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| A '''regular temperament''' is, loosely, a JI interpretation of a scale or scales that are not JI, where the JI intervals are all chosen from a special kind of set of JI intervals, called a [[subgroup]], which is "built out of" a [[basis|chosen set of "basic" JI intervals]]. In other words, a temperament is an attempt to have certain intervals and chords in such a scale approximate a JI intervals and chords. A given temperament interpretation is more believable
| | This article focuses on the mathematical theories, particularly the mathematical utilities to describe a regular temperament. For an introduction to regular temperaments, see [[Tour of Regular Temperaments]]. |
| * the closer a scale is to the optimal tuning of the temperament,
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| * the less mistuning the temperament requires, and
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| * the more the JI ratios and chords in question withstand mistuning for the composer's purpose.
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| {{See also| Tour of Regular Temperaments}}
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| == Characterizing a regular temperament == | | == Characterizing a regular temperament == |