Diminished sixth

In classical music from Western culture, a diminished sixth (Playⓘ) is an interval produced by narrowing a minor sixth by a chromatic semitone.[1][3] For example, the interval from A to F is a minor sixth, eight semitones wide, and both the intervals from A♯ to F, and from A to F♭ are diminished sixths, spanning seven semitones. Being diminished, it is considered a dissonant interval,[4] despite being equivalent to an interval known for its consonance.

Diminished sixth
Inverseaugmented third
Name
Other names-
Abbreviationd6[1]
Size
Semitones7
Interval class5
Just interval192:125,[2] 32:21,49:32
Cents
Equal temperament700
24 equal temperament700
Just intonation743
Diminished sixth (just) Playⓘ. In 12-TET, the interval is identical to a perfect fifth Playⓘ.

Its inversion is the augmented third, and its enharmonic equivalent is the perfect fifth.

"Wolf fifth"
Main article: Wolf interval

A severely dissonant diminished sixth is observed when the instrument is tuned using a Pythagorean or a meantone temperament tuning system. Typically, this is the interval between G♯ and E♭. Since it seems to "howl like a wolf" (because of the beating), and since it is meant to be the enharmonic equivalent to a fifth, this interval is called the "wolf" fifth. Notice that a justly tuned fifth is the most consonant interval after the perfect unison and the perfect octave.

References
  1. Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0. Specific example of an d6 not given but general example of minor intervals described.
  2. Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. ISBN 0-8247-4714-3. Classic diminished sixth.
  3. Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007.
  4. Benward & Saker (2003), p.92.
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