The following is a list of intervals of extended

meantone temperament Meantone temperaments are musical temperaments; that is, a variety of Musical tuning#Tuning systems, tuning systems constructed, similarly to Pythagorean tuning, as a sequence of equal fifths, both rising and descending, scaled to remain within th ...

. 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 In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), 19-ED2 ("Equal Division of 2:1) or 19 Equal temperament, ET, is the musical temperament, tempered scale derived by dividing the octave into 19 equal steps ...

, 31 EDO to

31 equal temperament In music, 31 equal temperament, which can also be abbreviated (31 tone ) or (equal division of the octave), also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equally-proportioned steps (e ...

, 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 the minor semitone creates a 31 note division of the octave, which, in turn, closely corresponds to extended-

quarter-comma meantone Quarter-comma meantone, or -comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. In this system the perfect fifth is flattened by one quarter of a syntonic comma with ...

... the 5:4 ratio extended-sixth-comma meantone corresponds to the 55 division ... extended-fifth-comma meantone the 43 division of the octave ratio of the major to minor semitone is 4:3." The other meantone correspondencies: : "a 1:1 ratio produces a 12 division" ( comma meantone) : "2:1 results in a 19 division" ( comma meantone) : "5:3, which results in a 50 division" ( comma meantone) are derived from these statements. 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 In modern Western tonal music theory an augmented unison or augmented prime is the interval between two notes on the same staff position, or denoted by the same note letter, whose alterations cause them, in ordinary equal temperament, to be one ...

, and a diminished interval decreased.

References

{{Reflist * Linear temperaments Meantone intervals

See also

References