Diminished fourth
In classical music from Western culture, a diminished fourth (Template:ErrorScript error: No such module "Category handler".) is an interval produced by narrowing a perfect fourth by a chromatic semitone.[1][2] 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.
- <score sound>
{ \override Score.TimeSignature
- 'stencil = ##f
\relative c' {
\time 4/4
\set Score.tempoHideNote = ##t \tempo 1 = 20
<cis f>1 <c? fes>
}
} </score>
Being diminished, it is considered a dissonant interval.[3] 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♭.[4] Template:ErrorScript error: No such module "Category handler".
See also
References
- ↑ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. Template:ISBN. 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.
- ↑ 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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