14L 3s: Difference between revisions

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Mos intro
Ganaram inukshuk (talk | contribs)
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Scale tree, reworded intro (removed redundant generator range)
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{{MOS intro}}
{{MOS intro}}
The '''14L 13s''' [[MOS scale]] consists of three small steps separated by intervals of 5L-5L-4L. The temperament it belongs to is called Squares 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). This puts the generator between 6/17edo (423.529{{cent}}) and 5/14edo (428.571{{cent}}).
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).
 
{| class="wikitable"
|-
| | 5/14
| |
| |
| |
| |
| | 428.571
|-
| |
| |
| |
| |
| | 26/73
| | 427.397
|-
| |
| |
| |
| | 21/59
| |
| | 427.119
|-
| |
| |
| |
| |
| | 37/104
| | 426.923
|-
| |
| |
| |
| |
| |
| | 426.747
|-
| |
| |
| | 16/45
| |
| |
| | 426.667
|-
| |
| |
| |
| |
| |
| | 426.484
|-
| |
| |
| |
| |
| | 43/121
| | 426.446
|-
| |
| |
| |
| |
| |
| | 426.41
|-
| |
| |
| |
| | 27/76
| |
| | 426.316
|-
| |
| |
| |
| |
| | 38/107
| | 426.168
|-
| |
| | 11/31
| |
| |
| |
| | 425.806
|-
| |
| |
| |
| |
| | 39/110
| | 425.4545
|-
| |
| |
| |
| |
| |
| | 425.426
|-
| |
| |
| |
| | 28/79
| |
| | 425.3165
|-
| |
| |
| |
| |
| |
| | 425.23
|-
| |
| |
| |
| |
| | 45/127
| | 425.197
|-
| |
| |
| |
| |
| |
| | 425.142
|-
| |
| |
| | 17/48
| |
| |
| | 425
|-
| |
| |
| |
| |
| | 40/113
| | 424.779
|-
| |
| |
| |
| | 23/65
| |
| | 424.615
|-
| |
| |
| |
| |
| | 29/82
| | 424.39
|-
| | 6/17
| |
| |
| |
| |
| | 423.529
|}


{{Scale tree}}
[[Category:17-tone scales]]
[[Category:17-tone scales]]

Revision as of 20:42, 28 February 2024

↖ 13L 2s ↑ 14L 2s 15L 2s ↗
← 13L 3s 14L 3s 15L 3s →
↙ 13L 4s ↓ 14L 4s 15L 4s ↘ 
┌╥╥╥╥╥┬╥╥╥╥╥┬╥╥╥╥┬┐
│║║║║║│║║║║║│║║║║││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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
Related to 3L 5s (checkertonic)
With tunings 3:1 to 4:1 (parahard)
Related MOS scales
Parent 3L 11s
Sister 3L 14s
Daughters 17L 14s, 14L 17s
Neutralized 11L 6s
2-Flought 31L 3s, 14L 20s
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 ¢)

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).

Template:Scale tree

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