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diminished fourth
In classical music from Western culture, a diminished fourth () is an interval produced by narrowing a perfect fourth by a chromatic semitone.〔Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. ISBN 978-0-07-294262-0. Specific example of an d4 not given but general example of perfect intervals described.〕〔Hoffmann, F.A. (1881). ''Music: Its Theory & Practice'', p.89-90. Thurgate & Sons. Digitized Aug 16, 2007.〕 For example, the interval from C to F is a perfect fourth, five semitones wide, and both the intervals from C to F, and from C to F are diminished fourths, spanning four semitones. Being diminished, it is considered a dissonant interval.〔Benward & Saker (2003), p.92.〕
A diminished fourth is enharmonically equivalent to a major third; that is, it spans the same number of semitones, and they are physically the same pitch in twelve-tone equal temperament. For example, B–D is a major third; but if the same pitches are spelled B and E, as occurs in the C harmonic minor scale, the interval is instead a diminished fourth. In other tunings, however, they are not necessarily identical. For example, in 31 equal temperament the diminished fourth is slightly wider than a major third, and is instead the same width as the septimal major third. The Pythagorean diminished fourth (F, 8192:6561 = 384.36 cents), also known as the schismatic major third, is closer to the just major third than the Pythagorean major third.
The 32:25 just diminished fourth arises in the C harmonic minor scale between B and E.〔Paul, Oscar (1885). ''(A manual of harmony for use in music-schools and seminaries and for self-instruction )'', p.165. Theodore Baker, trans. G. Schirmer.〕
==See also==
*Skhismic temperament
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