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.

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 audio speaker iconPlay equal temperament  or audio speaker iconJust .
Pythagorean augmented seventh on C (531441/262144 = 1223.46), a Pythagorean comma above the perfect octave. audio speaker iconPlay 

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 (audio speaker iconPlay ), 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 alsoEdit

SourcesEdit

  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. ^ a b c d e 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.