Tenney–Euclidean temperament measures: Difference between revisions

Line 57:

== TE error ==

We can consider '''TE error''' to be a weighted average of the error of each prime ~~harmonics~~ in TE tuning~~. Multiplying it by 1200~~, ~~we get~~ a ~~figure with values~~ in ~~cents~~.

We can consider '''TE error''' to be a weighted average of the error of each [[prime harmonic]]s in [[TE tuning]], that is, a weighted average of the [[error map]] in TE tuning. TE error may be expressed in any logarithmic [[interval size unit]]s such as [[cent]]s or [[octave]]s.

By Graham Breed's definition, TE error may be accessed via [[Tenney–Euclidean tuning|TE tuning map]]. If ''T''''W'' is the Tenney-weighted tuning map, then the TE error ''G'' can be found by

Line 69:

</math>

If ''T''''W'' is denominated in cents, then ''J''''W'' should be also, so that {{nowrap|''J''''W'' {{=}} {{val| 1200 1200 … 1200 }}}}. Here {{nowrap|''T''''W'' − ''J''''W''}} is the list of weighted ~~mistunings~~ of each prime ~~harmonics~~.

If ''T''''W'' is denominated in cents, then ''J''''W'' should be also, so that {{nowrap|''J''''W'' {{=}} {{val| 1200 1200 … 1200 }}}}. Here {{nowrap|''T''''W'' − ''J''''W''}} is the list of weighted errors of each prime harmonic.

: '''Note''': that is the definition used by Graham Breed's temperament finder.

@@ Line 57: / Line 57: @@
 == TE error ==
-We can consider '''TE error''' to be a weighted average of the error of each prime harmonics in TE tuning. Multiplying it by 1200, we get a figure with values in cents.
+We can consider '''TE error''' to be a weighted average of the error of each [[prime harmonic]]s in [[TE tuning]], that is, a weighted average of the [[error map]] in TE tuning. TE error may be expressed in any logarithmic [[interval size unit]]s such as [[cent]]s or [[octave]]s.
 By Graham Breed's definition, TE error may be accessed via [[Tenney–Euclidean tuning|TE tuning map]]. If ''T''<sub>''W''</sub> is the Tenney-weighted tuning map, then the TE error ''G'' can be found by
@@ Line 69: / Line 69: @@
 </math>
-If ''T''<sub>''W''</sub> is denominated in cents, then ''J''<sub>''W''</sub> should be also, so that {{nowrap|''J''<sub>''W''</sub> {{=}} {{val| 1200 1200 … 1200 }}}}. Here {{nowrap|''T''<sub>''W''</sub> − ''J''<sub>''W''</sub>}} is the list of weighted mistunings of each prime harmonics.
+If ''T''<sub>''W''</sub> is denominated in cents, then ''J''<sub>''W''</sub> should be also, so that {{nowrap|''J''<sub>''W''</sub> {{=}} {{val| 1200 1200 … 1200 }}}}. Here {{nowrap|''T''<sub>''W''</sub> − ''J''<sub>''W''</sub>}} is the list of weighted errors of each prime harmonic.
 : '''Note''': that is the definition used by Graham Breed's temperament finder.