14L 3s
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Scale structure
Step pattern
LLLLLsLLLLLsLLLLs
sLLLLsLLLLLsLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
6\17 to 5\14 (423.5¢ to 428.6¢)
Dark
9\14 to 11\17 (771.4¢ to 776.5¢)
TAMNAMS information
Descends from
3L 5s (checkertonic)
Required step ratio range
3:1 to 4:1 (parahard)
Related MOS scales
Parent
3L 11s
Sister
3L 14s
Daughters
17L 14s
14L 17s
Equal tunings
Equalized (L:s = 1:1)
6\17 (423.5¢)
Supersoft (L:s = 4:3)
23\65 (424.6¢)
Soft (L:s = 3:2)
17\48 (425.0¢)
Semisoft (L:s = 5:3)
28\79 (425.3¢)
Basic (L:s = 2:1)
11\31 (425.8¢)
Semihard (L:s = 5:2)
27\76 (426.3¢)
Hard (L:s = 3:1)
16\45 (426.7¢)
Superhard (L:s = 4:1)
21\59 (427.1¢)
Collapsed (L:s = 1:0)
5\14 (428.6¢)
| ↖13L 2s | ↑14L 2s | 15L 2s↗ |
| ←13L 3s | 14L 3s | 15L 3s→ |
| ↙13L 4s | ↓14L 4s | 15L 4s↘ |
┌╥╥╥╥╥┬╥╥╥╥╥┬╥╥╥╥┬┐ │║║║║║│║║║║║│║║║║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLsLLLLLsLLLLL
14L 17s
14L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 14 large steps and 3 small steps, repeating every octave. 14L 3s is a great-grandchild scale of 3L 5s, expanding it by 9 tones. Generators that produce this scale range from 423.5¢ to 428.6¢, or from 771.4¢ to 776.5¢.
This scale is associated with Squares temperament because the number of generators it takes to get to each of the primes 3, 5 and 7 is a square (3=-4 generators, 5=-16, 7=-9).
| Generator(edo) | Cents | Step Ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 6\17 | 423.529 | 776.471 | 1:1 | 1.000 | Equalized 14L 3s | |||||
| 35\99 | 424.242 | 775.758 | 6:5 | 1.200 | ||||||
| 29\82 | 424.390 | 775.610 | 5:4 | 1.250 | ||||||
| 52\147 | 424.490 | 775.510 | 9:7 | 1.286 | ||||||
| 23\65 | 424.615 | 775.385 | 4:3 | 1.333 | Supersoft 14L 3s | |||||
| 63\178 | 424.719 | 775.281 | 11:8 | 1.375 | ||||||
| 40\113 | 424.779 | 775.221 | 7:5 | 1.400 | ||||||
| 57\161 | 424.845 | 775.155 | 10:7 | 1.429 | ||||||
| 17\48 | 425.000 | 775.000 | 3:2 | 1.500 | Soft 14L 3s | |||||
| 62\175 | 425.143 | 774.857 | 11:7 | 1.571 | ||||||
| 45\127 | 425.197 | 774.803 | 8:5 | 1.600 | ||||||
| 73\206 | 425.243 | 774.757 | 13:8 | 1.625 | ||||||
| 28\79 | 425.316 | 774.684 | 5:3 | 1.667 | Semisoft 14L 3s | |||||
| 67\189 | 425.397 | 774.603 | 12:7 | 1.714 | ||||||
| 39\110 | 425.455 | 774.545 | 7:4 | 1.750 | ||||||
| 50\141 | 425.532 | 774.468 | 9:5 | 1.800 | ||||||
| 11\31 | 425.806 | 774.194 | 2:1 | 2.000 | Basic 14L 3s Scales with tunings softer than this are proper | |||||
| 49\138 | 426.087 | 773.913 | 9:4 | 2.250 | ||||||
| 38\107 | 426.168 | 773.832 | 7:3 | 2.333 | ||||||
| 65\183 | 426.230 | 773.770 | 12:5 | 2.400 | ||||||
| 27\76 | 426.316 | 773.684 | 5:2 | 2.500 | Semihard 14L 3s | |||||
| 70\197 | 426.396 | 773.604 | 13:5 | 2.600 | ||||||
| 43\121 | 426.446 | 773.554 | 8:3 | 2.667 | ||||||
| 59\166 | 426.506 | 773.494 | 11:4 | 2.750 | ||||||
| 16\45 | 426.667 | 773.333 | 3:1 | 3.000 | Hard 14L 3s | |||||
| 53\149 | 426.846 | 773.154 | 10:3 | 3.333 | ||||||
| 37\104 | 426.923 | 773.077 | 7:2 | 3.500 | ||||||
| 58\163 | 426.994 | 773.006 | 11:3 | 3.667 | ||||||
| 21\59 | 427.119 | 772.881 | 4:1 | 4.000 | Superhard 14L 3s | |||||
| 47\132 | 427.273 | 772.727 | 9:2 | 4.500 | ||||||
| 26\73 | 427.397 | 772.603 | 5:1 | 5.000 | ||||||
| 31\87 | 427.586 | 772.414 | 6:1 | 6.000 | ||||||
| 5\14 | 428.571 | 771.429 | 1:0 | → ∞ | Collapsed 14L 3s | |||||