3L 10s
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Scale structure
Step pattern
LsssLsssLssss
ssssLsssLsssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
4\13 to 1\3 (369.2¢ to 400.0¢)
Dark
2\3 to 9\13 (800.0¢ to 830.8¢)
TAMNAMS information
Descends from
3L 7s (sephiroid)
Ancestor's step ratio range
2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent
3L 7s
Sister
10L 3s
Daughters
13L 3s, 3L 13s
Neutralized
6L 7s
2-Flought
16L 10s, 3L 23s
Equal tunings
Equalized (L:s = 1:1)
4\13 (369.2¢)
Supersoft (L:s = 4:3)
13\42 (371.4¢)
Soft (L:s = 3:2)
9\29 (372.4¢)
Semisoft (L:s = 5:3)
14\45 (373.3¢)
Basic (L:s = 2:1)
5\16 (375.0¢)
Semihard (L:s = 5:2)
11\35 (377.1¢)
Hard (L:s = 3:1)
6\19 (378.9¢)
Superhard (L:s = 4:1)
7\22 (381.8¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
 |
Todo: review Review entries |
| ↖ 2L 9s | ↑ 3L 9s | 4L 9s ↗ |
| ← 2L 10s | 3L 10s | 4L 10s → |
| ↙ 2L 11s | ↓ 3L 11s | 4L 11s ↘ |
┌╥┬┬┬╥┬┬┬╥┬┬┬┬┐ │║│││║│││║│││││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssLsssLsssL
3L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 10 small steps, repeating every octave. 3L 10s is a child scale of 3L 7s, expanding it by 3 tones. Generators that produce this scale range from 369.2¢ to 400¢, or from 800¢ to 830.8¢. Some notable temperaments that form a MOS with this pattern are magic and würschmidt. Of course, magic[13] is still slightly improper and würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13 tone per octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13 tone circles favor multiple times over.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 12|0 | 1 | LsssLsssLssss |
| 11|1 | 5 | LsssLssssLsss |
| 10|2 | 9 | LssssLsssLsss |
| 9|3 | 13 | sLsssLsssLsss |
| 8|4 | 4 | sLsssLssssLss |
| 7|5 | 8 | sLssssLsssLss |
| 6|6 | 12 | ssLsssLsssLss |
| 5|7 | 3 | ssLsssLssssLs |
| 4|8 | 7 | ssLssssLsssLs |
| 3|9 | 11 | sssLsssLsssLs |
| 2|10 | 2 | sssLsssLssssL |
| 1|11 | 6 | sssLssssLsssL |
| 0|12 | 10 | ssssLsssLsssL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 4\13 | 369.231 | 830.769 | 1:1 | 1.000 | Equalized 3L 10s | |||||
| 21\68 | 370.588 | 829.412 | 6:5 | 1.200 | ||||||
| 17\55 | 370.909 | 829.091 | 5:4 | 1.250 | ||||||
| 30\97 | 371.134 | 828.866 | 9:7 | 1.286 | ||||||
| 13\42 | 371.429 | 828.571 | 4:3 | 1.333 | Supersoft 3L 10s | |||||
| 35\113 | 371.681 | 828.319 | 11:8 | 1.375 | ||||||
| 22\71 | 371.831 | 828.169 | 7:5 | 1.400 | ||||||
| 31\100 | 372.000 | 828.000 | 10:7 | 1.429 | ||||||
| 9\29 | 372.414 | 827.586 | 3:2 | 1.500 | Soft 3L 10s | |||||
| 32\103 | 372.816 | 827.184 | 11:7 | 1.571 | ||||||
| 23\74 | 372.973 | 827.027 | 8:5 | 1.600 | ||||||
| 37\119 | 373.109 | 826.891 | 13:8 | 1.625 | ||||||
| 14\45 | 373.333 | 826.667 | 5:3 | 1.667 | Semisoft 3L 10s | |||||
| 33\106 | 373.585 | 826.415 | 12:7 | 1.714 | ||||||
| 19\61 | 373.770 | 826.230 | 7:4 | 1.750 | ||||||
| 24\77 | 374.026 | 825.974 | 9:5 | 1.800 | ||||||
| 5\16 | 375.000 | 825.000 | 2:1 | 2.000 | Basic 3L 10s Scales with tunings softer than this are proper | |||||
| 21\67 | 376.119 | 823.881 | 9:4 | 2.250 | ||||||
| 16\51 | 376.471 | 823.529 | 7:3 | 2.333 | ||||||
| 27\86 | 376.744 | 823.256 | 12:5 | 2.400 | ||||||
| 11\35 | 377.143 | 822.857 | 5:2 | 2.500 | Semihard 3L 10s | |||||
| 28\89 | 377.528 | 822.472 | 13:5 | 2.600 | ||||||
| 17\54 | 377.778 | 822.222 | 8:3 | 2.667 | ||||||
| 23\73 | 378.082 | 821.918 | 11:4 | 2.750 | ||||||
| 6\19 | 378.947 | 821.053 | 3:1 | 3.000 | Hard 3L 10s | |||||
| 19\60 | 380.000 | 820.000 | 10:3 | 3.333 | ||||||
| 13\41 | 380.488 | 819.512 | 7:2 | 3.500 | ||||||
| 20\63 | 380.952 | 819.048 | 11:3 | 3.667 | ||||||
| 7\22 | 381.818 | 818.182 | 4:1 | 4.000 | Superhard 3L 10s | |||||
| 15\47 | 382.979 | 817.021 | 9:2 | 4.500 | ||||||
| 8\25 | 384.000 | 816.000 | 5:1 | 5.000 | ||||||
| 9\28 | 385.714 | 814.286 | 6:1 | 6.000 | ||||||
| 1\3 | 400.000 | 800.000 | 1:0 | → ∞ | Collapsed 3L 10s | |||||