Diminished sixth explained

Main Interval Name:Diminished sixth
Inverse:augmented third
Complement:augmented third
Other Names:-
Abbreviation:d6
Semitones:7
Interval Class:5
Just Interval:192:125,[1] 32:21,49:32
Cents Equal Temperament:700
Cents 24T Equal Temperament:700
Cents Just Intonation:743

In classical music from Western culture, a diminished sixth is an interval produced by narrowing a minor sixth by a chromatic semitone.[2] [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"

See main article: Wolf interval.

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. Notice that a justly tuned fifth is the most consonant interval after the perfect unison and the perfect octave.

References

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