Ditone
In
Pythagorean tuning
The Pythagorean ditone is the major third in
"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 (the pure major third is only 386c)."[4]
It may also be thought of as four justly tuned fifths minus two octaves.
The
Just intonation
In Didymus's diatonic and Ptolemy's syntonic tunings, the ditone is a just major third with a ratio of 5:4, made up of two unequal tones—a major 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]
Meantone temperament
In meantone 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]
Equal temperament
Modern writers occasionally use the word "ditone" to describe the interval of a major third in equal 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]
See also
References
- ^ Abraham Rees, "Ditone, Ditonum", in The Cyclopædia, or Universal Dictionary of Arts, Sciences, and Literature. In Thirty-Nine Volumes, vol. 12 (London: Longman, Hurst, Rees, Orme, & Brown, 1819) [not paginated].
- ISBN 978-0-486-43406-3.
- ^ Abraham Rees, "Inconcinnous", in The Cyclopædia, or Universal Dictionary of Arts, Sciences, and Literature. In Thirty-Nine Volumes, vol. 13 (London: Longman, Hurst, Rees, Orme, & Brown, 1819) [not paginated].
- ISBN 978-0-253-34866-1.
- ISBN 978-0-486-43406-3.
- ^ Mimi Waitzman, "Meantone Temperament in Theory and Practice", In Theory Only 5, no. 4 (May 1981): 3–15. Citation on 4.
- John Tyrrell(London: Macmillan Publishers, 2001).
- ISBN 3540437274.
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