13L 5s

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↖ 12L 4s ↑ 13L 4s 14L 4s ↗
← 12L 5s 13L 5s 14L 5s →
↙ 12L 6s ↓ 13L 6s 14L 6s ↘ 
┌╥╥╥┬╥╥╥┬╥╥┬╥╥╥┬╥╥┬┐
│║║║│║║║│║║│║║║│║║││
││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLLsLLsLLLsLLs
sLLsLLLsLLsLLLsLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\18 to 8\13 (733.3 ¢ to 738.5 ¢)
Dark 5\13 to 7\18 (461.5 ¢ to 466.7 ¢)
TAMNAMS information
Related to 5L 3s (oneirotonic)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 5L 8s
Sister 5L 13s
Daughters 18L 13s, 13L 18s
Neutralized 8L 10s
2-Flought 31L 5s, 13L 23s
Equal tunings
Equalized (L:s = 1:1) 11\18 (733.3 ¢)
Supersoft (L:s = 4:3) 41\67 (734.3 ¢)
Soft (L:s = 3:2) 30\49 (734.7 ¢)
Semisoft (L:s = 5:3) 49\80 (735.0 ¢)
Basic (L:s = 2:1) 19\31 (735.5 ¢)
Semihard (L:s = 5:2) 46\75 (736.0 ¢)
Hard (L:s = 3:1) 27\44 (736.4 ¢)
Superhard (L:s = 4:1) 35\57 (736.8 ¢)
Collapsed (L:s = 1:0) 8\13 (738.5 ¢)

13L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 5 small steps, repeating every octave. 13L 5s is a grandchild scale of 5L 3s, expanding it by 10 tones. Generators that produce this scale range from 733.3 ¢ to 738.5 ¢, or from 461.5 ¢ to 466.7 ¢.

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 13L 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 66.7 ¢
Major 1-mosstep M1ms L 66.7 ¢ to 92.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 92.3 ¢ to 133.3 ¢
Major 2-mosstep M2ms 2L 133.3 ¢ to 184.6 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 184.6 ¢ to 200.0 ¢
Major 3-mosstep M3ms 3L 200.0 ¢ to 276.9 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 184.6 ¢ to 266.7 ¢
Major 4-mosstep M4ms 3L + s 266.7 ¢ to 276.9 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 276.9 ¢ to 333.3 ¢
Major 5-mosstep M5ms 4L + s 333.3 ¢ to 369.2 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 369.2 ¢ to 400.0 ¢
Major 6-mosstep M6ms 5L + s 400.0 ¢ to 461.5 ¢
7-mosstep Perfect 7-mosstep P7ms 5L + 2s 461.5 ¢ to 466.7 ¢
Augmented 7-mosstep A7ms 6L + s 466.7 ¢ to 553.8 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 461.5 ¢ to 533.3 ¢
Major 8-mosstep M8ms 6L + 2s 533.3 ¢ to 553.8 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 553.8 ¢ to 600.0 ¢
Major 9-mosstep M9ms 7L + 2s 600.0 ¢ to 646.2 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 646.2 ¢ to 666.7 ¢
Major 10-mosstep M10ms 8L + 2s 666.7 ¢ to 738.5 ¢
11-mosstep Diminished 11-mosstep d11ms 7L + 4s 646.2 ¢ to 733.3 ¢
Perfect 11-mosstep P11ms 8L + 3s 733.3 ¢ to 738.5 ¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 738.5 ¢ to 800.0 ¢
Major 12-mosstep M12ms 9L + 3s 800.0 ¢ to 830.8 ¢
13-mosstep Minor 13-mosstep m13ms 9L + 4s 830.8 ¢ to 866.7 ¢
Major 13-mosstep M13ms 10L + 3s 866.7 ¢ to 923.1 ¢
14-mosstep Minor 14-mosstep m14ms 10L + 4s 923.1 ¢ to 933.3 ¢
Major 14-mosstep M14ms 11L + 3s 933.3 ¢ to 1015.4 ¢
15-mosstep Minor 15-mosstep m15ms 10L + 5s 923.1 ¢ to 1000.0 ¢
Major 15-mosstep M15ms 11L + 4s 1000.0 ¢ to 1015.4 ¢
16-mosstep Minor 16-mosstep m16ms 11L + 5s 1015.4 ¢ to 1066.7 ¢
Major 16-mosstep M16ms 12L + 4s 1066.7 ¢ to 1107.7 ¢
17-mosstep Minor 17-mosstep m17ms 12L + 5s 1107.7 ¢ to 1133.3 ¢
Major 17-mosstep M17ms 13L + 4s 1133.3 ¢ to 1200.0 ¢
18-mosstep Perfect 18-mosstep P18ms 13L + 5s 1200.0 ¢

