Diminished sixth

Diminished sixth

Inverse	augmented third
Name
Other names	-
Abbreviation	d6[1]
Size
Semitones	7
Interval class	5
Just interval	192:125[2], 32:21
Cents
Equal temperament	700
24 equal temperament	700
Just intonation	743

Diminished sixth  Play (help·info).

In classical music from Western culture, a diminished sixth ( Play (help·info)) 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].

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.

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 0824747143. 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.