Odd prime sum limit: Difference between revisions
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Tristanbay (talk | contribs) Added a table of minimal OPSL-consistent EDOs |
Tristanbay (talk | contribs) Added links for the different EDOs Tags: Visual edit Mobile edit Mobile web edit |
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|1 | |1 | ||
|1 | |[[1edo|1]] | ||
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|2 | |2 | ||
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|5 | |5 | ||
|3 | |[[3edo|3]] | ||
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|6 | |6 | ||
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|7 | |7 | ||
|5 | |[[5edo|5]] | ||
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|8 | |8 | ||
|12 | |[[12edo|12]] | ||
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|9 | |9 | ||
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|11 | |11 | ||
|31 | |[[31edo|31]] | ||
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|12 | |12 | ||
|72 | |[[72edo|72]] | ||
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|13 | |13 | ||
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|14 | |14 | ||
|130 | |[[130edo|130]] | ||
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|15 | |15 | ||
|270 | |[[270edo|270]] | ||
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|16 | |16 | ||
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|17 | |17 | ||
|954 | |[[954edo|954]] | ||
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|18 | |18 | ||
|1236 | |[[1236edo|1236]] | ||
|- | |- | ||
|19 | |19 | ||
|1578 | |[[1578edo|1578]] | ||
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|20 | |20 | ||
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|21 | |21 | ||
|3395 | |[[3395edo|3395]] | ||
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|22 | |22 | ||
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|23 | |23 | ||
|6079 | |[[6079edo|6079]] | ||
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|24 | |24 | ||
|8539 | |[[8539edo|8539]] | ||
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|25 | |25 | ||
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|28 | |28 | ||
|102557 | |[[102557edo|102557]] | ||
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|29 | |29 | ||
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|33 | |33 | ||
|258008 | |[[258008edo|258008]] | ||
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|34 | |34 | ||
Revision as of 00:19, 28 April 2024
The n-odd-prime-sum-limit (abbreviated n-OPSL) is the collection of all just ratios with a no-twos Wilson height that does not exceed the integer n.
This concept was noted by Tristan Bay as a way to measure how accurately an EDO approximates just intonation with lower primes weighted more heavily. Specifically, the idea is to use OPSLs as an alternative metric for consistency limit either instead of or alongside odd limits.
Minimal OPSL-consistent EDOs
| OPSL | Smallest Consistent EDO* |
|---|---|
| 1 | 1 |
| 2 | 1 |
| 3 | 1 |
| 4 | 1 |
| 5 | 3 |
| 6 | 3 |
| 7 | 5 |
| 8 | 12 |
| 9 | 12 |
| 10 | 12 |
| 11 | 31 |
| 12 | 72 |
| 13 | 72 |
| 14 | 130 |
| 15 | 270 |
| 16 | 270 |
| 17 | 954 |
| 18 | 1236 |
| 19 | 1578 |
| 20 | 1578 |
| 21 | 3395 |
| 22 | 3395 |
| 23 | 6079 |
| 24 | 8539 |
| 25 | 8539 |
| 26 | 8539 |
| 27 | 8539 |
| 28 | 102557 |
| 29 | 102557 |
| 30 | 102557 |
| 31 | 102557 |
| 32 | 102557 |
| 33 | 258008 |
| 34 | 258008 |
| 35 | 258008 |
| 36 | 258008 |
*apart from 0edo