Odd prime sum limit: Difference between revisions
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Tristanbay (talk | contribs) Fixed a period Tags: Mobile edit Mobile web edit |
Tristanbay (talk | contribs) Added a table of minimal OPSL-consistent EDOs |
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This concept was noted by [[User:Tristanbay|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|consistency limit]] either instead of or alongside [[Odd limit|odd limits]]. | This concept was noted by [[User:Tristanbay|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|consistency limit]] either instead of or alongside [[Odd limit|odd limits]]. | ||
==Minimal OPSL-consistent EDOs== | |||
{| class="wikitable" | |||
|+ | |||
!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 | |||
|} | |||
<nowiki>*</nowiki>apart from 0edo | |||
Revision as of 23:11, 27 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