Although every scale can be diagrammed using intervals and named using the numeric method, this does little to describe what a scale will sound like. Much like chords, the COF is the best way to dissect the overall sound of a scale. As can be seen above, as we progress through scales as we progressed through chords using the COF, the six perfect/symmetrical scales are generated.
These scales are very common and are used often in music today (especially the Dorian). With 2,048 possible formulas and only six being both perfect and symmetrical, we can say these six are rare and important in music. And because of this, they can be used as the beginning of a larger diagram that organizes all chords and scales harmonically as will be seen later.