Well temperament: Difference between revisions

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A '''well temperament''' (or '''circulating temperament''') is a [[tuning system]] which is regarded as an approximation of an [[equal tuning]], has the same [[equave]] as that equal tuning and preserves the transposability of the equal tuning, but is not exactly the equal tuning being approximated. Historical well temperaments were formed by stacking a combination of pure [[3/2]] and flattened fifths and had 12 nearly equal steps.

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 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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 A '''well temperament''' (or '''circulating temperament''') is a [[tuning system]] which is regarded as an approximation of an [[equal tuning]], has the same [[equave]] as that equal tuning and preserves the transposability of the equal tuning, but is not exactly the equal tuning being approximated. Historical well temperaments were formed by stacking a combination of pure [[3/2]] and flattened fifths and had 12 nearly equal steps.
 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 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 ==