Diminished sixth

Diminished sixth
Inverse	augmented third
Name
Other names	-
Abbreviation	d6
Size
Semitones	7
Interval class	5
Just interval	192:125, 32:21,49:32
Cents
Equal temperament	700
24-Tone equal temperament	700
Just intonation	743

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.

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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 a fixed-pitch instrument limited to twelve notes per octave is tuned using Pythagorean tuning or a meantone temperament with a fifth flatter than 700 cents. Typically, this is the interval between G♯ and E♭. Since this interval was considered to "howl like a wolf" (because of the beating), and since it sounded like a badly out-of-tune fifth, this interval is called the "wolf" fifth. A justly tuned fifth is the most consonant interval after the perfect unison and the perfect octave.

References

1 2 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.
↑ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. ISBN 0-8247-4714-3. Classic diminished sixth.
↑ Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007.
↑ Benward & Saker (2003), p.92.

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[B&S-1] 1 2 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.

[Haluska-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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"Wolf fifth"

References