Augmented seventh
Inverse | diminished second |
---|---|
Name | |
Other names | - |
Abbreviation | A7[1] |
Size | |
Semitones | 12 |
Interval class | 0 |
Just interval | 125:64[2][3] or 2025:1024[3] |
Cents | |
12-Tone equal temperament | 1200[3] |
24-Tone equal temperament | 1150 |
Just intonation | 1159[3] or 1180[3] |
In
perfect octave
.
Since an
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 (ⓘ), 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
References
- ISBN 978-0-07-294262-0. Specific example of an A7 not given but general example of major intervals described.
- ISBN 0-8247-4714-3. Classic augmented seventh.
- ^ ISBN 978-0-393-33420-3. Retrieved 28 June 2017.
- ^ Benward & Saker (2003), p.92.