Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 used in 12 equal temperament. The meantone temperament:
Quarter-comma meantone is the best known type of meantone temperament, and the term meantone temperament is often used to refer to it specifically.
"Meantone" can receive the following equivalent definitions:
The family of meantone temperaments share the common characteristic that they form a stack of identical fifths, the tone being the result of two fifths minus one octave, the major third of four fifths minus two octaves. Meantone temperaments are often described by the fraction of the syntonic comma by which the fifths are tempered: quarter-comma meantone, the most common type, tempers the fifths by 1/4 syntonic comma, with the result that four fifths produce a just major third, a syntonic comma lower than a Pythagorean major third; third-comma meantone tempers by 1/3 syntonic comma, three fifths producing a just major sixth, a syntonic comma lower than a Pythagorean one.
All meantone temperaments are linear temperaments, distinguished by the width of its generator in cents, as shown in the central column of Figure 1. Historically notable meantone temperaments, discussed below, occupy a narrow portion of this tuning continuum, ranging from approximately 695 to 699 cents.
While the term meantone temperament refers primarily to the tempering of 5-limit musical intervals, optimum values for the 5-limit also work well for the 7-limit, defining septimal meantone temperament. In Figure 1, the valid tuning ranges of 5-limit, 7-limit, and 11-limit tunings are shown, and can be seen to include many notable meantone tunings.
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