13L 5s

↖ 12L 4s	↑ 13L 4s	14L 4s ↗
← 12L 5s	13L 5s	14L 5s →
↙ 12L 6s	↓ 13L 6s	14L 6s ↘

┌╥╥╥┬╥╥╥┬╥╥┬╥╥╥┬╥╥┬┐ │║║║│║║║│║║│║║║│║║││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLsLLLsLLsLLLsLLs sLLsLLLsLLsLLLsLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	11\18 to 8\13 (733.3 ¢ to 738.5 ¢)
Dark	5\13 to 7\18 (461.5 ¢ to 466.7 ¢)
TAMNAMS information
Related to	5L 3s (oneirotonic)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	5L 8s
Sister	5L 13s
Daughters	18L 13s, 13L 18s
Neutralized	8L 10s
2-Flought	31L 5s, 13L 23s
Equal tunings
Equalized (L:s = 1:1)	11\18 (733.3 ¢)
Supersoft (L:s = 4:3)	41\67 (734.3 ¢)
Soft (L:s = 3:2)	30\49 (734.7 ¢)
Semisoft (L:s = 5:3)	49\80 (735.0 ¢)
Basic (L:s = 2:1)	19\31 (735.5 ¢)
Semihard (L:s = 5:2)	46\75 (736.0 ¢)
Hard (L:s = 3:1)	27\44 (736.4 ¢)
Superhard (L:s = 4:1)	35\57 (736.8 ¢)
Collapsed (L:s = 1:0)	8\13 (738.5 ¢)

13L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 5 small steps, repeating every octave. 13L 5s is a grandchild scale of 5L 3s, expanding it by 10 tones. Generators that produce this scale range from 733.3 ¢ to 738.5 ¢, or from 461.5 ¢ to 466.7 ¢.

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.

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

Scale tree

Scale tree and tuning spectrum of 13L 5s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
11\18						733.333	466.667	1:1	1.000	Equalized 13L 5s
					63\103	733.981	466.019	6:5	1.200
				52\85		734.118	465.882	5:4	1.250
					93\152	734.211	465.789	9:7	1.286
			41\67			734.328	465.672	4:3	1.333	Supersoft 13L 5s
					112\183	734.426	465.574	11:8	1.375
				71\116		734.483	465.517	7:5	1.400
					101\165	734.545	465.455	10:7	1.429
		30\49				734.694	465.306	3:2	1.500	Soft 13L 5s
					109\178	734.831	465.169	11:7	1.571
				79\129		734.884	465.116	8:5	1.600
					128\209	734.928	465.072	13:8	1.625
			49\80			735.000	465.000	5:3	1.667	Semisoft 13L 5s
					117\191	735.079	464.921	12:7	1.714
				68\111		735.135	464.865	7:4	1.750
					87\142	735.211	464.789	9:5	1.800
	19\31					735.484	464.516	2:1	2.000	Basic 13L 5s Scales with tunings softer than this are proper
					84\137	735.766	464.234	9:4	2.250
				65\106		735.849	464.151	7:3	2.333
					111\181	735.912	464.088	12:5	2.400
			46\75			736.000	464.000	5:2	2.500	Semihard 13L 5s
					119\194	736.082	463.918	13:5	2.600
				73\119		736.134	463.866	8:3	2.667
					100\163	736.196	463.804	11:4	2.750
		27\44				736.364	463.636	3:1	3.000	Hard 13L 5s
					89\145	736.552	463.448	10:3	3.333
				62\101		736.634	463.366	7:2	3.500
					97\158	736.709	463.291	11:3	3.667
			35\57			736.842	463.158	4:1	4.000	Superhard 13L 5s
					78\127	737.008	462.992	9:2	4.500
				43\70		737.143	462.857	5:1	5.000
					51\83	737.349	462.651	6:1	6.000
8\13						738.462	461.538	1:0	→ ∞	Collapsed 13L 5s

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