List_of_meantone_intervals
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 temperament, and 50 EDO to 50 equal temperament. Note that for brevity, several of the intervals for 31 EDO and 50 EDO are omitted from the table.
R.W. Duffin writes:
- "Specifying that the major semitone should be 3/ 2 the minor semitone [a 3:2 ratio] creates a 31 note division of the octave, which, in turn, closely corresponds to extended-quarter-comma meantone ... the 5:4 ratio [whose] extended-sixth-comma meantone corresponds to the 55 division ... extended-fifth-comma meantone [corresponds to] the 43 division of the octave [in which the] ratio of the major to minor semitone is 4:3."
The other meantone correspondencies: a 1:1 ratio produces a 12 division
- (1/ 11 comma meantone)... "2:1 [which] results in a 19 division
- (1/ 3 comma meantone) ... 5:3, which results in a 50 division"
- (2/ 7 comma meantone) are derived from these statements.[1][full citation needed]
[Brackets added for readability.]
The column of ratios gives a ratio or ratios approximated by the interval in septimal meantone temperament. An augmented interval is increased by a chromatic semitone, and a diminished interval decreased.
