The Architecture of Music


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Chord Inversions

Study the diagram below. Chord inversions are the process by which a chord’s formula and interval diagram stair-steps to create new chords called inversions. An alteration of popular slash notation has been used here to name inversions. Popular slash notation typically indicates a chord above a bass note, such as A maj3/E, with E being the bass note. However, using popular slash notation means the notes have to change for each chord as in the A maj3/E and C maj3/E. Therefore, a universal inversion nomenclature had to be created and used that was simple, intuitive, and legible. Since interval diagrams are generic representations of chords and do not have notes, an alteration of popular slash notation has been used in this book to indicate inversions. /1 has been used to indicate a 1st inversion, where the 3rd note is in the bass position as indicated by the triangle. And /2 has been used to indicate a 2nd inversion, where the chordal P5th is in the bass position as indicated by the X. In inversions, a chord’s semitone formula shifts one digit to the left to create the semitone formulas of the inversions. And as can be seen below, the interval name formulas for each inversion are unique.

4 3 5 = maj3 = M3 P5
3 5 4 = maj3/1 = m3 m6
5 4 3 = maj3/2 = P4 M6

Chord Inversions


Straying From Tradition

Traditional music theory names inversions by their root note and not their bass note. In the example above, the G# maj3/1 would be E maj3/1 in traditional theory. While E is the root note of the G# maj3/1 as indicated by the circle, and the G# maj3/1 is the 1st inversion of E maj3, the generic maj3/1 = 3 5 4 and m3 m6 chord formulas start from the bass note, G#. Since the bass note is typically used to name chords, and since chord formulas and interval diagrams always start from the bass note, it is far simpler and makes more sense to name inversions by their bass note and not their root note. In traditional music theory, if someone said “E maj3 1st inversion” you would have to work backwards to figure out the bass note. You would first have to know the notes of E maj3 and every note for every maj3 chord (and every chord for that matter), then you’d have to know which note is the P5th and which note is the 3rd note to put in the bass. By naming inversions by their bass note, you only have to remember the intervals of the inversions and start from any bass note and move forwards higher in pitch. This is far simpler than having to memorize every note in every chord and understanding the intervals of them.