3L 13s
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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¢)
↖ 2L 12s | ↑ 3L 12s | 4L 12s ↗ |
← 2L 13s | 3L 13s | 4L 13s → |
↙ 2L 14s | ↓ 3L 14s | 4L 14s ↘ |
┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║││││║││││││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssssLssssLssssL
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
UDP | Cyclic 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
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 |