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Diminished sixth

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(Redirected from Pythagorean diminished sixth) Musical interval
Diminished sixth
Inverseaugmented third
Name
Other names-
Abbreviationd6
Size
Semitones7
Interval class5
Just interval192:125, 32:21,49:32
Cents
12-Tone equal temperament700
24-Tone equal temperament700
Just intonation743
Diminished sixth (just) Play. In 12-TET, the interval is identical to a perfect fifth Play.

In classical music from Western culture, a diminished sixth (Play) is an interval produced by narrowing a minor sixth by a chromatic semitone. 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, 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"

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. 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.
Intervals
Twelve-
semitone

(post-Bach
Western)
(Numbers in brackets
are the number of
semitones in the
interval.)
Perfect
Major
Minor
Augmented
Diminished
Compound
Other
tuning
systems
24-tone equal temperament
(Numbers in brackets refer
to fractional semitones.)

Neutral

Just intonations
(Numbers in brackets
refer to pitch ratios.)
7-limit
Higher-limit
Other
intervals
Groups
Semitones
Quarter tones
Commas
Measurement
Others
List of pitch intervals
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