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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: * generates all non-octave intervals from a stack of tempered perfect fifths; and * by choosing an appropriate size for major and minor thirds, tempers the syntonic comma to unison. 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 temperaments== "Meantone" can receive the following equivalent definitions: * The meantone is the mean between the major whole tone (9/8 in just intonation) and the minor whole tone (10/9 in just intonation). * The meantone is the mean of the just major third, i.e. the square root of 5/4. 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. Such temperaments are also called "regular" or "syntonic". 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 fall on the syntonic temperament's tuning continuum, and as such are "syntonic tunings". The distinguishing feature of each unique syntonic tuning is 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 the syntonic temperament's tuning continuum, ranging from approximately 695 to 699 cents. The criteria which define the limits (if any) of the meantone range of tunings within the syntonic temperament's tuning continuum are not yet well-defined. 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 syntonic tunings are shown, and can be seen to include many notable meantone tunings. Meantone temperaments can be specified in various ways: by what fraction (logarithmically) of a syntonic comma the fifth is being flattened (as above), what equal temperament has the meantone fifth in question, the width of the tempered perfect fifth in cents, or the ratio of the whole tone to the diatonic semitone. This last ratio was termed "R" by American composer, pianist and theoretician Easley Blackwood, but in effect has been in use for much longer than that. It is useful because it gives us an idea of the melodic qualities of the tuning, and because if R is a rational number N/D, so is (3R+1)/(5R+2) or (3N+D)/(5N+2D), which is the size of fifth in terms of logarithms base 2, and which immediately tells us what division of the octave we will have. If we multiply by 1200, we have the size of fifth in cents. In these terms, some historically notable meantone tunings are listed below. The relationship between the first two columns is exact, while that between them and the third is closely approximate. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「meantone temperament」の詳細全文を読む スポンサード リンク
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