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.

Despite their sharing the word "temperament" in their names, well temperaments and the modern notion of [[regular temperament]]s are ~~best considered~~ two different concepts, ~~though~~ sometimes one of these could guide construction of the other.

Despite their sharing the word "temperament" in their names, well temperaments and the modern notion of [[regular temperament]]s are two different concepts. However, sometimes one of these could guide construction of the other. For example, 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. However, note that when nejis are considered well temperaments in this sense, the JI ratios the intervals are said to represent and the actual JI ratios of the neji tuning must be distinguished, and the JI ratios that occur in the neji should not be assumed to be consistent with the val.

== 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.
-Despite their sharing the word "temperament" in their names, well temperaments and the modern notion of [[regular temperament]]s are best considered two different concepts, though sometimes one of these could guide construction of the other.
+Despite their sharing the word "temperament" in their names, well temperaments and the modern notion of [[regular temperament]]s are two different concepts. However, sometimes one of these could guide construction of the other. For example, 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. However, note that when nejis are considered well temperaments in this sense, the JI ratios the intervals are said to represent and the actual JI ratios of the neji tuning must be distinguished, and the JI ratios that occur in the neji should not be assumed to be consistent with the val.
 == Historical well temperaments ==