Stacked Chords

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In Music, stacked chords are a set of well-defined pitches sounding together consisting of a stack of varying flavors or qualities of the same numerical interval. The most common stacked chords comprise of splitting a 3/2 or perfect fifth into two varying sizes of thirds. Stacked chords must be at least triadic as dyadic can only contain one interval.

5-limit tertiary harmonic triads

Name Divides interval Chord Formula Odd Limit
Major

Major

3/2 5/4 + 6/5 or M3 + m3 5
Minor 3/2 6/5 + 5/4 or m3 + M3 5
Augmented 25/16 5/4 + 5/4 or M3 + M3 25
Diminished

Diminished

25/18 6/5 + 6/5 or m3 + m3 25

7-limit tertiary harmonic triads

Name Divides interval Chord Formula Odd Limit
Septimal Major 3/2 9/7 + 7/6 or 7M3 + 7m3 9
Septimal Minor 3/2 7/6 + 9/7 or 7m3 + 7M3 9
Marvel-Tempered Augmented 14/9 5/4 + 5/4 or M3 + M3 9
Starling-Tempered Diminished 12/7 6/5 + 6/5 or m3 + m3 9

11-limit tertiary harmonic triads

Name Divides interval Chord Formula Odd Limit
Neutral 3/2 11/9 + 11/9 11
7:9:11 11/7 9/7 + 11/9 or SM3 + N3 11