8L 5s

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↖ 7L 4s ↑ 8L 4s 9L 4s ↗
← 7L 5s 8L 5s 9L 5s →
↙ 7L 6s ↓ 8L 6s 9L 6s ↘ 
┌╥╥┬╥╥┬╥┬╥╥┬╥┬┐
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLsLLsLs
sLsLLsLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 8\13 to 5\8 (738.5 ¢ to 750.0 ¢)
Dark 3\8 to 5\13 (450.0 ¢ to 461.5 ¢)
TAMNAMS information
Descends from 5L 3s (oneirotonic)
Ancestor's step ratio range 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 5L 3s
Sister 5L 8s
Daughters 13L 8s, 8L 13s
Neutralized 3L 10s
2-Flought 21L 5s, 8L 18s
Equal tunings
Equalized (L:s = 1:1) 8\13 (738.5 ¢)
Supersoft (L:s = 4:3) 29\47 (740.4 ¢)
Soft (L:s = 3:2) 21\34 (741.2 ¢)
Semisoft (L:s = 5:3) 34\55 (741.8 ¢)
Basic (L:s = 2:1) 13\21 (742.9 ¢)
Semihard (L:s = 5:2) 31\50 (744.0 ¢)
Hard (L:s = 3:1) 18\29 (744.8 ¢)
Superhard (L:s = 4:1) 23\37 (745.9 ¢)
Collapsed (L:s = 1:0) 5\8 (750.0 ¢)

8L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 5 small steps, repeating every octave. 8L 5s is a child scale of 5L 3s, expanding it by 5 tones. Generators that produce this scale range from 738.5 ¢ to 750 ¢, or from 450 ¢ to 461.5 ¢.

8L 5s represents the chromatic scale of Semidim, Tridec, Ammonite, and Petrtri temperaments. It represents tempered chains of the 13:10 or 17:13 semisixth, thus rendering 10:13:17 as an equidistant triad and tempering out 170:169. Also, the ratio between the generator of this MOS and its inverse is close to logarithmic phi, or even logarithmic phi itself.

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 8L 5s
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 150.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 150.0 ¢ to 184.6 ¢
Major 2-mosstep M2ms 2L 184.6 ¢ to 300.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 150.0 ¢ to 276.9 ¢
Major 3-mosstep M3ms 2L + s 276.9 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 300.0 ¢ to 369.2 ¢
Major 4-mosstep M4ms 3L + s 369.2 ¢ to 450.0 ¢
5-mosstep Perfect 5-mosstep P5ms 3L + 2s 450.0 ¢ to 461.5 ¢
Augmented 5-mosstep A5ms 4L + s 461.5 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 450.0 ¢ to 553.8 ¢
Major 6-mosstep M6ms 4L + 2s 553.8 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 600.0 ¢ to 646.2 ¢
Major 7-mosstep M7ms 5L + 2s 646.2 ¢ to 750.0 ¢
8-mosstep Diminished 8-mosstep d8ms 4L + 4s 600.0 ¢ to 738.5 ¢
Perfect 8-mosstep P8ms 5L + 3s 738.5 ¢ to 750.0 ¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 750.0 ¢ to 830.8 ¢
Major 9-mosstep M9ms 6L + 3s 830.8 ¢ to 900.0 ¢
10-mosstep Minor 10-mosstep m10ms 6L + 4s 900.0 ¢ to 923.1 ¢
Major 10-mosstep M10ms 7L + 3s 923.1 ¢ to 1050.0 ¢
11-mosstep Minor 11-mosstep m11ms 6L + 5s 900.0 ¢ to 1015.4 ¢
Major 11-mosstep M11ms 7L + 4s 1015.4 ¢ to 1050.0 ¢
12-mosstep Minor 12-mosstep m12ms 7L + 5s 1050.0 ¢ to 1107.7 ¢
Major 12-mosstep M12ms 8L + 4s 1107.7 ¢ to 1200.0 ¢
13-mosstep Perfect 13-mosstep P13ms 8L + 5s 1200.0 ¢

