The Architecture of Music

Chords

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Fifth-less Chords and Inversions

Although not included in the chord encyclopedia or incorporated with the scales portion of this book, all the fifth-less 3-note chords and inversions have been documented here for your exploration. If you study the interval diagrams of the fifth-less chords you will find that between no two notes in these chords can a P5th be found. Since these chords have no perfect 5th interval anywhere in them they are considered fifth-less. When we combine the chords on the previous page with the chords below, we get all 55 mathematically possible unique 3-note chords as generated by the 3-note chord matrix that can be found in Organizing All The Scales portion of this tutorial, where the 55 existing 3-note chords (and the 11 dyads) are created in a systematic matrix.

Most of the fifth-less chords do not have preexisting names (with the exception of the augmented triad and diminished triad). I simply named these chords by their intervals, consistent with the rest of the book. It is also unclear which chord would be considered the root position and the others the 1st or 2nd inversion. There is no single distinguishing characteristic all these chords share (such as a P5th interval) that would organize them and name the inversions. They can be explored in the book using the generic fretboard and piano diagrams provided.

Fifth-less chords and inversions

Fifth-less Chords and Inversions