13L 3s

↖ 12L 2s	↑ 13L 2s	14L 2s ↗
← 12L 3s	13L 3s	14L 3s →
↙ 12L 4s	↓ 13L 4s	14L 4s ↘

┌╥╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐ │║║║║║│║║║║│║║║║││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLsLLLLsLLLLs sLLLLsLLLLsLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	11\16 to 9\13 (825.0 ¢ to 830.8 ¢)
Dark	4\13 to 5\16 (369.2 ¢ to 375.0 ¢)
TAMNAMS information
Related to	3L 7s (sephiroid)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	3L 10s
Sister	3L 13s
Daughters	16L 13s, 13L 16s
Neutralized	10L 6s
2-Flought	29L 3s, 13L 19s
Equal tunings
Equalized (L:s = 1:1)	11\16 (825.0 ¢)
Supersoft (L:s = 4:3)	42\61 (826.2 ¢)
Soft (L:s = 3:2)	31\45 (826.7 ¢)
Semisoft (L:s = 5:3)	51\74 (827.0 ¢)
Basic (L:s = 2:1)	20\29 (827.6 ¢)
Semihard (L:s = 5:2)	49\71 (828.2 ¢)
Hard (L:s = 3:1)	29\42 (828.6 ¢)
Superhard (L:s = 4:1)	38\55 (829.1 ¢)
Collapsed (L:s = 1:0)	9\13 (830.8 ¢)

13L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 3 small steps, repeating every octave. 13L 3s is a grandchild scale of 3L 7s, expanding it by 6 tones. Generators that produce this scale range from 825 ¢ to 830.8 ¢, or from 369.2 ¢ to 375 ¢.

Modes

Modes of 13L 3s

UDP	Cyclic order	Step pattern
15|0	1	LLLLLsLLLLsLLLLs
14|1	12	LLLLsLLLLLsLLLLs
13|2	7	LLLLsLLLLsLLLLLs
12|3	2	LLLLsLLLLsLLLLsL
11|4	13	LLLsLLLLLsLLLLsL
10|5	8	LLLsLLLLsLLLLLsL
9|6	3	LLLsLLLLsLLLLsLL
8|7	14	LLsLLLLLsLLLLsLL
7|8	9	LLsLLLLsLLLLLsLL
6|9	4	LLsLLLLsLLLLsLLL
5|10	15	LsLLLLLsLLLLsLLL
4|11	10	LsLLLLsLLLLLsLLL
3|12	5	LsLLLLsLLLLsLLLL
2|13	16	sLLLLLsLLLLsLLLL
1|14	11	sLLLLsLLLLLsLLLL
0|15	6	sLLLLsLLLLsLLLLL

Intervals

Intervals of 13L 3s

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 75.0 ¢
	Major 1-mosstep	M1ms	L	75.0 ¢ to 92.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	92.3 ¢ to 150.0 ¢
	Major 2-mosstep	M2ms	2L	150.0 ¢ to 184.6 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	184.6 ¢ to 225.0 ¢
	Major 3-mosstep	M3ms	3L	225.0 ¢ to 276.9 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	276.9 ¢ to 300.0 ¢
	Major 4-mosstep	M4ms	4L	300.0 ¢ to 369.2 ¢
5-mosstep	Perfect 5-mosstep	P5ms	4L + s	369.2 ¢ to 375.0 ¢
	Augmented 5-mosstep	A5ms	5L	375.0 ¢ to 461.5 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	369.2 ¢ to 450.0 ¢
	Major 6-mosstep	M6ms	5L + s	450.0 ¢ to 461.5 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	461.5 ¢ to 525.0 ¢
	Major 7-mosstep	M7ms	6L + s	525.0 ¢ to 553.8 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	553.8 ¢ to 600.0 ¢
	Major 8-mosstep	M8ms	7L + s	600.0 ¢ to 646.2 ¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	646.2 ¢ to 675.0 ¢
	Major 9-mosstep	M9ms	8L + s	675.0 ¢ to 738.5 ¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	738.5 ¢ to 750.0 ¢
	Major 10-mosstep	M10ms	9L + s	750.0 ¢ to 830.8 ¢
11-mosstep	Diminished 11-mosstep	d11ms	8L + 3s	738.5 ¢ to 825.0 ¢
	Perfect 11-mosstep	P11ms	9L + 2s	825.0 ¢ to 830.8 ¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	830.8 ¢ to 900.0 ¢
	Major 12-mosstep	M12ms	10L + 2s	900.0 ¢ to 923.1 ¢
13-mosstep	Minor 13-mosstep	m13ms	10L + 3s	923.1 ¢ to 975.0 ¢
	Major 13-mosstep	M13ms	11L + 2s	975.0 ¢ to 1015.4 ¢
14-mosstep	Minor 14-mosstep	m14ms	11L + 3s	1015.4 ¢ to 1050.0 ¢
	Major 14-mosstep	M14ms	12L + 2s	1050.0 ¢ to 1107.7 ¢
15-mosstep	Minor 15-mosstep	m15ms	12L + 3s	1107.7 ¢ to 1125.0 ¢
	Major 15-mosstep	M15ms	13L + 2s	1125.0 ¢ to 1200.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	13L + 3s	1200.0 ¢

Scale tree

This page is a stub. You can help the Xenharmonic Wiki by expanding it.