The Architecture of Music


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Numeric Scale Formulas

numeric scale formulas

Just like chords, scales can be depicted using interval diagrams (to visualize a scale’s formula) and the linear circle of fifths (to visualize the P5 intervals of the notes of a scale); in both cases, they work in exactly the same way as with chords. Just like chords, scale formulas can be represented using the number of semitones between the notes of a scale. As can be seen below, the Suspended Pentatonic = 2 3 2 3 2.

Using numbers to describe scale formulas is useful, because scales—just like chord inversions and negative chords—also have inversions (called modes) and negative counterparts (called inverses); using numbers to describe the formulas helps to illustrate these properties. And the sum of all the numbers of a scale’s formula will always add to twelve. This is true of chord formulas as well. Because of the simplicity of using numbers to describe the semitones between the notes in chord and scale formulas, this book uses numbers to describe the formulas of chords and scales instead of using binary or the whole-step/half-step method. There are other, more complex ways to describe scale formulas as well, but this book chooses simplicity over complexity.