3L 13s

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

┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║││││║││││││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssLssssLsssss sssssLssssLssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	5\16 to 1\3 (375.0 ¢ to 400.0 ¢)
Dark	2\3 to 11\16 (800.0 ¢ to 825.0 ¢)
TAMNAMS information
Related to	3L 7s (sephiroid)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	3L 10s
Sister	13L 3s
Daughters	16L 3s, 3L 16s
Neutralized	6L 10s
2-Flought	19L 13s, 3L 29s
Equal tunings
Equalized (L:s = 1:1)	5\16 (375.0 ¢)
Supersoft (L:s = 4:3)	16\51 (376.5 ¢)
Soft (L:s = 3:2)	11\35 (377.1 ¢)
Semisoft (L:s = 5:3)	17\54 (377.8 ¢)
Basic (L:s = 2:1)	6\19 (378.9 ¢)
Semihard (L:s = 5:2)	13\41 (380.5 ¢)
Hard (L:s = 3:1)	7\22 (381.8 ¢)
Superhard (L:s = 4:1)	8\25 (384.0 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)

3L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 13 small steps, repeating every octave. 3L 13s is a grandchild scale of 3L 7s, expanding it by 6 tones. Generators that produce this scale range from 375 ¢ to 400 ¢, or from 800 ¢ to 825 ¢. This MOS, having its large steps separated by intervals of 4s, 4s and 5s; is the quasi-enharmonic scale of Magic temperament. It is also the smallest MOS which is ideal for composing melodies in Magic temperament, owing to the fact that the optimal generator range for it is the range where Magic temperament is tuned most accurately (6/19edo to 7/22edo); and is generated by a small major third no smaller than 5/16edo (375 cents).

Modes

Modes of 3L 13s

UDP	Cyclic order	Step pattern
15|0	1	LssssLssssLsssss
14|1	6	LssssLsssssLssss
13|2	11	LsssssLssssLssss
12|3	16	sLssssLssssLssss
11|4	5	sLssssLsssssLsss
10|5	10	sLsssssLssssLsss
9|6	15	ssLssssLssssLsss
8|7	4	ssLssssLsssssLss
7|8	9	ssLsssssLssssLss
6|9	14	sssLssssLssssLss
5|10	3	sssLssssLsssssLs
4|11	8	sssLsssssLssssLs
3|12	13	ssssLssssLssssLs
2|13	2	ssssLssssLsssssL
1|14	7	ssssLsssssLssssL
0|15	12	sssssLssssLssssL

Scale tree

1/3						0	0
					10\31	154.839	193.548
				9/28		171.429	214.286
					17/53	181.132	226.415
			8/25			192	240
					23/72	200	250
				15/47		204.255	255.319
					22/69	208.696	260.87
						214.049	267.561
		7/22				218.182	272.727
					27/85	225.882	282.353
						226.898	283.623
				20/63		228.571	285.714
						230.1705	287.713
					33/104	230.769	288.4615
			13/41			234.146	292.683
					32/101	237.624	297.03
				19/60		240	300
					25/79	243.038	303.7975
	6/19					252.632	315.789
					29/92	260.87	326.087
				23/73		263.014	328.767
						263.792	329.74
					40/127	264.567	330.709
			17/54			266.667	333.333
					45/143	264.828	331.034
						268.846	336.057
				28/89		269.663	337.079
					39/124	270.968	338.71
						270.997	338.746
		11/35				274.286	342.857
					38/121	277.686	347.107
				27/86		279.07	348.837
					43/137	280.292	350.365
			16/51			282.353	352.941
					37/118	284.746	355.932
				21/67		286.567	358.209
					26/83	289.157	361.446
5/16						300	375