3L 8s

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↖ 2L 7s ↑3L 7s 4L 7s ↗
← 2L 8s3L 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
Descends from 3L 5s (checkertonic)
Required step ratio range 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¢)

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.

Modes

Modes of 3L 8s
UDP Rotational 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

Scale Tree and Tuning Spectrum of 3L 8s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
7\11 763.636 436.364 1:1 1.000 Equalized 3L 8s
37\58 765.517 434.483 6:5 1.200
30\47 765.957 434.043 5:4 1.250
53\83 766.265 433.735 9:7 1.286
23\36 766.667 433.333 4:3 1.333 Supersoft 3L 8s
62\97 767.010 432.990 11:8 1.375
39\61 767.213 432.787 7:5 1.400
55\86 767.442 432.558 10:7 1.429
16\25 768.000 432.000 3:2 1.500 Soft 3L 8s
57\89 768.539 431.461 11:7 1.571
41\64 768.750 431.250 8:5 1.600
66\103 768.932 431.068 13:8 1.625
25\39 769.231 430.769 5:3 1.667 Semisoft 3L 8s
59\92 769.565 430.435 12:7 1.714
34\53 769.811 430.189 7:4 1.750
43\67 770.149 429.851 9:5 1.800
9\14 771.429 428.571 2:1 2.000 Basic 3L 8s
Scales with tunings softer than this are proper
38\59 772.881 427.119 9:4 2.250
29\45 773.333 426.667 7:3 2.333
49\76 773.684 426.316 12:5 2.400
20\31 774.194 425.806 5:2 2.500 Semihard 3L 8s
Squares
51\79 774.684 425.316 13:5 2.600
31\48 775.000 425.000 8:3 2.667
42\65 775.385 424.615 11:4 2.750
11\17 776.471 423.529 3:1 3.000 Hard 3L 8s
35\54 777.778 422.222 10:3 3.333
24\37 778.378 421.622 7:2 3.500 Bossier
37\57 778.947 421.053 11:3 3.667
13\20 780.000 420.000 4:1 4.000 Superhard 3L 8s
28\43 781.395 418.605 9:2 4.500
15\23 782.609 417.391 5:1 5.000
17\26 784.615 415.385 6:1 6.000 Ditonic, Roman
2\3 800.000 400.000 1:0 → ∞ Collapsed 3L 8s