Augmented second

Augmented second

Inverse	diminished seventh
Name
Other names	-
Abbreviation	A2[1]
Size
Semitones	3
Interval class	3
Just interval	75:64,[2] 125:108, 15:13, 19:16, 19683:16384
Cents
12-Tone equal temperament	300
Just intonation	275, 253, 247.7, 298, 318

Augmented second on C Play^ⓘ.

In classical music from Western culture, an augmented second is an interval that, in 12-tone equal temperament, is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone.^[1][3] For instance, the interval from C to D is a major second, two semitones wide, and the interval from C to D♯ is an augmented second, spanning three semitones.

Usage

Augmented seconds occur in many scales, most importantly the harmonic minor and its various modes. They also occur in the various Gypsy scales (which consist almost entirely of augmented and minor seconds). In harmonic minor scales, the augmented second occurs between the sixth and seventh scale degrees. For example, in the scale of A harmonic minor, the notes F and G♯ form the interval of an augmented second. This distinguishing feature of harmonic minor scales occurs as a consequence of the seventh scale degree having been chromatically raised in order to allow chords in a minor key to follow the same rules of cadence observed in major keys, where the V chord is "dominant" (that is, contains a major triad plus a minor seventh).

Tuning

An augmented second is enharmonically equivalent to a minor third (Play^ⓘ) in 12-tone equal temperament, but this does not hold true in most tunings. In any tuning close to quarter-comma meantone it will be close to the 7:6 ratio of the septimal minor third.

The 75:64 just augmented second arises in the justly tuned C harmonic minor scale between A♭ and B.^[4] Play^ⓘ

References

1. Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0. Specific example of an A2 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 second.
3. Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007. Archaically: redundant or extreme sharp second.
4. Paul, Oscar (1885). A manual of harmony for use in music-schools and seminaries and for self-instruction, p.165. Theodore Baker, trans. G. Schirmer.