The Architecture of Music

Chord, Scale, and Mode Lessons

The Chord Matrix Art\


The Aranda Method

Do you ever wonder how chords, scales, modes, and intervals speak to each other? Longing for a meaningful, comprehensive, and rational system of explanation? This treatise tackles it all. This book is filled with innovative visual models of pitch, and stimulating insights. Early in the treatise, we learn about the four symbols of circle, X, triangle, and square that represent the root, fifth, third note, and added note, respectively. These accessible, universal symbols let the reader easily identify and learn the various chordal members. This memorable system is independent of language, and has the potential to be adopted into music education anywhere in the world. The four symbols are identical to what you find on a PlayStation video game controller and were in fact inspired by the simple and elegant design of the controller and its universally understood symbology.

At the broadest level, it is a two-part treatise, beginning with chords and ending with scales (and modes). This book elegantly unites the two concepts of chord and scale through the interval formula method and Linear Circle of Fifths (LCOF). Interval formulas, which can represent any chord or scale via a sum-12 string of semitonal intervals, help the reader to understand that chords and scales are really two sides of the same coin. The chief difference between chords and scales is that the former is usually played simultaneously and is smaller (often 3 or 4 notes), while the latter is a background collection you can draw your melodies and chords from, and tends to be larger. But in principle, both have sum-12 interval formulas. In tandem with the interval formulas, the LCOF, which models ascending perfect fifths from left to right, shows how any chord or scale can be represented on the LCOF, delving into features such as symmetry and asymmetry, perfection and imperfection, and considerations of chord substitution and dissonance. Modes play an important role in the book, too, and this book shows throughout how modes can be modeled in terms of shifts within both interval formulas and LCOFs.

One major advantage of the book is its incorporation of real, practical instruments: the guitar and keyboard. The book has ample, systematic charts showing chords and scales in various keys and voicings on the two instruments. Hearkening back to the older, more integrated days of music theory, before the isolation of theory from performance and composition, the book has plenty to stimulate both the practically and the theoretically-minded. The practical reader will find much here in the way of reference charts for their instrument. (The use of instrument charts and other visual representations means that this book does not need to use any music notation at all. This is an advantage, increasing its accessibility to readers who don’t read notation.) However, the book does not shy away from more speculative aspects of theory, and there are no shortages of intellectual challenges in here. In short, you can get out of this book what you choose to, making the experience somewhat modular.

Perhaps the boldest decision of all is challenging the contemporary view of inversion. Instead of the usual root-oriented nomenclature (where, for instance, C E G, E G C, and G C E are all named as C chords), this book uses a bass-oriented nomenclature (where C E G is a C chord, E G C is an E chord, and G C E is a G chord). While this is certainly unusual, the concept of rootedness was a human invention in the first place, after all—not some God-given truth. This bold approach will no doubt be controversial in certain quarters, however, and will hopefully generate discussion. With that said, the book does not discard the concept of roots entirely; they are incorporated nicely into the discussion of chords and, later on, into a discussion of triads and tonality derived from scale degrees in modes and scales.

To students, performers, and non-specialists, I urge you to sit with the book’s concepts, taking your time and challenging yourself to wrap your head around it. To academics, I urge you to keep an open mind and recognize Aranda’s unique vision, and his deviance from tradition as being a positive contribution, rather than some sort of violation of law. Aranda is not concerned with citation of, or commentary on, academic music theory research. You will not find literature reviews in here. Instead, as I see it, this book seeks to build a self-standing, independent system which depends neither on traditional Western classical models, nor math-intensive approaches. This gives it a sort of timelessness. Basically, it takes someone from outside of the establishment to have the unfettered mind to introduce many of the concepts in this book.


By Ethan Lustig, MA Music Theory