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