Generator chain

Generator chain of 8L 5s
Bright gens Scale degree Abbrev.
20 Augmented 4-mosdegree A4md
19 Augmented 9-mosdegree A9md
18 Augmented 1-mosdegree A1md
17 Augmented 6-mosdegree A6md
16 Augmented 11-mosdegree A11md
15 Augmented 3-mosdegree A3md
14 Augmented 8-mosdegree A8md
13 Augmented 0-mosdegree A0md
12 Augmented 5-mosdegree A5md
11 Major 10-mosdegree M10md
10 Major 2-mosdegree M2md
9 Major 7-mosdegree M7md
8 Major 12-mosdegree M12md
7 Major 4-mosdegree M4md
6 Major 9-mosdegree M9md
5 Major 1-mosdegree M1md
4 Major 6-mosdegree M6md
3 Major 11-mosdegree M11md
2 Major 3-mosdegree M3md
1 Perfect 8-mosdegree P8md
0 Perfect 0-mosdegree
Perfect 13-mosdegree		 P0md
P13md
−1 Perfect 5-mosdegree P5md
−2 Minor 10-mosdegree m10md
−3 Minor 2-mosdegree m2md
−4 Minor 7-mosdegree m7md
−5 Minor 12-mosdegree m12md
−6 Minor 4-mosdegree m4md
−7 Minor 9-mosdegree m9md
−8 Minor 1-mosdegree m1md
−9 Minor 6-mosdegree m6md
−10 Minor 11-mosdegree m11md
−11 Minor 3-mosdegree m3md
−12 Diminished 8-mosdegree d8md
−13 Diminished 13-mosdegree d13md
−14 Diminished 5-mosdegree d5md
−15 Diminished 10-mosdegree d10md
−16 Diminished 2-mosdegree d2md
−17 Diminished 7-mosdegree d7md
−18 Diminished 12-mosdegree d12md
−19 Diminished 4-mosdegree d4md
−20 Diminished 9-mosdegree d9md

Modes

Scale degrees of the modes of 8L 5s
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 LLsLLsLsLLsLs Perf. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
11|1 9 LLsLsLLsLLsLs Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
10|2 4 LLsLsLLsLsLLs Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Min. Maj. Maj. Perf.
9|3 12 LsLLsLLsLsLLs Perf. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Min. Maj. Maj. Perf.
8|4 7 LsLLsLsLLsLLs Perf. Maj. Min. Maj. Maj. Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Perf.
7|5 2 LsLLsLsLLsLsL Perf. Maj. Min. Maj. Maj. Perf. Maj. Min. Perf. Maj. Min. Maj. Min. Perf.
6|6 10 LsLsLLsLLsLsL Perf. Maj. Min. Maj. Min. Perf. Maj. Min. Perf. Maj. Min. Maj. Min. Perf.
5|7 5 LsLsLLsLsLLsL Perf. Maj. Min. Maj. Min. Perf. Maj. Min. Perf. Min. Min. Maj. Min. Perf.
4|8 13 sLLsLLsLsLLsL Perf. Min. Min. Maj. Min. Perf. Maj. Min. Perf. Min. Min. Maj. Min. Perf.
3|9 8 sLLsLsLLsLLsL Perf. Min. Min. Maj. Min. Perf. Min. Min. Perf. Min. Min. Maj. Min. Perf.
2|10 3 sLLsLsLLsLsLL Perf. Min. Min. Maj. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Perf.
1|11 11 sLsLLsLLsLsLL Perf. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Perf.
0|12 6 sLsLLsLsLLsLL Perf. Min. Min. Min. Min. Perf. Min. Min. Dim. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 8L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
8\13 738.462 461.538 1:1 1.000 Equalized 8L 5s
45\73 739.726 460.274 6:5 1.200
37\60 740.000 460.000 5:4 1.250
66\107 740.187 459.813 9:7 1.286
29\47 740.426 459.574 4:3 1.333 Supersoft 8L 5s
79\128 740.625 459.375 11:8 1.375
50\81 740.741 459.259 7:5 1.400
71\115 740.870 459.130 10:7 1.429
21\34 741.176 458.824 3:2 1.500 Soft 8L 5s
76\123 741.463 458.537 11:7 1.571
55\89 741.573 458.427 8:5 1.600
89\144 741.667 458.333 13:8 1.625
34\55 741.818 458.182 5:3 1.667 Semisoft 8L 5s
81\131 741.985 458.015 12:7 1.714
47\76 742.105 457.895 7:4 1.750
60\97 742.268 457.732 9:5 1.800
13\21 742.857 457.143 2:1 2.000 Basic 8L 5s
Scales with tunings softer than this are proper
57\92 743.478 456.522 9:4 2.250
44\71 743.662 456.338 7:3 2.333
75\121 743.802 456.198 12:5 2.400
31\50 744.000 456.000 5:2 2.500 Semihard 8L 5s
80\129 744.186 455.814 13:5 2.600
49\79 744.304 455.696 8:3 2.667
67\108 744.444 455.556 11:4 2.750
18\29 744.828 455.172 3:1 3.000 Hard 8L 5s
59\95 745.263 454.737 10:3 3.333
41\66 745.455 454.545 7:2 3.500
64\103 745.631 454.369 11:3 3.667
23\37 745.946 454.054 4:1 4.000 Superhard 8L 5s
51\82 746.341 453.659 9:2 4.500
28\45 746.667 453.333 5:1 5.000
33\53 747.170 452.830 6:1 6.000
5\8 750.000 450.000 1:0 → ∞ Collapsed 8L 5s
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