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.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

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 ¢

Generator chain

Generator chain of 5L 8s
Bright gens Scale degree Abbrev.
17 Augmented 7-mosdegree A7md
16 Augmented 2-mosdegree A2md
15 Augmented 10-mosdegree A10md
14 Augmented 5-mosdegree A5md
13 Augmented 0-mosdegree A0md
12 Augmented 8-mosdegree A8md
11 Major 3-mosdegree M3md
10 Major 11-mosdegree M11md
9 Major 6-mosdegree M6md
8 Major 1-mosdegree M1md
7 Major 9-mosdegree M9md
6 Major 4-mosdegree M4md
5 Major 12-mosdegree M12md
4 Major 7-mosdegree M7md
3 Major 2-mosdegree M2md
2 Major 10-mosdegree M10md
1 Perfect 5-mosdegree P5md
0 Perfect 0-mosdegree
Perfect 13-mosdegree		 P0md
P13md
−1 Perfect 8-mosdegree P8md
−2 Minor 3-mosdegree m3md
−3 Minor 11-mosdegree m11md
−4 Minor 6-mosdegree m6md
−5 Minor 1-mosdegree m1md
−6 Minor 9-mosdegree m9md
−7 Minor 4-mosdegree m4md
−8 Minor 12-mosdegree m12md
−9 Minor 7-mosdegree m7md
−10 Minor 2-mosdegree m2md
−11 Minor 10-mosdegree m10md
−12 Diminished 5-mosdegree d5md
−13 Diminished 13-mosdegree d13md
−14 Diminished 8-mosdegree d8md
−15 Diminished 3-mosdegree d3md
−16 Diminished 11-mosdegree d11md
−17 Diminished 6-mosdegree d6md

Modes

Scale degrees of the modes of 5L 8s
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
12|0 1 LsLssLsLssLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Perf.
11|1 6 LsLssLssLsLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
10|2 11 LssLsLssLsLss Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
9|3 3 LssLsLssLssLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Perf.
8|4 8 LssLssLsLssLs Perf. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
7|5 13 sLsLssLsLssLs Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
6|6 5 sLsLssLssLsLs Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
5|7 10 sLssLsLssLsLs Perf. Min. Maj. Min. Min. Perf. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
4|8 2 sLssLsLssLssL Perf. Min. Maj. Min. Min. Perf. Min. Maj. Perf. Min. Maj. Min. Min. Perf.
3|9 7 sLssLssLsLssL Perf. Min. Maj. Min. Min. Perf. Min. Min. Perf. Min. Maj. Min. Min. Perf.
2|10 12 ssLsLssLsLssL Perf. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Maj. Min. Min. Perf.
1|11 4 ssLsLssLssLsL Perf. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Perf.
0|12 9 ssLssLsLssLsL Perf. Min. Min. Min. Min. Dim. Min. Min. Perf. Min. Min. Min. Min. Perf.

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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