8L 13s

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↖ 7L 12s ↑ 8L 12s 9L 12s ↗
← 7L 13s 8L 13s 9L 13s →
↙ 7L 14s ↓ 8L 14s 9L 14s ↘ 
┌╥┬╥┬┬╥┬╥┬┬╥┬┬╥┬╥┬┬╥┬┬┐
│║│║││║│║││║││║│║││║│││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLssLsLssLssLsLssLss
ssLssLsLssLssLsLssLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 13\21 to 5\8 (742.9 ¢ to 750.0 ¢)
Dark 3\8 to 8\21 (450.0 ¢ to 457.1 ¢)
TAMNAMS information
Related to 5L 3s (oneirotonic)
With tunings 1:1 to 3:2 (soft)
Related MOS scales
Parent 8L 5s
Sister 13L 8s
Daughters 21L 8s, 8L 21s
Neutralized 16L 5s
2-Flought 29L 13s, 8L 34s
Equal tunings
Equalized (L:s = 1:1) 13\21 (742.9 ¢)
Supersoft (L:s = 4:3) 44\71 (743.7 ¢)
Soft (L:s = 3:2) 31\50 (744.0 ¢)
Semisoft (L:s = 5:3) 49\79 (744.3 ¢)
Basic (L:s = 2:1) 18\29 (744.8 ¢)
Semihard (L:s = 5:2) 41\66 (745.5 ¢)
Hard (L:s = 3:1) 23\37 (745.9 ¢)
Superhard (L:s = 4:1) 28\45 (746.7 ¢)
Collapsed (L:s = 1:0) 5\8 (750.0 ¢)

8L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 13 small steps, repeating every octave. 8L 13s is a grandchild scale of 5L 3s, expanding it by 13 tones. Generators that produce this scale range from 742.9 ¢ to 750 ¢, or from 450 ¢ to 457.1 ¢.

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 interval regions.

Intervals

Intervals of 8L 13s
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 57.1 ¢
Major 1-mosstep M1ms L 57.1 ¢ to 150.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 114.3 ¢
Major 2-mosstep M2ms L + s 114.3 ¢ to 150.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 150.0 ¢ to 171.4 ¢
Major 3-mosstep M3ms 2L + s 171.4 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 150.0 ¢ to 228.6 ¢
Major 4-mosstep M4ms 2L + 2s 228.6 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 150.0 ¢ to 285.7 ¢
Major 5-mosstep M5ms 2L + 3s 285.7 ¢ to 300.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 300.0 ¢ to 342.9 ¢
Major 6-mosstep M6ms 3L + 3s 342.9 ¢ to 450.0 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 300.0 ¢ to 400.0 ¢
Major 7-mosstep M7ms 3L + 4s 400.0 ¢ to 450.0 ¢
8-mosstep Perfect 8-mosstep P8ms 3L + 5s 450.0 ¢ to 457.1 ¢
Augmented 8-mosstep A8ms 4L + 4s 457.1 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 450.0 ¢ to 514.3 ¢
Major 9-mosstep M9ms 4L + 5s 514.3 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 450.0 ¢ to 571.4 ¢
Major 10-mosstep M10ms 4L + 6s 571.4 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 600.0 ¢ to 628.6 ¢
Major 11-mosstep M11ms 5L + 6s 628.6 ¢ to 750.0 ¢
12-mosstep Minor 12-mosstep m12ms 4L + 8s 600.0 ¢ to 685.7 ¢
Major 12-mosstep M12ms 5L + 7s 685.7 ¢ to 750.0 ¢
13-mosstep Diminished 13-mosstep d13ms 4L + 9s 600.0 ¢ to 742.9 ¢
Perfect 13-mosstep P13ms 5L + 8s 742.9 ¢ to 750.0 ¢
14-mosstep Minor 14-mosstep m14ms 5L + 9s 750.0 ¢ to 800.0 ¢
Major 14-mosstep M14ms 6L + 8s 800.0 ¢ to 900.0 ¢
15-mosstep Minor 15-mosstep m15ms 5L + 10s 750.0 ¢ to 857.1 ¢
Major 15-mosstep M15ms 6L + 9s 857.1 ¢ to 900.0 ¢
16-mosstep Minor 16-mosstep m16ms 6L + 10s 900.0 ¢ to 914.3 ¢
Major 16-mosstep M16ms 7L + 9s 914.3 ¢ to 1050.0 ¢
17-mosstep Minor 17-mosstep m17ms 6L + 11s 900.0 ¢ to 971.4 ¢
Major 17-mosstep M17ms 7L + 10s 971.4 ¢ to 1050.0 ¢
18-mosstep Minor 18-mosstep m18ms 6L + 12s 900.0 ¢ to 1028.6 ¢
Major 18-mosstep M18ms 7L + 11s 1028.6 ¢ to 1050.0 ¢
19-mosstep Minor 19-mosstep m19ms 7L + 12s 1050.0 ¢ to 1085.7 ¢
Major 19-mosstep M19ms 8L + 11s 1085.7 ¢ to 1200.0 ¢
20-mosstep Minor 20-mosstep m20ms 7L + 13s 1050.0 ¢ to 1142.9 ¢
Major 20-mosstep M20ms 8L + 12s 1142.9 ¢ to 1200.0 ¢
21-mosstep Perfect 21-mosstep P21ms 8L + 13s 1200.0 ¢

