Augmented third

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

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.

${ \override Score.TimeSignature #'stencil = ##f \relative c' { \time 4/4 \set Score.tempoHideNote = ##t \tempo 1 = 20 <ces e>1 <c? eis> } }$

Being augmented, it is considered a dissonant interval.^[4]

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

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[B&S-1] 1 2 Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0.

[Haluska-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.

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References