Well temperament: Difference between revisions

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A '''well temperament''' is a [[~~circulating temperament~~]] ~~where~~ the intervals in ~~a class are not all tuned~~ the ~~same. As a consequence~~ of ~~their irregularity~~, it is ~~possible in extreme cases for well temperaments to have classes where they tune each instance of~~ an ~~interval in that class uniquely, as if they were~~ [[~~Just intonation|just~~]] ~~scales~~ of the ~~same [[rank]] as their cardinality~~.

A '''well temperament''' or a '''circulating temperament''' is a scale with the property that for at least one [[interval class]] (the interval class is viewed as forming a closed circle within the tuning, hence the name), all of the intervals in the "circle" can be regarded as approximations of some targeted interval, but which is not an [[equal temperament]]. The targeted (circulating) interval can be a fixed just interval (like a just perfect fifth), or an n-edo interval when the goal is to produce an unequal coloring of n-edo. In the best known examples, the interval approximated is a fifth and the scale has twelve notes to an octave.

One of the advantages of these tunings, is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.

== Types ==

A well temperament may be classified by method as follows:

* [[Maximal evenness|Maximally even]] set in a large [[EDO|edo]] or another [[equal-step tuning]]

* A quasi-equal [[Detempering|detemperament]] (though not all detemperaments of an edo are well temperaments)

* [[Neji]]

== Historical well temperaments ==

* [[Kirnberger]] – Kirnberger temperament

# the fifths are [[3/2|pure]], except for

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* [[Well tempered nonet]]

== Articles ==

* [http://www.kylegann.com/histune.html An Introduction to Historical Tunings] by [[Kyle Gann]] [http://www.webcitation.org/5xe2pcAue Permalink]

* [http://lumma.org/tuning/gws/circ.html Circulating Temperaments] by [[Gene Ward Smith]] [http://www.webcitation.org/5xemAJsWE Permalink]

* [http://www.math.uwaterloo.ca/%7Emrubinst/tuning/tuning.html Well v.s. Equal Temperament] by [[Michael Rubinstein]] [http://www.webcitation.org/5xemm0tvx Permalink]

* [http://www.piano-tuners.org/edfoote/well_tempered_piano.html Six Degrees Of Tonality: The Well Tempered Piano] by [[Edward Foote]] [http://www.webcitation.org/5xenGg2uG Permalink]

* [http://www.rollingball.com/images/HT5.htm Five

[[Category:Theory]]

[[Category:~~Terms~~]]

[[Category:Scale theory]]

[[Category:~~Well~~ temperament| ]]

[[Category:Circulating temperament| ]]

~~[[Category:Circulating temperament]]~~

@@ Line 1: / Line 1: @@
-A '''well temperament''' is a [[circulating temperament]] where the intervals in a class are not all tuned the same. As a consequence of their irregularity, it is possible in extreme cases for well temperaments to have classes where they tune each instance of an interval in that class uniquely, as if they were [[Just intonation|just]] scales of the same [[rank]] as their cardinality.
+A '''well temperament''' or a '''circulating temperament''' is a scale with the property that for at least one [[interval class]] (the interval class is viewed as forming a closed circle within the tuning, hence the name), all of the intervals in the "circle" can be regarded as approximations of some targeted interval, but which is not an [[equal temperament]]. The targeted (circulating) interval can be a fixed just interval (like a just perfect fifth), or an n-edo interval when the goal is to produce an unequal coloring of n-edo. In the best known examples, the interval approximated is a fifth and the scale has twelve notes to an octave.
+One of the advantages of these tunings, is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.
+== Types ==
+A well temperament may be classified by method as follows:
+* [[Maximal evenness|Maximally even]] set in a large [[EDO|edo]] or another [[equal-step tuning]]
+* A quasi-equal [[Detempering|detemperament]] (though not all detemperaments of an edo are well temperaments)
+* [[Neji]]
+== Historical well temperaments ==
 * [[Kirnberger]] – Kirnberger temperament
 # the fifths are [[3/2|pure]], except for
@@ Line 20: / Line 29: @@
 * [[Well tempered nonet]]
+== Articles ==
+* [http://www.kylegann.com/histune.html An Introduction to Historical Tunings] by [[Kyle Gann]] [http://www.webcitation.org/5xe2pcAue Permalink]
+* [http://lumma.org/tuning/gws/circ.html Circulating Temperaments] by [[Gene Ward Smith]] [http://www.webcitation.org/5xemAJsWE Permalink]
+* [http://www.math.uwaterloo.ca/%7Emrubinst/tuning/tuning.html Well v.s. Equal Temperament] by [[Michael Rubinstein]] [http://www.webcitation.org/5xemm0tvx Permalink]
+* [http://www.piano-tuners.org/edfoote/well_tempered_piano.html Six Degrees Of Tonality: The Well Tempered Piano] by [[Edward Foote]] [http://www.webcitation.org/5xenGg2uG Permalink]
+* [http://www.rollingball.com/images/HT5.htm Five
 [[Category:Theory]]
-[[Category:Terms]]
+[[Category:Scale theory]]
-[[Category:Well temperament| ]] <!-- main article -->
+[[Category:Circulating temperament| ]] <!-- main article -->
-[[Category:Circulating temperament]]
 {{todo| expand }}