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.
^ abBenward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN978-0-07-294262-0. 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. ISBN0-8247-4714-3. Classic diminished fourth.
^Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007.
