Diminished Sixth
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Diminished Sixth
Inverse augmented third - d6[1] 7 5 192:125,[2] 32:21,49:32 700 700 743
Diminished sixth (just)  . In 12-TET, the interval is identical to a perfect fifth  .

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

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

## Wolf fifth

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.

## Sources

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 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.