Diminished octave

diminished octave
Inverse	Augmented unison
Name
Other names	Diminished eighth
Abbreviation	d8
Size
Semitones	11
Interval class	1
Just interval	48:25, 49:26 (13-limit), 256:135, 4096:2187
Cents
Equal temperament	1100
Just intonation	1129, 1108, 1086

In music from Western culture, a diminished octave (Play^ⓘ) is an interval produced by narrowing a perfect octave by a chromatic semitone.^[1] 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.

${ \override Score.TimeSignature #'stencil = ##f \relative c' { \time 4/4 \set Score.tempoHideNote = ##t \tempo 1 = 20 <cis c'?>1 <c? ces'> } }$

Being diminished, it is considered a dissonant interval.^[3] The diminished octave is enharmonically equivalent to the major seventh.

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 d8 not given but general example of perfect intervals described.
1 2 3 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.
↑ 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 d8 not given but general example of perfect intervals described.

[Duffin-2] 1 2 3 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.

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References