Tenney–Euclidean temperament measures: Difference between revisions

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{{Texops}}{{Todo|rewrite|inline=1|text=Remove all references to wedgies, as per [[User:VectorGraphics/Operation_Loosen_Underpants]]}}

The '''Tenney–Euclidean temperament measures''' ('''TE temperament measures''') consist of TE complexity, TE error, and TE simple badness. These are evaluations of a temperament's [[complexity]], [[error]], and [[badness]], respectively, and they follow the identity

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== TE complexity ==

~~{{Todo|rework|inline=1|text=Explain without wedgies}}~~

Given a [[wedgie]] ''M'', that is a canonically reduced ''r''-val correspondng to a temperament of rank ''r'', the norm ‖''M''‖ is a measure of the complexity of ''M''; that is, how many notes in some sort of weighted average it takes to get to intervals. For 1-vals, for instance, it is approximately equal to the number of scale steps it takes to reach an octave.

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+{{Texops}}{{Todo|rewrite|inline=1|text=Remove all references to wedgies, as per [[User:VectorGraphics/Operation_Loosen_Underpants]]}}
 The '''Tenney–Euclidean temperament measures''' ('''TE temperament measures''') consist of TE complexity, TE error, and TE simple badness. These are evaluations of a temperament's [[complexity]], [[error]], and [[badness]], respectively, and they follow the identity
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 == TE complexity ==
-{{Todo|rework|inline=1|text=Explain without wedgies}}
 Given a [[wedgie]] ''M'', that is a canonically reduced ''r''-val correspondng to a temperament of rank ''r'', the norm ‖''M''‖ is a measure of the complexity of ''M''; that is, how many notes in some sort of weighted average it takes to get to intervals. For 1-vals, for instance, it is approximately equal to the number of scale steps it takes to reach an octave.