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Diminished octave

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(Redirected from Pythagorean diminished octave) Musical interval
diminished octave
InverseAugmented unison
Name
Other namesDiminished eighth
Abbreviationd8
Size
Semitones11
Interval class1
Just interval48:25, 256:135, 4096:2187
Cents
12-Tone equal temperament1100
Just intonation1129, 1108, 1086
Diminished octave on C Play.
Diminished octave on C-sharp Play.

In music from Western culture, a diminished octave (Play) is an interval produced by narrowing a perfect octave by a chromatic semitone. As such, the two notes are denoted by the same letter but have different accidentals. For instance, the interval from C4 to C5 is a perfect octave, twelve semitones wide, and both the intervals from C♯4 to C5 and from C4 to C♭5 are diminished octaves, spanning eleven semitones. Being diminished, it is considered a dissonant interval.

The diminished octave is enharmonically equivalent to the major seventh.

References

  1. ^ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0. Specific example of an d8 not given but general example of perfect intervals described.
  2. ^ Duffin, Ross W. (2008). How equal temperament ruined harmony : (and why you should care) (First published as a Norton paperback. ed.). New York: W. W. Norton. p. 163. ISBN 978-0-393-33420-3. Retrieved 28 June 2017.
  3. 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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