Optimization: Difference between revisions

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== Common tunings ==

A good number of tunings have been given names.

A good number of tunings have been given names. The following table shows some common tuning schemes by weight-skew against the order.

{| class="wikitable"

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! Weight-skew\Order !! Chebyshevian (''L''1 tuning) !! Euclidean (''L''2 tuning) !! Minkowskian (''L''infinity tuning)

|-

| Tenney Tenney-Weil || || [[TE tuning]] TWE tuning || [[TOP tuning]]

| Tenney Tenney-Weil || || [[TE tuning]] [[TWE tuning]] || [[TOP tuning]]

|-

| Frobenius Frobenius-Weil || || Frobenius tuning FWE tuning ||

| Frobenius Frobenius-Weil || || [[Frobenius tuning]] FWE tuning ||

|-

| Benedetti Benedetti-Weil || || BE tuning BWE tuning || [[BOP tuning]]

| Benedetti Benedetti-Weil || || [[BE tuning]] BWE tuning || [[BOP tuning]]

|}

Each has a constrained and/or destretched variant. E.g. for TE tuning there is [[CTE tuning]], and for TWE tuning there is CTWE tuning, which is also known as the KE tuning (Kees-Euclidean tuning).

Each has a constrained and/or destretched variant. E.g. for TE tuning there is [[CTE tuning]], and for TWE tuning there is [[CTWE tuning]], which is also known as the KE tuning (Kees-Euclidean tuning).

== See also ==

* [[:File:MiddlePath2015.pdf|''A Middle Path between Just Intonation and the Equal Temperaments – Part 1'']] ("middle path") by [[Paul Erlich]]

* [http://x31eq.com/temper/primerr.pdf|''Prime Based Error and Complexity Measures''] ("primerr.pdf") by [[Graham Breed]]

@@ Line 73: / Line 73: @@
 == Common tunings ==
-A good number of tunings have been given names.
+A good number of tunings have been given names. The following table shows some common tuning schemes by weight-skew against the order.
 {| class="wikitable"
@@ Line 80: / Line 80: @@
 ! Weight-skew\Order !! Chebyshevian<br>(''L''<sup>1</sup> tuning) !! Euclidean<br>(''L''<sup>2</sup> tuning) !! Minkowskian<br>(''L''<sup>infinity</sup> tuning)
 |-
-| Tenney<br>Tenney-Weil || || [[TE tuning]]<br>TWE tuning || [[TOP tuning]]<br>
+| Tenney<br>Tenney-Weil || || [[TE tuning]]<br>[[TWE tuning]] || [[TOP tuning]]<br>
 |-
-| Frobenius<br>Frobenius-Weil || || Frobenius tuning<br>FWE tuning ||
+| Frobenius<br>Frobenius-Weil || || [[Frobenius tuning]]<br>FWE tuning ||
 |-
-| Benedetti<br>Benedetti-Weil || || BE tuning<br>BWE tuning || [[BOP tuning]]<br>
+| Benedetti<br>Benedetti-Weil || || [[BE tuning]]<br>BWE tuning || [[BOP tuning]]<br>
 |}
-Each has a constrained and/or destretched variant. E.g. for TE tuning there is [[CTE tuning]], and for TWE tuning there is CTWE tuning, which is also known as the KE tuning (Kees-Euclidean tuning).
+Each has a constrained and/or destretched variant. E.g. for TE tuning there is [[CTE tuning]], and for TWE tuning there is [[CTWE tuning]], which is also known as the KE tuning (Kees-Euclidean tuning).
 == See also ==
 * [[:File:MiddlePath2015.pdf|''A Middle Path between Just Intonation and the Equal Temperaments – Part 1'']] ("middle path") by [[Paul Erlich]]
 * [http://x31eq.com/temper/primerr.pdf|''Prime Based Error and Complexity Measures''] ("primerr.pdf") by [[Graham Breed]]