Diminished third

diminished third
Inverse	augmented sixth
Name
Other names	-
Abbreviation	d3
Size
Semitones	2
Interval class	2
Just interval	144:125, 8:7
Cents
12-Tone equal temperament	200
24-Tone equal temperament	200
Just intonation	245

In music, a diminished third (Play^ⓘ) is the interval produced by flattening a minor third by a chromatic semitone. In equal temperament it is enharmonic with the major second, both having a value of 200 cents. However in meantone tunings with fifths flatter than the 700 cents of equal temperament, the diminished third is wider than the major second. In 19 equal temperament it is in fact enharmonically equivalent to an augmented second, both having a value of 262.6 cents. In 31 equal temperament it has a more typical value of 232.3 cents. In a twelve-note keyboard tuned in a meantone tuning from E♭ to G♯, the dimininished third appears between C♯ and E♭, and again between G♯ and B♭.

In septimal meantone temperament the diminished third is considered to approximate the interval of a septimal major second (play^ⓘ), with ratio 8/7, and in any meantone tuning in the vicinity of quarter-comma meantone, such as 31-equal temperament, it will come close to that value; for instance in 31-equal temperament the diminished third is a cent sharp of 8/7.

The complementary interval to the diminished third is the augmented sixth, and the numerous chords of common practice music described as augmented sixth chords thereby contain the diminished third as well. For example, a German sixth chord E♭-G-B♭-C♯-E♭' exhibits a diminished third between C♯ and E♭' which complements the augmented sixth between E♭ and C♯.

See also