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). 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 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.

== 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). 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 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.
 == Historical well temperaments ==