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 ¢.

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

Tuning spectrum

generator								L	s	L/s	gen (cents)	comment
5\13								1	0		461.538
							42\109	8	1	8.000	462.385
						37\96		7	1	7.000	462.500
					32\83			6	1	6.000	462.651
				27\70				5	1	5.000	462.857
					49\127			9	2	4.500	462.992
			22\57					4	1	4.000	463.158
				39\101				7	2	3.500	463.366
					56\145			10	3	3.333	463.448
		17\44						3	1	3.000	463.636
				46\119				8	3	2.667	463.866
			29\75					5	2	2.500	464.000
				41\106				7	3	2.333	464.151
					53\137			9	4	2.250	464.234
	12\31							2	1	2.000	464.516
					55\142			9	5	1.800	464.789
				43\111				7	4	1.750	464.865
			31\80					5	3	1.667	465.000
				50\129				8	5	1.600	465.116
		19\49						3	2	1.500	465.306
				45\116				7	5	1.400	465.517
			26\67					4	3	1.333	465.672
				33\85				5	4	1.250	465.882
					40\103			6	5	1.200	466.019
						47\121		7	6	1.167	466.116
							54\139	8	7	1.143	466.187
7\18								1	1	1.000	466.667