The Architecture of Music

Chords

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Chord Inversions

Chord Inversions Interval Diagram

Study the diagram above. 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 to indicate an alternate bassline and name the inversions. Popular slash notation typically uses notes to indicate an inversion and an alternate bassline such as the A maj3/E with E being an alternate bassline. However, using popular slash notation means the notes have to change for each chord so a universal inversion naming nomenclature had to be found and used that was both simple, intuitive, and legible at a small scale. Since interval diagrams are generic representations of chords and do not have notes, popular slash notation was altered and has been used in the book to indicate inversions. /1 has been used to indicate a 1st inversion where the third note is in the bass position as indicated by the triangle. And /2 has been used to indicate a 2nd inversion where the 5th 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 as well.

4 3 5 = maj3
3 5 4 = maj3/1
5 4 3 = maj3/2

maj3 = M3 P5
maj3/1 = m3 m6
maj3/2 = P4 M6

Traditional music theory names inversions by their root note and not their bass note. In the example above, the G# maj3/1 would be named the 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 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 major 1st inversion” you would have to work backwards to figure out the bass note. Traditional theory argues that since the same notes are used inversions are not unique chords. However, even though the chords above contain the exact same notes, E G# B, the semitone formulas have to change for the inversions to contain the same notes depending on which note is in the bass position. Hence the semitone and interval name formulas for the chords above are each different and unique.