13L 6s

↖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
Descends from	6L 1s (archaeotonic)
Required step ratio range	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	6L 7s
Sister	6L 13s
Daughters	19L 13s 13L 19s
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¢)

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¢.

Modes

Modes of 13L 6s

UDP	Rotational 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

Scale tree

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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