Inmusic, aditone (Latin:ditonus, fromAncient Greek:δίτονος, "of two tones") is theinterval of amajor third. The size of a ditone varies according to the sizes of the two tones of which it is compounded. The largest is the Pythagorean ditone, with a ratio of 81:64, also called a comma-redundant major third; the smallest is the interval with a ratio of 100:81, also called a comma-deficient major third.[1]
ThePythagorean ditone is the major third inPythagorean tuning, which has an interval ratio of 81:64,[2] which is 407.82cents. The Pythagorean ditone is evenly divisible by twomajor tones (9/8 or 203.91 cents) and is wider than a just major third (5/4, 386.31 cents) by asyntonic comma (81/80, 21.51 cents). Because it is a comma wider than a "perfect" major third of 5:4, it is called a "comma-redundant" interval.[3]Playⓘ
"The major third that appears commonly in the [Pythagorean] system (C–E, D–F♯, etc.) is more properly known as the Pythagorean ditone and consists of two major and two minor semitones (2M+2m). This is the interval that is extremely sharp, at 408c (thepure major third is only 386c)."[4]
It may also be thought of as four justly tunedfifths minus twooctaves.
Theprime factorization of the 81:64 ditone is 3^4/2^6 (or 3/1 * 3/1 * 3/1 * 3/1 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2).
InDidymus's diatonic andPtolemy'ssyntonic tunings, the ditone is a just major third with a ratio of 5:4, made up of two unequal tones—amajor and a minor tone of 9:8 and 10:9, respectively. The difference between the two systems is that Didymus places the minor tone below the major, whereas Ptolemy does the opposite.[5]
Inmeantone temperaments, the major tone and minor tone are replaced by a "mean tone" which is somewhere in between the two. Two of these tones make a ditone or major third. This major third is exactly the just (5:4) major third in quarter-comma meantone. This is the source of the name: the note exactly halfway between the bounding tones of the major third is called the "mean tone".[6]
Modern writers occasionally use the word "ditone" to describe the interval of a major third inequal temperament.[7] For example, "In modern acoustics, the equal-tempered semitone has 100 cents, the tone 200 cents, the ditone or major third 400 cents, the perfect fourth 500 cents, and so on. …”[8]
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