Generator chain

Generator chain of 13L 5s
Bright gens Scale degree Abbrev.
30 Augmented 6-mosdegree A6md
29 Augmented 13-mosdegree A13md
28 Augmented 2-mosdegree A2md
27 Augmented 9-mosdegree A9md
26 Augmented 16-mosdegree A16md
25 Augmented 5-mosdegree A5md
24 Augmented 12-mosdegree A12md
23 Augmented 1-mosdegree A1md
22 Augmented 8-mosdegree A8md
21 Augmented 15-mosdegree A15md
20 Augmented 4-mosdegree A4md
19 Augmented 11-mosdegree A11md
18 Augmented 0-mosdegree A0md
17 Augmented 7-mosdegree A7md
16 Major 14-mosdegree M14md
15 Major 3-mosdegree M3md
14 Major 10-mosdegree M10md
13 Major 17-mosdegree M17md
12 Major 6-mosdegree M6md
11 Major 13-mosdegree M13md
10 Major 2-mosdegree M2md
9 Major 9-mosdegree M9md
8 Major 16-mosdegree M16md
7 Major 5-mosdegree M5md
6 Major 12-mosdegree M12md
5 Major 1-mosdegree M1md
4 Major 8-mosdegree M8md
3 Major 15-mosdegree M15md
2 Major 4-mosdegree M4md
1 Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 18-mosdegree		 P0md
P18md
−1 Perfect 7-mosdegree P7md
−2 Minor 14-mosdegree m14md
−3 Minor 3-mosdegree m3md
−4 Minor 10-mosdegree m10md
−5 Minor 17-mosdegree m17md
−6 Minor 6-mosdegree m6md
−7 Minor 13-mosdegree m13md
−8 Minor 2-mosdegree m2md
−9 Minor 9-mosdegree m9md
−10 Minor 16-mosdegree m16md
−11 Minor 5-mosdegree m5md
−12 Minor 12-mosdegree m12md
−13 Minor 1-mosdegree m1md
−14 Minor 8-mosdegree m8md
−15 Minor 15-mosdegree m15md
−16 Minor 4-mosdegree m4md
−17 Diminished 11-mosdegree d11md
−18 Diminished 18-mosdegree d18md
−19 Diminished 7-mosdegree d7md
−20 Diminished 14-mosdegree d14md
−21 Diminished 3-mosdegree d3md
−22 Diminished 10-mosdegree d10md
−23 Diminished 17-mosdegree d17md
−24 Diminished 6-mosdegree d6md
−25 Diminished 13-mosdegree d13md
−26 Diminished 2-mosdegree d2md
−27 Diminished 9-mosdegree d9md
−28 Diminished 16-mosdegree d16md
−29 Diminished 5-mosdegree d5md
−30 Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 13L 5s
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
17|0 1 LLLsLLLsLLsLLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|1 12 LLLsLLsLLLsLLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|2 5 LLLsLLsLLLsLLsLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf.
14|3 16 LLsLLLsLLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf.
13|4 9 LLsLLLsLLsLLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf.
12|5 2 LLsLLLsLLsLLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf.
11|6 13 LLsLLsLLLsLLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf.
10|7 6 LLsLLsLLLsLLsLLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf.
9|8 17 LsLLLsLLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf.
8|9 10 LsLLLsLLsLLLsLLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf.
7|10 3 LsLLLsLLsLLLsLLsLL Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf.
6|11 14 LsLLsLLLsLLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf.
5|12 7 LsLLsLLLsLLsLLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf.
4|13 18 sLLLsLLLsLLsLLLsLL Perf. Min. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf.
3|14 11 sLLLsLLsLLLsLLLsLL Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf.
2|15 4 sLLLsLLsLLLsLLsLLL Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|16 15 sLLsLLLsLLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|17 8 sLLsLLLsLLsLLLsLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 13L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\18 733.333 466.667 1:1 1.000 Equalized 13L 5s
63\103 733.981 466.019 6:5 1.200
52\85 734.118 465.882 5:4 1.250
93\152 734.211 465.789 9:7 1.286
41\67 734.328 465.672 4:3 1.333 Supersoft 13L 5s
112\183 734.426 465.574 11:8 1.375
71\116 734.483 465.517 7:5 1.400
101\165 734.545 465.455 10:7 1.429
30\49 734.694 465.306 3:2 1.500 Soft 13L 5s
109\178 734.831 465.169 11:7 1.571
79\129 734.884 465.116 8:5 1.600
128\209 734.928 465.072 13:8 1.625
49\80 735.000 465.000 5:3 1.667 Semisoft 13L 5s
117\191 735.079 464.921 12:7 1.714
68\111 735.135 464.865 7:4 1.750
87\142 735.211 464.789 9:5 1.800
19\31 735.484 464.516 2:1 2.000 Basic 13L 5s
Scales with tunings softer than this are proper
84\137 735.766 464.234 9:4 2.250
65\106 735.849 464.151 7:3 2.333
111\181 735.912 464.088 12:5 2.400
46\75 736.000 464.000 5:2 2.500 Semihard 13L 5s
119\194 736.082 463.918 13:5 2.600
73\119 736.134 463.866 8:3 2.667
100\163 736.196 463.804 11:4 2.750
27\44 736.364 463.636 3:1 3.000 Hard 13L 5s
89\145 736.552 463.448 10:3 3.333
62\101 736.634 463.366 7:2 3.500
97\158 736.709 463.291 11:3 3.667
35\57 736.842 463.158 4:1 4.000 Superhard 13L 5s
78\127 737.008 462.992 9:2 4.500
43\70 737.143 462.857 5:1 5.000
51\83 737.349 462.651 6:1 6.000
8\13 738.462 461.538 1:0 → ∞ Collapsed 13L 5s
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