Odd prime sum limit: Difference between revisions

Line 2:

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.

== Comparison with odd limit ==

The 1- and 2-odd-prime-sum-limit are equivalent to the [[1-odd-limit]], which only contains a single interval pair {[[1/1]], [[2/1]]}. The 3- and 4-odd-prime-sum-limit are equivalent to the [[3-odd-limit]], which adds {[[3/2]], [[4/3]]}. All edos are consistent in those limits.

The 5-odd-prime-sum-limit adds {[[5/4]], [[8/5]]} without {[[5/3]], [[6/5]]} from the [[5-odd-limit]], so it is the first OPSL that differs from the corresponding odd limit. The 6-odd-prime-sum-limit adds {[[9/8]], [[16/9]]}. The 7-odd-prime-sum-limit adds {[[7/4]], [[8/7]]} without {[[7/6]], [[12/7]]}, and the 8-odd-prime-sum-limit adds {5/3, 6/5} as well as {[[15/8]], [[16/15]]}. The 9-odd-prime-sum-limit adds {[[27/16]], [[32/27]]}, and the 10-odd-prime-sum-limit adds {7/6, 12/7}, {[[21/16]], [[32/21]]}, and {[[25/16]], [[32/25]]}. The 11-odd-prime-sum-limit adds {[[11/8]], [[16/11]]}, {[[9/5]], [[10/9]]}, and {[[45/32]], [[64/45]]}. The 12-odd-prime-sum-limit adds {[[7/5]], [[10/7]]}, {[[35/32]], [[64/35]]} and {[[81/64]], [[128/81]]}.

== Minimal OPSL-consistent edos ==

@@ Line 2: / Line 2: @@
 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.
+== Comparison with odd limit ==
+The 1- and 2-odd-prime-sum-limit are equivalent to the [[1-odd-limit]], which only contains a single interval pair {[[1/1]], [[2/1]]}. The 3- and 4-odd-prime-sum-limit are equivalent to the [[3-odd-limit]], which adds {[[3/2]], [[4/3]]}. All edos are consistent in those limits.
+The 5-odd-prime-sum-limit adds {[[5/4]], [[8/5]]} without {[[5/3]], [[6/5]]} from the [[5-odd-limit]], so it is the first OPSL that differs from the corresponding odd limit. The 6-odd-prime-sum-limit adds {[[9/8]], [[16/9]]}. The 7-odd-prime-sum-limit adds {[[7/4]], [[8/7]]} without {[[7/6]], [[12/7]]}, and the 8-odd-prime-sum-limit adds {5/3, 6/5} as well as {[[15/8]], [[16/15]]}. The 9-odd-prime-sum-limit adds {[[27/16]], [[32/27]]}, and the 10-odd-prime-sum-limit adds {7/6, 12/7}, {[[21/16]], [[32/21]]}, and {[[25/16]], [[32/25]]}. The 11-odd-prime-sum-limit adds {[[11/8]], [[16/11]]}, {[[9/5]], [[10/9]]}, and {[[45/32]], [[64/45]]}. The 12-odd-prime-sum-limit adds {[[7/5]], [[10/7]]}, {[[35/32]], [[64/35]]} and {[[81/64]], [[128/81]]}.
 == Minimal OPSL-consistent edos ==