Generator chain

Generator chain of 8L 13s
Bright gens Scale degree Abbrev.
28 Augmented 7-mosdegree A7md
27 Augmented 15-mosdegree A15md
26 Augmented 2-mosdegree A2md
25 Augmented 10-mosdegree A10md
24 Augmented 18-mosdegree A18md
23 Augmented 5-mosdegree A5md
22 Augmented 13-mosdegree A13md
21 Augmented 0-mosdegree A0md
20 Augmented 8-mosdegree A8md
19 Major 16-mosdegree M16md
18 Major 3-mosdegree M3md
17 Major 11-mosdegree M11md
16 Major 19-mosdegree M19md
15 Major 6-mosdegree M6md
14 Major 14-mosdegree M14md
13 Major 1-mosdegree M1md
12 Major 9-mosdegree M9md
11 Major 17-mosdegree M17md
10 Major 4-mosdegree M4md
9 Major 12-mosdegree M12md
8 Major 20-mosdegree M20md
7 Major 7-mosdegree M7md
6 Major 15-mosdegree M15md
5 Major 2-mosdegree M2md
4 Major 10-mosdegree M10md
3 Major 18-mosdegree M18md
2 Major 5-mosdegree M5md
1 Perfect 13-mosdegree P13md
0 Perfect 0-mosdegree
Perfect 21-mosdegree		 P0md
P21md
−1 Perfect 8-mosdegree P8md
−2 Minor 16-mosdegree m16md
−3 Minor 3-mosdegree m3md
−4 Minor 11-mosdegree m11md
−5 Minor 19-mosdegree m19md
−6 Minor 6-mosdegree m6md
−7 Minor 14-mosdegree m14md
−8 Minor 1-mosdegree m1md
−9 Minor 9-mosdegree m9md
−10 Minor 17-mosdegree m17md
−11 Minor 4-mosdegree m4md
−12 Minor 12-mosdegree m12md
−13 Minor 20-mosdegree m20md
−14 Minor 7-mosdegree m7md
−15 Minor 15-mosdegree m15md
−16 Minor 2-mosdegree m2md
−17 Minor 10-mosdegree m10md
−18 Minor 18-mosdegree m18md
−19 Minor 5-mosdegree m5md
−20 Diminished 13-mosdegree d13md
−21 Diminished 21-mosdegree d21md
−22 Diminished 8-mosdegree d8md
−23 Diminished 16-mosdegree d16md
−24 Diminished 3-mosdegree d3md
−25 Diminished 11-mosdegree d11md
−26 Diminished 19-mosdegree d19md
−27 Diminished 6-mosdegree d6md
−28 Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 8L 13s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
20|0 1 LsLssLsLssLssLsLssLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
19|1 14 LsLssLssLsLssLsLssLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
18|2 6 LsLssLssLsLssLssLsLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf.
17|3 19 LssLsLssLsLssLssLsLss Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf.
16|4 11 LssLsLssLssLsLssLsLss Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf.
15|5 3 LssLsLssLssLsLssLssLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf.
14|6 16 LssLssLsLssLsLssLssLs Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf.
13|7 8 LssLssLsLssLssLsLssLs Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf.
12|8 21 sLsLssLsLssLssLsLssLs Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf.
11|9 13 sLsLssLssLsLssLsLssLs Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf.
10|10 5 sLsLssLssLsLssLssLsLs Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf.
9|11 18 sLssLsLssLsLssLssLsLs Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf.
8|12 10 sLssLsLssLssLsLssLsLs Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf.
7|13 2 sLssLsLssLssLsLssLssL Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf.
6|14 15 sLssLssLsLssLsLssLssL Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf.
5|15 7 sLssLssLsLssLssLsLssL Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Perf.
4|16 20 ssLsLssLsLssLssLsLssL Perf. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Perf.
3|17 12 ssLsLssLssLsLssLsLssL Perf. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Perf.
2|18 4 ssLsLssLssLsLssLssLsL Perf. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.
1|19 17 ssLssLsLssLsLssLssLsL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.
0|20 9 ssLssLsLssLssLsLssLsL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 8L 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\21 742.857 457.143 1:1 1.000 Equalized 8L 13s
70\113 743.363 456.637 6:5 1.200
57\92 743.478 456.522 5:4 1.250
101\163 743.558 456.442 9:7 1.286
44\71 743.662 456.338 4:3 1.333 Supersoft 8L 13s
119\192 743.750 456.250 11:8 1.375
75\121 743.802 456.198 7:5 1.400
106\171 743.860 456.140 10:7 1.429
31\50 744.000 456.000 3:2 1.500 Soft 8L 13s
111\179 744.134 455.866 11:7 1.571
80\129 744.186 455.814 8:5 1.600
129\208 744.231 455.769 13:8 1.625
49\79 744.304 455.696 5:3 1.667 Semisoft 8L 13s
116\187 744.385 455.615 12:7 1.714
67\108 744.444 455.556 7:4 1.750
85\137 744.526 455.474 9:5 1.800
18\29 744.828 455.172 2:1 2.000 Basic 8L 13s
Scales with tunings softer than this are proper
77\124 745.161 454.839 9:4 2.250
59\95 745.263 454.737 7:3 2.333
100\161 745.342 454.658 12:5 2.400
41\66 745.455 454.545 5:2 2.500 Semihard 8L 13s
105\169 745.562 454.438 13:5 2.600
64\103 745.631 454.369 8:3 2.667
87\140 745.714 454.286 11:4 2.750
23\37 745.946 454.054 3:1 3.000 Hard 8L 13s
74\119 746.218 453.782 10:3 3.333
51\82 746.341 453.659 7:2 3.500
79\127 746.457 453.543 11:3 3.667
28\45 746.667 453.333 4:1 4.000 Superhard 8L 13s
61\98 746.939 453.061 9:2 4.500
33\53 747.170 452.830 5:1 5.000
38\61 747.541 452.459 6:1 6.000
5\8 750.000 450.000 1:0 → ∞ Collapsed 8L 13s
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