3L 13s

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↖ 2L 12s ↑3L 12s 4L 12s ↗
← 2L 13s3L 13s 4L 13s →
↙ 2L 14s ↓3L 14s 4L 14s ↘
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│║││││║││││║││││││
││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssLssssLsssss
sssssLssssLssssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 5\16 to 1\3 (375.0¢ to 400.0¢)
Dark 2\3 to 11\16 (800.0¢ to 825.0¢)
TAMNAMS information
Descends from 3L 7s (sephiroid)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 3L 10s
Sister 13L 3s
Daughters 16L 3s, 3L 16s
Neutralized 6L 10s
2-Flought 19L 13s, 3L 29s
Equal tunings
Equalized (L:s = 1:1) 5\16 (375.0¢)
Supersoft (L:s = 4:3) 16\51 (376.5¢)
Soft (L:s = 3:2) 11\35 (377.1¢)
Semisoft (L:s = 5:3) 17\54 (377.8¢)
Basic (L:s = 2:1) 6\19 (378.9¢)
Semihard (L:s = 5:2) 13\41 (380.5¢)
Hard (L:s = 3:1) 7\22 (381.8¢)
Superhard (L:s = 4:1) 8\25 (384.0¢)
Collapsed (L:s = 1:0) 1\3 (400.0¢)

3L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 13 small steps, repeating every octave. 3L 13s is a grandchild scale of 3L 7s, expanding it by 6 tones. Generators that produce this scale range from 375¢ to 400¢, or from 800¢ to 825¢. This MOS, having its large steps separated by intervals of 4s, 4s and 5s; is the quasi-enharmonic scale of Magic temperament. It is also the smallest MOS which is ideal for composing melodies in Magic temperament, owing to the fact that the optimal generator range for it is the range where Magic temperament is tuned most accurately (6/19edo to 7/22edo); and is generated by a small major third no smaller than 5/16edo (375 cents).

Modes

Modes of 3L 13s
UDP Rotational order Step pattern
15|0 1 LssssLssssLsssss
14|1 6 LssssLsssssLssss
13|2 11 LsssssLssssLssss
12|3 16 sLssssLssssLssss
11|4 5 sLssssLsssssLsss
10|5 10 sLsssssLssssLsss
9|6 15 ssLssssLssssLsss
8|7 4 ssLssssLsssssLss
7|8 9 ssLsssssLssssLss
6|9 14 sssLssssLssssLss
5|10 3 sssLssssLsssssLs
4|11 8 sssLsssssLssssLs
3|12 13 ssssLssssLssssLs
2|13 2 ssssLssssLsssssL
1|14 7 ssssLsssssLssssL
0|15 12 sssssLssssLssssL

Scale tree

Scale Tree and Tuning Spectrum of 3L 13s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
5\16 375.000 825.000 1:1 1.000 Equalized 3L 13s
26\83 375.904 824.096 6:5 1.200
21\67 376.119 823.881 5:4 1.250
37\118 376.271 823.729 9:7 1.286
16\51 376.471 823.529 4:3 1.333 Supersoft 3L 13s
43\137 376.642 823.358 11:8 1.375
27\86 376.744 823.256 7:5 1.400
38\121 376.860 823.140 10:7 1.429
11\35 377.143 822.857 3:2 1.500 Soft 3L 13s
39\124 377.419 822.581 11:7 1.571
28\89 377.528 822.472 8:5 1.600
45\143 377.622 822.378 13:8 1.625
17\54 377.778 822.222 5:3 1.667 Semisoft 3L 13s
40\127 377.953 822.047 12:7 1.714
23\73 378.082 821.918 7:4 1.750
29\92 378.261 821.739 9:5 1.800
6\19 378.947 821.053 2:1 2.000 Basic 3L 13s
Scales with tunings softer than this are proper
25\79 379.747 820.253 9:4 2.250
19\60 380.000 820.000 7:3 2.333
32\101 380.198 819.802 12:5 2.400
13\41 380.488 819.512 5:2 2.500 Semihard 3L 13s
33\104 380.769 819.231 13:5 2.600
20\63 380.952 819.048 8:3 2.667
27\85 381.176 818.824 11:4 2.750
7\22 381.818 818.182 3:1 3.000 Hard 3L 13s
22\69 382.609 817.391 10:3 3.333
15\47 382.979 817.021 7:2 3.500
23\72 383.333 816.667 11:3 3.667
8\25 384.000 816.000 4:1 4.000 Superhard 3L 13s
17\53 384.906 815.094 9:2 4.500
9\28 385.714 814.286 5:1 5.000
10\31 387.097 812.903 6:1 6.000
1\3 400.000 800.000 1:0 → ∞ Collapsed 3L 13s