Diminished fourth

In classical music from Western culture, a diminished fourth () 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♭.

Musical interval

diminished fourth

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 (Play^ⓘ) 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.

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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] Play^ⓘ

See also

[edit]

• Schismatic temperament

References

[edit]

1. ^ ^{a b} 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.
2. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxv. ISBN 0-8247-4714-3. Classic diminished fourth.
3. ^ Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007.
4. ^ Benward & Saker (2003), p.92.
5. ^ 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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