The Architecture of Music

The Circle of Fifths

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Analyzing Chords Using Geometry and The Circle of Fifths

When one analyzes chords using the COF, it is important to realize the min2 chord sounds more dissonant than the dim5. And even though the maj3 is four P5 intervals away from the root note, it is one of the most well known chords used today. This most likely has to do with the underlying frequency ratios of the intervals of the circle of fifths helps to visually describe using geometrical objects that can be found below.

For instance, the maj3 divides the COF into 1/3 and creates a triangle and the aug4 divides it in 1/2, while the min2 divides the circle into 1/12. While we could spend a lot of time dissecting the frequency ratios of the intervals in relation to each other mathematically, it is far simpler just to look at the geometrical objects created by the intervals using the circle of fifths and associate them with their sounds. These diagrams help to visually describe the sounds of the intervals (and chords they’re in) and hopefully will aid you in exploring chords and inversions you might not normally think to use. For instance, the maj2 sounds good, why not explore its negative chord the sus4/2?

geometry and the circle of fifths