Well temperament

A well temperament is a scale (formally an irregular temperament) approximating an equal tuning, which has the same average step size as said equal temperament (that is, in general no single note in an equal tuning becomes two different ones in a well temperament). Like musical scales in general, they are generally assumed to be periodic (usually octave-equivalent) unless otherwise specified.

Historically, the usage of the term "well temperament" was limited to specifically 12-tone well temperaments, due to the conceptualization of a temperament as a circle of twelve fifths, which could be tuned equally (equal temperament), as a chain of eleven fifths "broken" by one diminished sixth (a 12-note scale belonging to a regular temperament), or in a number of other combinations of tunings. On top of this, well temperaments were generally expected to be closer to 12edo than meantone or pythagorean tunings, which were considered their own categories of temperament due to the objectives of tempering at the time. Additionally, note that 12edo was considered a well temperament.

In terms of modern xenharmonic theory, a well temperament can be considered a 1-to-1 detempering of an equal tuning, and this is the sense used on the wiki. As a result, they have historically attracted very little attention from xenharmonic theorists interested in abstract formalism. However, they do have musical utility.

TODO: complete page