Augmented seventh

In classical music from Western culture, an augmented seventh is an interval produced by widening a major seventh by a chromatic semitone. For instance, the interval from C to B is a major seventh, eleven semitones wide, and both the intervals from C♭ to B, and from C to B♯ are augmented sevenths, spanning twelve semitones. Being augmented, it is classified as a dissonant interval.[4] However, it is enharmonically equivalent to the perfect octave.

This article is about the musical interval. For the chord, see Augmented seventh chord.
augmented seventh
Inversediminished second
Name
Other names-
AbbreviationA7[1]
Size
Semitones12
Interval class0
Just interval125:64[2][3] or 2025:1024[3]
Cents
Equal temperament1200[3]
24 equal temperament1150
Just intonation1159[3] or 1180[3]
Augmented seventh on C Play equal temperament  or Just .
Pythagorean augmented seventh on C (531441/262144 = 1223.46), a Pythagorean comma above the perfect octave. Play 

Since an octave can be described as a major seventh augmented by a diatonic semitone, the augmented seventh is the sum of an octave, plus the difference between the chromatic and diatonic semitones, which makes it a highly variable quantity between one meantone tuning and the next. In standard equal temperament, in fact, it is identical to the perfect octave (Play ), because both semitones have the same size. In 19 equal temperament, on the other hand, the interval is 63 cents short of an octave, i.e. 1137 cents. More typical meantone tunings fall between these extremes, giving it an intermediate size.

In just intonation, three major thirds in succession make up an augmented seventh, which is just short of an octave by 41.05 cents. Adding a diesis to this makes up an octave. Hence, this interval's complement, the diminished second, is often referred to as a diesis.

See also

Sources
  1. Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0. Specific example of an A7 not given but general example of major intervals described.
  2. Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. ISBN 0-8247-4714-3. Classic augmented seventh.
  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.
  4. Benward & Saker (2003), p.92.
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