Diminished fourth

{{Infobox Interval|

main_interval_name = diminished fourth|

inverse = augmented fifth|

complement = augmented fifth|

other_names = -|

abbreviation = d4|

semitones = 4|

interval_class = 4|

just_interval = 32:25,Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxv. {{ISBN|0-8247-4714-3}}. Classic diminished fourth. 8192:6561, 14:11|

cents_equal_temperament = 400|

cents_24T_equal_temperament = |

cents_just_intonation = 427, 384, 417.5

}}

File:Diminished fourth on C.png

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.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.Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007. 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. Being diminished, it is considered a dissonant interval.Benward & Saker (2003), p.92.

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}}{{music|minus}}{{music|minus}}, 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}}.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. {{audio|Just diminished fourth in scale.mid|Play}}