When one analyzes 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 steps away from the bass note, it is one of the most beloved chords used today. This most likely has to do with the underlying relationship of notes the COF helps to describe.
For instance, the maj3 divides the COF into thirds and the dim5 divides it in half, while the min2/maj7 divides the circle into twelfths. While we could spend a lot of time dissecting the frequencies of notes in relation to each other, it is simpler just to look at the geometries made by the COF and associate them with sounds.