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The name "meantone temperament" derives from the fact that in all such temperaments the size of the whole tone, within the diatonic scale, is somewhere between the major and minor tones (9:8 and 10:9 respectively) of just intonation, which differ from each other by a syntonic comma.
The following is a list of intervals of extended meantone temperament.These intervals constitute the standard vocabulary of intervals for the Western common practice era. . Here 12 EDO refers to the size of the interval in the temperament with 12 equal divisions of the octave, which is the most common meantone temperament in the modern era, 19 EDO to 19 equal temperament, 31 EDO to 31 equal ...
In a meantone temperament, each fifth is narrowed ("tempered") by the same small amount. The most common of meantone temperaments is the quarter-comma meantone , in which each fifth is tempered by 1 ⁄ 4 of the syntonic comma, so that after four steps the major third (as C-G-D-A-E) is a full syntonic comma lower than the Pythagorean one.
In meantone temperament, this effect is even more pronounced (the fifth over the break in the circle is known as the Wolf interval, as its intense beating was likened to a "howling"). 53 equal temperament provides an extension of Pythagorean tuning, and 31 equal temperament is used nowadays to extend quarter-comma meantone.
However, meantone temperaments (except for 12 TET) cannot fit into a 12 note keyboard; and like quarter-comma meantone, most require an infinite number of notes (although there is a very close approximation to quarter-comma that can fit into a keyboard with 31 keys).
However, the fifth may be flattened to a greater or lesser degree than this and the tuning system retains the essential qualities of meantone temperament. Historical examples include 1 / 3 comma and 2 / 7 comma meantone. Well temperament Prelude No. 1, C major, BWV 846, from the Well-Tempered Clavier by Johann Sebastian Bach.
In this sense, "just intonation" is differentiated from equal temperaments and the "tempered" tunings of the early renaissance and baroque, such as Well temperament, or Meantone temperament. Since 5-limit has been the most prevalent just intonation used in western music, western musicians have subsequently tended to consider this scale to be ...
In music, septimal meantone temperament, also called standard septimal meantone or simply septimal meantone, refers to the tempering of 7-limit musical intervals by a meantone temperament tuning in the range from fifths flattened by the amount of fifths for 12 equal temperament to those as flat as 19 equal temperament, with 31 equal temperament being a more or less optimal tuning for both the ...