The Architecture of Music


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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 that 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. This phenomenon is also known as interval inversion. If you study the linear circle of fifths diagrams on top of the interval diagrams (explained in the next section) of any two negative chords you will find they too mirror about the mirror line and are negative versions of each other. What this essentially means is these chords are opposites of each other and one chord describes ascending around the circle of fifths while the other chord descends in the exact opposite manner from the bass note. 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 note add variations of chords as well.

What is interesting about negative chords is that each root position chord and its inversions are 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 simply know the two root position chords that have a negative chord relationship. For instance, since we know the min3 and maj3 hold a negative chord relationship, we know a negative maj3 (-maj3) 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; its formula inverse would be itself. Also note how the inversions of the sus4 are negative chords with each other. This same phenomenon occurs with symmetrical scales and their modes, as will be seen later.

Negative Chords and Inversions

Negative Chords and Inversions