The Architecture of Music


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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, and their interval diagrams and interval name formulas are each unique. 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 maj3 inversions. Interval diagrams are in a sense an expanded musical staff and work similarly to the musical staff, so the chords below show how differently the chords would look on the staff starting from the same bass note. On the musical staff, the chords below would still show E as the bass note, would look similar to their interval diagrams, and be annotated as inversions using figured bass, a more complex and less intuitive inversion nomenclature than the altered popular slash notation used in this book. 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 inversion sound difference is much more noticeable and root note less discernible from the bass note, especially when inversions are thought of as negative chords.

Chord Inversions

Seeing inversions as unique chords and naming them in relation to the bass note was absolutely necessary to be able to do basically everything that can be found in this book. The 3-note chord matrix that can be found in Appendix A and all the chord matrices found in this book are based on the interval diagrams of chords starting from the bass note. The simple, two-page chord reference charts for all the root position chords, inversions, and add variations for every single note could not exist. 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. All the integration of chords, scales, and modes that can be found in the scale encyclopedia would not be possible. And most importantly, the fundamental interval diagram itself, which is a universal depiction of what a chord would look like on an expanded staff, would not work. This small change to traditional theory makes all these things possible and the root note can still be identified and be used to name the inversions if so desired. Instead of working backwards to figure out all the notes, we now only need to identify one, the root note, which traditional theory already does and can also be easily done using the diagrams in this book. All chord interval diagrams clearly identify the root, P5th, and 3rd notes using geometric identification and the unique linear circle of fifths diagrams of chords can also easily be used to identify the root note even without geometric identification.