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 chord is four harmonic 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 relationship of the intervals the circle of fifths helps to describe using geometrical objects that can be found below. For instance, the maj3 divides the COF into thirds and creates a triangle and the aug4 divides it in half, while the min2 divides the circle into 5/12. 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 hopefully will aid you in exploring chords. |