4 ¢
16-mosstep	Diminished 16-mosstep	d16ms	10L + 6s	923.1 ¢ to 1010.5 ¢
	Perfect 16-mosstep	P16ms	11L + 5s	1010.5 ¢ to 1015.4 ¢
17-mosstep	Minor 17-mosstep	m17ms	11L + 6s	1015.4 ¢ to 1073.7 ¢
	Major 17-mosstep	M17ms	12L + 5s	1073.7 ¢ to 1107.7 ¢
18-mosstep	Minor 18-mosstep	m18ms	12L + 6s	1107.7 ¢ to 1136.8 ¢
	Major 18-mosstep	M18ms	13L + 5s	1136.8 ¢ to 1200.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	13L + 6s	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 6s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
16\19						1010.526	189.474	1:1	1.000	Equalized 13L 6s
					91\108	1011.111	188.889	6:5	1.200
				75\89		1011.236	188.764	5:4	1.250
					134\159	1011.321	188.679	9:7	1.286
			59\70			1011.429	188.571	4:3	1.333	Supersoft 13L 6s
					161\191	1011.518	188.482	11:8	1.375
				102\121		1011.570	188.430	7:5	1.400
					145\172	1011.628	188.372	10:7	1.429
		43\51				1011.765	188.235	3:2	1.500	Soft 13L 6s
					156\185	1011.892	188.108	11:7	1.571
				113\134		1011.940	188.060	8:5	1.600
					183\217	1011.982	188.018	13:8	1.625
			70\83			1012.048	187.952	5:3	1.667	Semisoft 13L 6s
					167\198	1012.121	187.879	12:7	1.714
				97\115		1012.174	187.826	7:4	1.750
					124\147	1012.245	187.755	9:5	1.800
	27\32					1012.500	187.500	2:1	2.000	Basic 13L 6s Scales with tunings softer than this are proper
					119\141	1012.766	187.234	9:4	2.250
				92\109		1012.844	187.156	7:3	2.333
					157\186	1012.903	187.097	12:5	2.400
			65\77			1012.987	187.013	5:2	2.500	Semihard 13L 6s
					168\199	1013.065	186.935	13:5	2.600
				103\122		1013.115	186.885	8:3	2.667
					141\167	1013.174	186.826	11:4	2.750
		38\45				1013.333	186.667	3:1	3.000	Hard 13L 6s
					125\148	1013.514	186.486	10:3	3.333
				87\103		1013.592	186.408	7:2	3.500
					136\161	1013.665	186.335	11:3	3.667
			49\58			1013.793	186.207	4:1	4.000	Superhard 13L 6s
					109\129	1013.953	186.047	9:2	4.500
				60\71		1014.085	185.915	5:1	5.000
					71\84	1014.286	185.714	6:1	6.000
11\13						1015.385	184.615	1:0	→ ∞	Collapsed 13L 6s

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