Tenney–Euclidean temperament measures: Difference between revisions

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\text{TE simple badness} = \text{TE complexity} \times \text{TE error} </math>

TE temperament measures have been extensively studied by [[Graham Breed]] (see [http://x31eq.com/temper/primerr.pdf| ''Prime Based Error and Complexity Measures''], often referred to as ''primerr.pdf''), who also proposed [[Cangwu badness]], an important derived measure, which adds a free parameter to TE simple badness that enables one to specify a tradeoff between complexity and error.

TE temperament measures have been extensively studied by [[Graham Breed]] (see [http://x31eq.com/temper/primerr.pdf ''Prime Based Error and Complexity Measures''], often referred to as ''primerr.pdf''), who also proposed [[Cangwu badness]], an important derived measure, which adds a free parameter to TE simple badness that enables one to specify a tradeoff between complexity and error.

== Introduction ==

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# Taking an RMS

# Taking an RMS and also normalizing for the temperament rank

# Any of the above and also dividing by the norm of the [[JIP]] (just ~~initonation~~ points).

# Any of the above and also dividing by the norm of the [[JIP]] (just intonation points).

Graham Breed's original definitions from his ''primerr.pdf'' paper tend to use the third definition, as do parts of his [http://x31eq.com/temper/ temperament finder], although other scaling and normalization methods are sometimes used as well.

@@ Line 6: / Line 6: @@
 \text{TE simple badness} = \text{TE complexity} \times \text{TE error} </math>
-TE temperament measures have been extensively studied by [[Graham Breed]] (see [http://x31eq.com/temper/primerr.pdf| ''Prime Based Error and Complexity Measures''], often referred to as ''primerr.pdf''), who also proposed [[Cangwu badness]], an important derived measure, which adds a free parameter to TE simple badness that enables one to specify a tradeoff between complexity and error.
+TE temperament measures have been extensively studied by [[Graham Breed]] (see [http://x31eq.com/temper/primerr.pdf ''Prime Based Error and Complexity Measures''], often referred to as ''primerr.pdf''), who also proposed [[Cangwu badness]], an important derived measure, which adds a free parameter to TE simple badness that enables one to specify a tradeoff between complexity and error.
 == Introduction ==
@@ Line 23: / Line 23: @@
 # Taking an RMS
 # Taking an RMS and also normalizing for the temperament rank
-# Any of the above and also dividing by the norm of the [[JIP]] (just initonation points).
+# Any of the above and also dividing by the norm of the [[JIP]] (just intonation points).
 Graham Breed's original definitions from his ''primerr.pdf'' paper tend to use the third definition, as do parts of his [http://x31eq.com/temper/ temperament finder], although other scaling and normalization methods are sometimes used as well.