Well temperament: Difference between revisions

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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.

Through the lens of [[regular temperament theory]], a well temperament can be viewed as a result of applying an irregular [[tuning map]] to the abstract intervals of an [[equal temperament]] (i.e. a [[rank]]-1 abstract regular temperament), though tuning maps are ~~normally~~ defined to be regular. This point of view can suggest what JI ratios the well temperament could include as detunings of a given interval of an equal tuning. For example, in a 12-tone well temperament, one might want some major thirds to be equal (or close to) 5/4 and some equal (or close to) 81/64, though 81/64 is identified with 5/4 in 12 equal temperament.

Through the lens of [[regular temperament theory]], a well temperament can be viewed as a result of applying an irregular [[tuning map]] to the abstract intervals of an [[equal temperament]] (i.e. a [[rank]]-1 abstract regular temperament), though tuning maps in the technical sense are defined to be regular. This point of view can suggest what JI ratios the well temperament could include as detunings of a given interval of an equal tuning. For example, in a 12-tone well temperament, one might want some major thirds to be equal (or close to) 5/4 and some equal (or close to) 81/64, though 81/64 is identified with 5/4 in 12 equal temperament.

== Historical well temperaments ==

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 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.
-Through the lens of [[regular temperament theory]], a well temperament can be viewed as a result of applying an irregular [[tuning map]] to the abstract intervals of an [[equal temperament]] (i.e. a [[rank]]-1 abstract regular temperament), though tuning maps are normally defined to be regular. This point of view can suggest what JI ratios the well temperament could include as detunings of a given interval of an equal tuning. For example, in a 12-tone well temperament, one might want some major thirds to be equal (or close to) 5/4 and some equal (or close to) 81/64, though 81/64 is identified with 5/4 in 12 equal temperament.
+Through the lens of [[regular temperament theory]], a well temperament can be viewed as a result of applying an irregular [[tuning map]] to the abstract intervals of an [[equal temperament]] (i.e. a [[rank]]-1 abstract regular temperament), though tuning maps in the technical sense are defined to be regular. This point of view can suggest what JI ratios the well temperament could include as detunings of a given interval of an equal tuning. For example, in a 12-tone well temperament, one might want some major thirds to be equal (or close to) 5/4 and some equal (or close to) 81/64, though 81/64 is identified with 5/4 in 12 equal temperament.
 == Historical well temperaments ==