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
Descends from	5L 3s
Ancestor's step ratio range	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 ¢.

Modes

Modes of 13L 5s

UDP	Cyclic order	Step pattern
17|0	1	LLLsLLLsLLsLLLsLLs
16|1	12	LLLsLLsLLLsLLLsLLs
15|2	5	LLLsLLsLLLsLLsLLLs
14|3	16	LLsLLLsLLLsLLsLLLs
13|4	9	LLsLLLsLLsLLLsLLLs
12|5	2	LLsLLLsLLsLLLsLLsL
11|6	13	LLsLLsLLLsLLLsLLsL
10|7	6	LLsLLsLLLsLLsLLLsL
9|8	17	LsLLLsLLLsLLsLLLsL
8|9	10	LsLLLsLLsLLLsLLLsL
7|10	3	LsLLLsLLsLLLsLLsLL
6|11	14	LsLLsLLLsLLLsLLsLL
5|12	7	LsLLsLLLsLLsLLLsLL
4|13	18	sLLLsLLLsLLsLLLsLL
3|14	11	sLLLsLLsLLLsLLLsLL
2|15	4	sLLLsLLsLLLsLLsLLL
1|16	15	sLLsLLLsLLLsLLsLLL
0|17	8	sLLsLLLsLLsLLLsLLL

Intervals

Intervals of 13L 5s

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 66.7 ¢
	Major 1-mosstep	M1ms	L	66.7 ¢ to 92.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	92.3 ¢ to 133.3 ¢
	Major 2-mosstep	M2ms	2L	133.3 ¢ to 184.6 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	184.6 ¢ to 200.0 ¢
	Major 3-mosstep	M3ms	3L	200.0 ¢ to 276.9 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	184.6 ¢ to 266.7 ¢
	Major 4-mosstep	M4ms	3L + s	266.7 ¢ to 276.9 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	276.9 ¢ to 333.3 ¢
	Major 5-mosstep	M5ms	4L + s	333.3 ¢ to 369.2 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	369.2 ¢ to 400.0 ¢
	Major 6-mosstep	M6ms	5L + s	400.0 ¢ to 461.5 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	461.5 ¢ to 466.7 ¢
	Augmented 7-mosstep	A7ms	6L + s	466.7 ¢ to 553.8 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	461.5 ¢ to 533.3 ¢
	Major 8-mosstep	M8ms	6L + 2s	533.3 ¢ to 553.8 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	553.8 ¢ to 600.0 ¢
	Major 9-mosstep	M9ms	7L + 2s	600.0 ¢ to 646.2 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	646.2 ¢ to 666.7 ¢
	Major 10-mosstep	M10ms	8L + 2s	666.7 ¢ to 738.5 ¢
11-mosstep	Diminished 11-mosstep	d11ms	7L + 4s	646.2 ¢ to 733.3 ¢
	Perfect 11-mosstep	P11ms	8L + 3s	733.3 ¢ to 738.5 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	738.5 ¢ to 800.0 ¢
	Major 12-mosstep	M12ms	9L + 3s	800.0 ¢ to 830.8 ¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	830.8 ¢ to 866.7 ¢
	Major 13-mosstep	M13ms	10L + 3s	866.7 ¢ to 923.1 ¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	923.1 ¢ to 933.3 ¢
	Major 14-mosstep	M14ms	11L + 3s	933.3 ¢ to 1015.4 ¢
15-mosstep	Minor 15-mosstep	m15ms	10L + 5s	923.1 ¢ to 1000.0 ¢
	Major 15-mosstep	M15ms	11L + 4s	1000.0 ¢ to 1015.4 ¢
16-mosstep	Minor 16-mosstep	m16ms	11L + 5s	1015.4 ¢ to 1066.7 ¢
	Major 16-mosstep	M16ms	12L + 4s	1066.7 ¢ to 1107.7 ¢
17-mosstep	Minor 17-mosstep	m17ms	12L + 5s	1107.7 ¢ to 1133.3 ¢
	Major 17-mosstep	M17ms	13L + 4s	1133.3 ¢ to 1200.0 ¢
18-mosstep	Perfect 18-mosstep	P18ms	13L + 5s	1200.0¢

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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