Diminished fourth
Template:Short descriptionPage Module:Infobox/styles.css has no content.
| Inverse | augmented fifth |
|---|---|
| Name | |
| Other names | - |
| Abbreviation | d4[1] |
| Size | |
| Semitones | 4 |
| Interval class | 4 |
| Just interval | 32:25,[2] 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 (<phonos file="Major third on C.mid">Play</phonos>) 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.
- <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.[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.
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♭.[5] <phonos file="Just diminished fourth in scale.mid">Play</phonos>
See also
References
- ^ a b 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.
- ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxv. Template:ISBN. 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.
Lua error in package.lua at line 80: module 'Module:Navbox/configuration' not found.
