Augmented third

In classical music from Western culture, an augmented third (Play^ⓘ) is an interval of five semitones. It may be produced by widening a major third by a chromatic semitone.^[1][3] For instance, the interval from C to E is a major third, four semitones wide, and both the intervals from C♭ to E, and from C to E♯ are augmented thirds, spanning five semitones. Being augmented, it is considered a dissonant interval.^[4]

Augmented third

Inverse	diminished sixth
Name
Other names	-
Abbreviation	A3[1]
Size
Semitones	5
Interval class	5
Just interval	125:96,[2] 21:16, 64:49
Cents
12-Tone equal temperament	500
24-Tone equal temperament	500
Just intonation	457

Augmented third on C Play^ⓘ.

Its inversion is the diminished sixth, and its enharmonic equivalent is the perfect fourth.

The just augmented third, E♯, is 456.99 cents or 125:96. Play^ⓘ The Pythagorean augmented third, E♯+++, is 521.51 cents or 177147:131072, eleven just perfect fifths. Play^ⓘ

References

1. Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0.
2. Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. ISBN 0-8247-4714-3. Classic augmented third.
3. Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007. Archaically: superfluous third.
4. Benward & Saker (2003), p.92.