Tenney–Euclidean temperament measures: Difference between revisions

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G and ψ error both have the advantage that higher rank temperament error corresponds directly to rank one error, but the RMS normalization has the further advantage that in the rank one case, G = sin θ, where θ is the angle between J and the val in question. Multiplying by 1200 to obtain a result in cents leads to 1200 sin θ, TE error as it appears on the temperament finder pages.

== ~~Example in~~ each ~~definitions~~ ==

== Examples of each definition ==

The different definitions yield different results, but they are related ~~from~~ each other by a factor of rank and limit. ~~Meaningful~~ comparison of temperaments in the same rank and limit ~~will~~ be provided by picking any one of them.

The different definitions yield different results, but they are related to each other by a factor derived only from the rank and limit. A meaningful comparison of temperaments in the same rank and limit can be provided by picking any one of them.

Here is a demonstration from [[7-limit]] [[magic]] and [[meantone]] ~~compared in~~ each definitions.

Here is a demonstration from [[7-limit]] [[magic]] and [[meantone]], comparing each of the definitions.

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@@ Line 99: / Line 99: @@
 G and ψ error both have the advantage that higher rank temperament error corresponds directly to rank one error, but the RMS normalization has the further advantage that in the rank one case,  G = sin θ, where θ is the angle between J and the val in question. Multiplying by 1200 to obtain a result in cents leads to 1200 sin θ, TE error as it appears on the temperament finder pages.
-== Example in each definitions ==
+== Examples of each definition ==
-The different definitions yield different results, but they are related from each other by a factor of rank and limit. Meaningful comparison of temperaments in the same rank and limit will be provided by picking any one of them.
+The different definitions yield different results, but they are related to each other by a factor derived only from the rank and limit. A meaningful comparison of temperaments in the same rank and limit can be provided by picking any one of them.
-Here is a demonstration from [[7-limit]] [[magic]] and [[meantone]] compared in each definitions.
+Here is a demonstration from [[7-limit]] [[magic]] and [[meantone]], comparing each of the definitions.
 {| class="wikitable center-all"