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Augmented second

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Inverse
  
diminished seventh

Semitones
  
3

Equal temperament
  
300

Abbreviation
  
A2

Interval class
  
3

Augmented second

Just interval
  
75:64 or 125:108 or 19:16

In classical music from Western culture, an augmented second is an interval that is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone. 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.

Augmented seconds occur in many scales, most important 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 equal temperament, but is not the same interval in other meantone tunings. In any tuning close to quarter-comma meantone it will be close to the 7:6 ratio of the septimal minor third. Hence the distinction is not, as often thought and even taught, a purely formal and contextual one, but reflects the tuning practice of much of the common practice period.

The 75:64 just augmented second arises in the C harmonic minor scale between A and B.  Play 

References

Augmented second Wikipedia