{{Infobox Interval| main_interval_name = diminished fourth| inverse = augmented fifth| complement = augmented fifth| other_names = -| abbreviation = d4<ref name="B&S"/>| semitones = 4| interval_class = 4| just_interval = 32:25,<ref name="Haluska">Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxv. {{ISBN|0-8247-4714-3}}. Classic diminished fourth.</ref> 8192:6561, 14:11| cents_equal_temperament = 400| cents_24T_equal_temperament = | cents_just_intonation = 427, 384, 417.5 }}
In classical music from Western culture, a '''diminished fourth''' ({{Audio|Major third on C.mid|Play}}) is an interval produced by narrowing a perfect fourth by a chromatic semitone.<ref name="B&S">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.</ref><ref>Hoffmann, F.A. (1881). ''Music: Its Theory & Practice'', p.89-90. Thurgate & Sons. Digitized Aug 16, 2007.</ref> For example, the interval from C to F is a perfect fourth, five semitones wide, and both the intervals from C{{Music|sharp}} to F, and from C to F{{Music|b}} 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.<ref>Benward & Saker (2003), p.92.</ref> 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{{Music|sharp}} is a major third; but if the same pitches are spelled B and E{{Music|flat}}, 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{{music|b}}, 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{{Music|sharp}} to F, a diatonic minor second plus a pure minor third, or the interval C to F{{Music|flat}}, 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{{music|b}}.<ref>Paul, Oscar (1885). ''[https://books.google.com/books?id=4WEJAQAAMAAJ&q=musical+interval+%22pythagorean+major+third%22 A manual of harmony for use in music-schools and seminaries and for self-instruction]'', p.165. Theodore Baker, trans. G. Schirmer.</ref> {{audio|Just diminished fourth in scale.mid|Play}}
==See also== *Schismatic temperament
==References== <references/>
{{Intervals}}
{{DEFAULTSORT:Diminished Fourth}} Category:Diminished intervals Category:Fourths (music)
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