Augmented triad

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Augmented triad

The augmented triad is a triad traditionally described as comprising a root, major third, and augmented fifth. In contemporary 12edo music, the augmented fifth is enharmonically equivalent to a minor sixth, approximating 8/5, with the major third approximating 5/4, so it is a stack of two ~5/4's making up ~8/5, tempering out 128/125. In other words, three identical ~5/4's close at the octave, which implies it is a 5-odd-limit essentially tempered chord of the augmented temperament, the temperament named after this chord.

• (Augmented) 1 – 5/4 – 8/5, with steps 5/4, 5/4, 5/4.

In meantone

Before the ubiquity of 12edo, an augmented triad did not imply an equal tuning of all three thirds (technically, two major thirds and a diminished fourth). It can be viewed as a 9-odd-limit essentially tempered chord of marvel. See marvel chords. This is still compatible with 12edo and is perhaps as authentic as the 5-odd-limit interpretation above.

In just intonation

In the 5-limit:

• 16:20:25 is found on the ♭II+ (16⁄15), ♭III+ (6⁄5) ♭VI+ (8⁄5), and ♭VII+ (9⁄5) of the duodene.

In the 3-limit:

• 4096:5184:6561 may be considered a 3-limit approximation of 16:20:25.