Temperament

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A temperament is a tuning system that slightly compromises the pure intervals of just intonation (or, more generally, of any target tuning) to meet other requirements.

In regular temperament theory, the term temperament usually refers to a regular temperament.

History

In Western music history, the first temperaments to be described by theorists were meantone temperaments, in the beginning of the 16th century. These were developed in an attempt to solve some of the issues of the Pythagorean tuning, the most commonly used tuning system until then. In particular, the pure fifths (3/2) are slightly compromised in order to obtain either pure major thirds (5/4), in quarter-comma meantone, or slightly compromised major thirds in other meantone temperaments. The linear structure of meantone temperaments has laid the foundations for the development of regular temperament theory.

Because meantone temperaments have their own issues, a new kind of temperaments appeared in the 17th century: well temperaments. These have an irregular structure that allow for more flexibility in the way each note is tuned, and thus how each interval is compromised. As a result, most scales sound different when they are transposed to a different key.

See also