The Architecture of Music

Chords

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Seeing Inversions as Unique Chords

Traditional theory argues that since the same notes are used (previous page), inversions are not unique chords. However, if we look at the maj3 and its inversions side by side and start all the chords from the same bass note, we can see inversions are indeed unique chords as each of the chords below contain different notes. In the E maj3/1 the root note is C and in the E maj3/2 the root note is A. Traditional music theory would thus name these inversions by their root note so the E maj3/1 would be C maj3/1, and the E maj3/2 would be A maj3/2. However, these chords are not C maj3 or A maj3, they are inversions of the maj3. On the musical staff, the notes of the chords below would still show E as the bass note and then annotate them as inversions using figured bass, a more complex and less intuitive inversion nomenclature than the altered popular slash notation used in this book to indicate the bass note. The interval diagrams clearly indicate the root, P5th, and 3rd notes using geometric identification and the linear circle of fifths diagrams above the interval diagrams indicates the bass note in relation to the other notes. Interval diagrams are in a sense an expanded musical staff and work similarly to the musical staff, so the chords below are show how differently the chords would look on the staff. And most importantly, inversions sound different. Some chords, like the maj3 and its inversions, the sound difference is subtle and the root note and maj3 can easily be heard. But the change, however subtle, is audible. And in other chords, the sound difference is much more noticeable.

Chord Inversions

Seeing inversions as unique chords and naming them in relation to the bass note was absolutely necessary to be able to do many things, such as creating a chord encyclopedia that included inversions, as well as creating chord lists including the inversions for every note in a scale being used as the bass note in a chord. The 3-note chord matrix that can be found in the appendix generates inversions as unique chords and their semitone and interval name formulas show them as unique chords as well. Though this naming methodology differs from traditional music theory, just remember in traditional theory the root note is used to name inversions and can still be used to name the inversions. However, I would not have been able to accomplish many of the things I have done in this book—such as simple two-page chord reference charts for all the root position chords and inversions—had I used traditional music theory’s inversion nomenclature based on the root note. The chord encyclopedia could not exist if the inversions were based on the root note because all the 4th-note add variations would also be based on the root note and would be different for the root position, 1st, and 2nd inversions. And most importantly, all the integration of chords, scales, and modes that can be found in this book would not be possible if inversions were named based on the root note and not the bass note. This small change to traditional theory makes all of these things possible and the root note can still be identified and used to name the inversions if so desired.