3L 8s

3L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 8 small steps, repeating every octave. 3L 8s is a child scale of 3L 5s, expanding it by 3 tones. Generators that produce this scale range from 763.6 ¢ to 800 ¢, or from 400 ¢ to 436.4 ¢. This scale has versions relating to ditonic/coditone, roman, bossier, sqrtphi and squares.

↖ 2L 7s	↑ 3L 7s	4L 7s ↗
← 2L 8s	3L 8s	4L 8s →
↙ 2L 9s	↓ 3L 9s	4L 9s ↘

Scale structure
Step pattern	LssLsssLsss sssLsssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	7\11 to 2\3 (763.6 ¢ to 800.0 ¢)
Dark	1\3 to 4\11 (400.0 ¢ to 436.4 ¢)
TAMNAMS information
Related to	3L 5s (checkertonic)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	3L 5s
Sister	8L 3s
Daughters	11L 3s, 3L 11s
Neutralized	6L 5s
2-Flought	14L 8s, 3L 19s
Equal tunings
Equalized (L:s = 1:1)	7\11 (763.6 ¢)
Supersoft (L:s = 4:3)	23\36 (766.7 ¢)
Soft (L:s = 3:2)	16\25 (768.0 ¢)
Semisoft (L:s = 5:3)	25\39 (769.2 ¢)
Basic (L:s = 2:1)	9\14 (771.4 ¢)
Semihard (L:s = 5:2)	20\31 (774.2 ¢)
Hard (L:s = 3:1)	11\17 (776.5 ¢)
Superhard (L:s = 4:1)	13\20 (780.0 ¢)
Collapsed (L:s = 1:0)	2\3 (800.0 ¢)
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Modes

Modes of 3L 8s

UDP	Cyclic order	Step pattern
10|0	1	LssLsssLsss
9|1	8	LsssLssLsss
8|2	4	LsssLsssLss
7|3	11	sLssLsssLss
6|4	7	sLsssLssLss
5|5	3	sLsssLsssLs
4|6	10	ssLssLsssLs
3|7	6	ssLsssLssLs
2|8	2	ssLsssLsssL
1|9	9	sssLssLsssL
0|10	5	sssLsssLssL

Scale tree

Gen		Cents	L:s	Comments
1\3		400	∞	Paucitonic, 3edo
18\53		407.547		Ditonic
17\50		408.000
16\47		408.511
15\44		409.091
14\41		409.756
13\38		410.526
12\35		411.429
11\32		412.500
10\29		413.793		Roman
9\26		415.385
	17\49	416.3265
	25\72	416.667		Sqrtphi
8\23		417.391
7\20		420	4:1
	13\37	421.621		Bossier
		422.956
6\17		423.529	3:1
		424.76
	17\48	425
		425.23
	11\31	425.806	5:2	Squares
	16\45	426.667
5\14		428.521	2:1
	19\53	430.187
		430.312
	14\39	430.769
		431.1185
	23\64	431.25
		431.465
9\25		432	3:2
	22\61	432.787
13\36		433.333
17\47		434.043
21\58		434.483
25\69		434.783	7:6
29\80		435	8:7
33\91		435.164	9:8
4\11		436.364	1:1	Equalized, 11edo