5L 8s

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↖ 4L 7s ↑ 5L 7s 6L 7s ↗
← 4L 8s 5L 8s 6L 8s →
↙ 4L 9s ↓ 5L 9s 6L 9s ↘ 
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│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLssLsLssLss
ssLssLsLssLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 5\13 to 2\5 (461.5¢ to 480.0¢)
Dark 3\5 to 8\13 (720.0¢ to 738.5¢)
TAMNAMS information
Descends from 5L 3s (oneirotonic)
Ancestor's step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 5L 3s
Sister 8L 5s
Daughters 13L 5s, 5L 13s
Neutralized 10L 3s
2-Flought 18L 8s, 5L 21s
Equal tunings
Equalized (L:s = 1:1) 5\13 (461.5¢)
Supersoft (L:s = 4:3) 17\44 (463.6¢)
Soft (L:s = 3:2) 12\31 (464.5¢)
Semisoft (L:s = 5:3) 19\49 (465.3¢)
Basic (L:s = 2:1) 7\18 (466.7¢)
Semihard (L:s = 5:2) 16\41 (468.3¢)
Hard (L:s = 3:1) 9\23 (469.6¢)
Superhard (L:s = 4:1) 11\28 (471.4¢)
Collapsed (L:s = 1:0) 2\5 (480.0¢)

5L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 8 small steps, repeating every octave. 5L 8s is a child scale of 5L 3s, expanding it by 5 tones. Generators that produce this scale range from 461.5¢ to 480¢, or from 720¢ to 738.5¢.

5L 8s represents the chromatic scales of Semisept, A-Team and Vulture temperaments.

Modes

Modes of 5L 8s
UDP Cyclic
order		 Step
pattern
12|0 1 LsLssLsLssLss
11|1 6 LsLssLssLsLss
10|2 11 LssLsLssLsLss
9|3 3 LssLsLssLssLs
8|4 8 LssLssLsLssLs
7|5 13 sLsLssLsLssLs
6|6 5 sLsLssLssLsLs
5|7 10 sLssLsLssLsLs
4|8 2 sLssLsLssLssL
3|9 7 sLssLssLsLssL
2|10 12 ssLsLssLsLssL
1|11 4 ssLsLssLssLsL
0|12 9 ssLssLsLssLsL

Intervals

Intervals of 5L 8s
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 92.3¢
Major 1-mosstep M1ms L 92.3¢ to 240.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 184.6¢
Major 2-mosstep M2ms L + s 184.6¢ to 240.0¢
3-mosstep Minor 3-mosstep m3ms L + 2s 240.0¢ to 276.9¢
Major 3-mosstep M3ms 2L + s 276.9¢ to 480.0¢
4-mosstep Minor 4-mosstep m4ms L + 3s 240.0¢ to 369.2¢
Major 4-mosstep M4ms 2L + 2s 369.2¢ to 480.0¢
5-mosstep Diminished 5-mosstep d5ms L + 4s 240.0¢ to 461.5¢
Perfect 5-mosstep P5ms 2L + 3s 461.5¢ to 480.0¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 480.0¢ to 553.8¢
Major 6-mosstep M6ms 3L + 3s 553.8¢ to 720.0¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 480.0¢ to 646.2¢
Major 7-mosstep M7ms 3L + 4s 646.2¢ to 720.0¢
8-mosstep Perfect 8-mosstep P8ms 3L + 5s 720.0¢ to 738.5¢
Augmented 8-mosstep A8ms 4L + 4s 738.5¢ to 960.0¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 720.0¢ to 830.8¢
Major 9-mosstep M9ms 4L + 5s 830.8¢ to 960.0¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 720.0¢ to 923.1¢
Major 10-mosstep M10ms 4L + 6s 923.1¢ to 960.0¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 960.0¢ to 1015.4¢
Major 11-mosstep M11ms 5L + 6s 1015.4¢ to 1200.0¢
12-mosstep Minor 12-mosstep m12ms 4L + 8s 960.0¢ to 1107.7¢
Major 12-mosstep M12ms 5L + 7s 1107.7¢ to 1200.0¢
13-mosstep Perfect 13-mosstep P13ms 5L + 8s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 5L 8s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\13 461.538 738.462 1:1 1.000 Equalized 5L 8s
27\70 462.857 737.143 6:5 1.200
22\57 463.158 736.842 5:4 1.250
39\101 463.366 736.634 9:7 1.286
17\44 463.636 736.364 4:3 1.333 Supersoft 5L 8s
46\119 463.866 736.134 11:8 1.375
29\75 464.000 736.000 7:5 1.400
41\106 464.151 735.849 10:7 1.429
12\31 464.516 735.484 3:2 1.500 Soft 5L 8s
43\111 464.865 735.135 11:7 1.571
31\80 465.000 735.000 8:5 1.600
50\129 465.116 734.884 13:8 1.625
19\49 465.306 734.694 5:3 1.667 Semisoft 5L 8s
45\116 465.517 734.483 12:7 1.714
26\67 465.672 734.328 7:4 1.750
33\85 465.882 734.118 9:5 1.800
7\18 466.667 733.333 2:1 2.000 Basic 5L 8s
Scales with tunings softer than this are proper
30\77 467.532 732.468 9:4 2.250
23\59 467.797 732.203 7:3 2.333
39\100 468.000 732.000 12:5 2.400
16\41 468.293 731.707 5:2 2.500 Semihard 5L 8s
41\105 468.571 731.429 13:5 2.600
25\64 468.750 731.250 8:3 2.667
34\87 468.966 731.034 11:4 2.750
9\23 469.565 730.435 3:1 3.000 Hard 5L 8s
29\74 470.270 729.730 10:3 3.333
20\51 470.588 729.412 7:2 3.500
31\79 470.886 729.114 11:3 3.667
11\28 471.429 728.571 4:1 4.000 Superhard 5L 8s
24\61 472.131 727.869 9:2 4.500
13\33 472.727 727.273 5:1 5.000
15\38 473.684 726.316 6:1 6.000
2\5 480.000 720.000 1:0 → ∞ Collapsed 5L 8s
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