Diminished Fourth
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Diminished Fourth
Inverse augmented fifth - d4[1] 4 4 32:25[2], 8192:6561 400 400 427, 384
Diminished fourth  .

In classical music from Western culture, a diminished fourth ( ) is an interval produced by narrowing a perfect fourth by a chromatic semitone.[1][3] 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.[4]

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.[5]

## Sources

1. ^ a b 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.
2. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxv. ISBN 0-8247-4714-3. Classic diminished fourth.
3. ^ Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007.
4. ^ Benward & Saker (2003), p.92.
5. ^ 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.