User talk:Cmloegcmluin: Difference between revisions

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: Thanks for letting me know about this, and for correcting it on my recent pages. I'll be cognizant of this moving forward. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:02, 6 March 2022 (UTC)

== Uniform map/generalized patent val always best? ==

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)

::: So another way of writing the quote would be "The map with the overall best tuning accuracy for an EDO will always be the patent val"? You just worded it this way because you prefer the term uniform map to patent val? Originally I interpreted the sentence differently to mean that even if the EDO doesn't use the patent val for its most accurate tuning (by whatever metric), it would still be a uniform map taken from some none edo. Pages like [[23-limit]] often show other uniform maps as the "most accurate" for EDOs (or ETs) which made it confusing. In that case uniform maps are only used to simplify the computation but there could theoretically be a more accurate non uniform map that has been missed. Thanks for clarifying. --[[User:Currywurst44|Currywurst44]] ([[User talk:Currywurst44|talk]]) 15:56, 11 October 2026 (UTC)

@@ Line 70: / Line 70: @@
 : Thanks for letting me know about this, and for correcting it on my recent pages. I'll be cognizant of this moving forward. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:02, 6 March 2022 (UTC)
+== Uniform map/generalized patent val always best? ==
+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)
+::: So another way of writing the quote would be "The map with the overall best tuning accuracy for an EDO will always be the patent val"? You just worded it this way because you prefer the term uniform map to patent val? Originally I interpreted the sentence differently to mean that even if the EDO doesn't use the patent val for its most accurate tuning (by whatever metric), it would still be a uniform map taken from some none edo. Pages like [[23-limit]] often show other uniform maps as the "most accurate" for EDOs (or ETs) which made it confusing. In that case uniform maps are only used to simplify the computation but there could theoretically be a more accurate non uniform map that has been missed. Thanks for clarifying. --[[User:Currywurst44|Currywurst44]] ([[User talk:Currywurst44|talk]]) 15:56, 11 October 2026 (UTC)