The Architecture of Music

Chords

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Negative Chords

All the root position chords and their inversions have been diagrammed below. If you study the chord inversions you will notice every chord’s formula mirrors or is a negative chord with another chord. For instance, the maj3 = 4 3 5 ≠ 5 3 4 = min3/2. All chords and inversions have a negative chord whose formula mirrors theirs. If you study the diagrams on top of the interval diagrams [discussed in the next chapter] of any two negative chords you will notice they too mirror or are negative versions of each other. What this essentially means is these chords are polar opposites of each other and one describes ascending around the circle of fifths while the other descends in the exact opposite manner. If you find a chord that sounds good, explore its negative chord as it most likely will sound good as well. This is true of 4th-tone add variations of chords as well.

What is interesting about negative chords is a root position chord and its inversions are all negative chords with just one other root position chord and its inversions. The min7 and its inversions are negative chords with the maj6 and its inversions. The same is true for the maj7 and min6, maj3 and min3, and aug4 and min2. All root position chords are negative chords with 2nd inversions, and all 1st inversions are negative chords with other 1st inversions. This means we can quickly and easily identify a negative chord if we know the two root chords that have a negative chord relationship. For instance, since we know the min3 and maj3 hold a negative chord relationship, we know the maj3’s negative chord is the min3/2. And we also know the maj3/1 and the min3/1 are negative chords and so on. The only exception to negative chords are symmetrical chords. If you study the sus4’s chord formula below you will see it is symmetrical (5 2 5). This is why it lies on the mirror line and its interval diagram has been modified to show its symmetry. The sus4 chord has no negative chord or its formula inverse would be itself. Also note how the inversions of the sus4 are negative chords with each other.

Root Chord Inversions Diagram

Root Chord Inversions Diagram