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]] | |||
Revision as of 07:03, 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