| Inverse | augmented fifth |
|---|---|
| Name | |
| Other names | - |
| Abbreviation | d4 |
| Size | |
| Semitones | 4 |
| Interval class | 4 |
| Just interval | 32:25, 8192:6561, 14:11 |
| Cents | |
| 12-Tone equal temperament | 400 |
| Just intonation | 427, 384, 417.5 |
In classical music from Western culture, a diminished fourth (Play) is an interval produced by narrowing a perfect fourth by a chromatic semitone. 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.
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.
In just intonation the usual diminished fourth: the interval C♯ to F, a diatonic minor second plus a pure minor third, or the interval C to F♭, a minor third plus a diatonic minor second, is 16/15 * 6/5 = 32/25.
The 32:25 just diminished fourth arises in the C harmonic minor scale between B and E♭. Play
See also
References
- ^ 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.
- Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxv. ISBN 0-8247-4714-3. Classic diminished fourth.
- Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007.
- Benward & Saker (2003), p.92.
- 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.
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