User talk:Cmloegcmluin: Difference between revisions

Line 74:

In https://en.xen.wiki/index.php?title=Uniform_map&diff=prev&oldid=81884 you wrote that: "The map with the overall best tuning accuracy for an EDO will always be a uniform map". How did you come to that conclusion? Can't there be exceptions? --[[User:Currywurst44|Currywurst44]] ([[User talk:Currywurst44|talk]]) 19:27, 4 October 2026 (UTC)

: It is true if one takes “accuracy” to mean simply the errors of the primes; any non-uniform map you could find would always be improved by moving toward a uniform map. To understand why, think of a uniform map as one you get by — for some step size you’re considering tuning your ET to — rounding each prime to its nearest number of steps at that tuning. So any non-uniform map must have at least one prime that is ''not'' on its nearest number of steps at that tuning. And so if you changed that one prime’s map entry to its nearest number of steps, you would shrink that prime’s error without changing any other prime’s, thereby improving the tuning.

: By that definition, there are no exceptions. But "best tuning" is not strictly defined. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:34, 11 October 2026 (UTC)

@@ Line 74: / Line 74: @@
 In https://en.xen.wiki/index.php?title=Uniform_map&diff=prev&oldid=81884 you wrote that: "The map with the overall best tuning accuracy for an EDO will always be a uniform map". How did you come to that conclusion? Can't there be exceptions? --[[User:Currywurst44|Currywurst44]] ([[User talk:Currywurst44|talk]]) 19:27, 4 October 2026 (UTC)
+: It is true if one takes “accuracy” to mean simply the errors of the primes; any non-uniform map you could find would always be improved by moving toward a uniform map. To understand why, think of a uniform map as one you get by — for some step size you’re considering tuning your ET to — rounding each prime to its nearest number of steps at that tuning. So any non-uniform map must have at least one prime that is ''not'' on its nearest number of steps at that tuning. And so if you changed that one prime’s map entry to its nearest number of steps, you would shrink that prime’s error without changing any other prime’s, thereby improving the tuning.
+: By that definition, there are no exceptions. But "best tuning" is not strictly defined. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:34, 11 October 2026 (UTC)