13L 2s

13L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 2 small steps, repeating every octave. 13L 2s is a great-grandchild scale of 2L 7s, expanding it by 6 tones. Generators that produce this scale range from 640 ¢ to 646.2 ¢, or from 553.8 ¢ to 560 ¢.

↖ 12L 1s	↑ 13L 1s	14L 1s ↗
← 12L 2s	13L 2s	14L 2s →
↙ 12L 3s	↓ 13L 3s	14L 3s ↘

Scale structure
Step pattern	LLLLLLLsLLLLLLs sLLLLLLsLLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	8\15 to 7\13 (640.0 ¢ to 646.2 ¢)
Dark	6\13 to 7\15 (553.8 ¢ to 560.0 ¢)
TAMNAMS information
Related to	2L 7s (balzano)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	2L 11s
Sister	2L 13s
Daughters	15L 13s, 13L 15s
Neutralized	11L 4s
2-Flought	28L 2s, 13L 17s
Equal tunings
Equalized (L:s = 1:1)	8\15 (640.0 ¢)
Supersoft (L:s = 4:3)	31\58 (641.4 ¢)
Soft (L:s = 3:2)	23\43 (641.9 ¢)
Semisoft (L:s = 5:3)	38\71 (642.3 ¢)
Basic (L:s = 2:1)	15\28 (642.9 ¢)
Semihard (L:s = 5:2)	37\69 (643.5 ¢)
Hard (L:s = 3:1)	22\41 (643.9 ¢)
Superhard (L:s = 4:1)	29\54 (644.4 ¢)
Collapsed (L:s = 1:0)	7\13 (646.2 ¢)
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The dark generator for this scale corresponds to a superfourth (interval sharper than 4/3). This generator has almost no sensible interpretation except to be taken as 11/8, meaning the MOS is an 11+-limit scale.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Template:MOS data is deprecated. Details: Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Scale tree

Scale tree and tuning spectrum of 13L 2s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
8\15						640.000	560.000	1:1	1.000	Equalized 13L 2s
					47\88	640.909	559.091	6:5	1.200
				39\73		641.096	558.904	5:4	1.250
					70\131	641.221	558.779	9:7	1.286
			31\58			641.379	558.621	4:3	1.333	Supersoft 13L 2s
					85\159	641.509	558.491	11:8	1.375
				54\101		641.584	558.416	7:5	1.400
					77\144	641.667	558.333	10:7	1.429
		23\43				641.860	558.140	3:2	1.500	Soft 13L 2s
					84\157	642.038	557.962	11:7	1.571
				61\114		642.105	557.895	8:5	1.600
					99\185	642.162	557.838	13:8	1.625
			38\71			642.254	557.746	5:3	1.667	Semisoft 13L 2s
					91\170	642.353	557.647	12:7	1.714
				53\99		642.424	557.576	7:4	1.750
					68\127	642.520	557.480	9:5	1.800
	15\28					642.857	557.143	2:1	2.000	Basic 13L 2s Scales with tunings softer than this are proper
					67\125	643.200	556.800	9:4	2.250
				52\97		643.299	556.701	7:3	2.333
					89\166	643.373	556.627	12:5	2.400
			37\69			643.478	556.522	5:2	2.500	Semihard 13L 2s
					96\179	643.575	556.425	13:5	2.600
				59\110		643.636	556.364	8:3	2.667
					81\151	643.709	556.291	11:4	2.750
		22\41				643.902	556.098	3:1	3.000	Hard 13L 2s
					73\136	644.118	555.882	10:3	3.333
				51\95		644.211	555.789	7:2	3.500
					80\149	644.295	555.705	11:3	3.667
			29\54			644.444	555.556	4:1	4.000	Superhard 13L 2s
					65\121	644.628	555.372	9:2	4.500
				36\67		644.776	555.224	5:1	5.000
					43\80	645.000	555.000	6:1	6.000
7\13						646.154	553.846	1:0	→ ∞	Collapsed 13L 2s