Odd prime sum limit: Difference between revisions
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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''. | 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 [[User:Tristanbay|Tristan Bay]] as a way to measure how accurately an [[ | 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]]s. | ||
==Minimal OPSL-consistent | == Minimal OPSL-consistent edos == | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
!OPSL | ! OPSL | ||
!Smallest Consistent | ! Smallest Consistent Edo* | ||
|- | |- | ||
|1 | | 1 | ||
|[[1edo|1]] | | [[1edo|1]] | ||
|- | |- | ||
|2 | | 2 | ||
|1 | | 1 | ||
|- | |- | ||
|3 | | 3 | ||
|1 | | 1 | ||
|- | |- | ||
|4 | | 4 | ||
|1 | | 1 | ||
|- | |- | ||
|5 | | 5 | ||
|[[3edo|3]] | | [[3edo|3]] | ||
|- | |- | ||
|6 | | 6 | ||
|3 | | 3 | ||
|- | |- | ||
|7 | | 7 | ||
|[[5edo|5]] | | [[5edo|5]] | ||
|- | |- | ||
|8 | | 8 | ||
|[[12edo|12]] | | [[12edo|12]] | ||
|- | |- | ||
|9 | | 9 | ||
|12 | | 12 | ||
|- | |- | ||
|10 | | 10 | ||
|12 | | 12 | ||
|- | |- | ||
|11 | | 11 | ||
|[[31edo|31]] | | [[31edo|31]] | ||
|- | |- | ||
|12 | | 12 | ||
|[[72edo|72]] | | [[72edo|72]] | ||
|- | |- | ||
|13 | | 13 | ||
|72 | | 72 | ||
|- | |- | ||
|14 | | 14 | ||
|[[130edo|130]] | | [[130edo|130]] | ||
|- | |- | ||
|15 | | 15 | ||
|[[270edo|270]] | | [[270edo|270]] | ||
|- | |- | ||
|16 | | 16 | ||
|270 | | 270 | ||
|- | |- | ||
|17 | | 17 | ||
|[[954edo|954]] | | [[954edo|954]] | ||
|- | |- | ||
|18 | | 18 | ||
|[[1236edo|1236]] | | [[1236edo|1236]] | ||
|- | |- | ||
|19 | | 19 | ||
|[[1578edo|1578]] | | [[1578edo|1578]] | ||
|- | |- | ||
|20 | | 20 | ||
|1578 | | 1578 | ||
|- | |- | ||
|21 | | 21 | ||
|[[3395edo|3395]] | | [[3395edo|3395]] | ||
|- | |- | ||
|22 | | 22 | ||
|3395 | | 3395 | ||
|- | |- | ||
|23 | | 23 | ||
|[[6079edo|6079]] | | [[6079edo|6079]] | ||
|- | |- | ||
|24 | | 24 | ||
|[[8539edo|8539]] | | [[8539edo|8539]] | ||
|- | |- | ||
|25 | | 25 | ||
|8539 | | 8539 | ||
|- | |- | ||
|26 | | 26 | ||
|8539 | | 8539 | ||
|- | |- | ||
|27 | | 27 | ||
|8539 | | 8539 | ||
|- | |- | ||
|28 | | 28 | ||
|[[102557edo|102557]] | | [[102557edo|102557]] | ||
|- | |- | ||
|29 | | 29 | ||
|102557 | | 102557 | ||
|- | |- | ||
|30 | | 30 | ||
|102557 | | 102557 | ||
|- | |- | ||
|31 | | 31 | ||
|102557 | | 102557 | ||
|- | |- | ||
|32 | | 32 | ||
|102557 | | 102557 | ||
|- | |- | ||
|33 | | 33 | ||
|[[258008edo|258008]] | | [[258008edo|258008]] | ||
|- | |- | ||
|34 | | 34 | ||
|258008 | | 258008 | ||
|- | |- | ||
|35 | | 35 | ||
|258008 | | 258008 | ||
|- | |- | ||
|36 | | 36 | ||
|258008 | | 258008 | ||
|} | |} | ||
<nowiki>*</nowiki>apart from 0edo | <nowiki>*</nowiki>apart from 0edo | ||
[[Category:Limit]] | |||
[[Category:Terms]] | |||