Odd prime sum limit: Difference between revisions

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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