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 ~~meantone~~ fifths and had 12 nearly equal steps.

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.

In the lens of [[regular temperament theory]], a well temperament can also be viewed as a ~~specific~~ tuning of an equal temperament. ~~See individual [[edo]] pages for contemporary~~ well ~~temperaments based on the corresponding~~ equal temperament.

In the lens of [[regular temperament theory]], a well temperament can also be viewed as a result of applying an irregular tuning map to the abstract intervals of an equal temperament. This point of view can suggest what JI ratios you could include as detunings of a specific interval in a well temperament. For example, in a 12-WT, you might want some major thirds 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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 {{Wikipedia|Well temperament}}
-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 meantone fifths and had 12 nearly equal steps.
+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.
-In the lens of [[regular temperament theory]], a well temperament can also be viewed as a specific tuning of an equal temperament. See individual [[edo]] pages for contemporary well temperaments based on the corresponding equal temperament.
+In the lens of [[regular temperament theory]], a well temperament can also be viewed as a result of applying an irregular tuning map to the abstract intervals of an equal temperament. This point of view can suggest what JI ratios you could include as detunings of a specific interval in a well temperament. For example, in a 12-WT, you might want some major thirds 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 ==