Diminished triad

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Diminished triad

A diminished triad is a triad comprising a root, minor third, and diminished fifth.

In just intonation

In the 7-limit:

• 5:6:7 is an upper structure of 4:5:6:7, the harmonic seventh chord.
• 30:35:42 (1/1 - 7/6 - 7/5) is a subharmonic chord.

In the 5-limit:

• 45:54:64 is found on vii^o (45⁄32) in Ptolemy's intense diatonic scale (Zarlino), perhaps the most common 5-limit diatonic.
• 25:30:36 is obtained by stacking two 6/5 minor thirds, and found on iii^o (5⁄4) and vi^o (5⁄3) in the duodene.
• 135:160:192 is found on ii^o (9⁄8) and ♯vi^o (45⁄32) in the duodene.

In the 3-limit:

• 729:864:1024 is found on the vii^o of the Pythagorean diatonic scale.

Todo: expand, add examples needs information about temperaments