Music, and mathematics have nothing more to do with it. Already the Law of Position has guided the genesis upward in the major; and while mathematical primes were generating the chords one after another in precisely the same way and form, like peas in a pod, the Law of Position was arranging them one over the other, and so appointing them in their relative position each its own peculiar musical effect bright and brighter. And when the major had been thus evolved and arranged by ratios and position, another law, the Law of Duality, gave the mathematical operation its downward direction in the minor; and while the primes which measured the upward fifths of the major also measure the downward fifths of the minor, the Law of Position is placing them in their relative position, and appointing each its own peculiar effect grave and graver.
     The peculiar effects are exhibited when the chord-scale is next set forth. We have seen that there are six chords evolved in the genesis upward and downward, 3 in the major form and 3 in the minor. In the fifths of the minor the semitone is always in the lower third, occurring between the second and third in the subdominant and tonic, and between the first and second in the dominant chord; whereas in the major it is always in the upper third, between the fourth and fifth in the subdominant, and between the third and fourth in the tonic and dominant chords. While the thirds which the fifths contain are thus so varied, the fifths themselves have always one magnitude, whether major or minor.
     Chords in a harmony are not at liberty to succeed each other in the way that single notes in a melody may. The notes in a melody may succeed in seconds, or they may succeed in larger intervals, any interval in the octave, even sometimes very effectively there may be a leap or fall of a whole octave. Chords cannot follow each other in this free way; they are under law, and must succeed accordingly. Their law is that they must be linked together either by having something in common in their elements, or have small intervals, semitonic progressions, between them. The former way, by notes in common, is the most usual way in diatonic succession of chords, the latter way, by semitonic progression, is a chief feature and charm in chromatic succession; but both in diatonic and chromatic progression of chords in harmony, notes in common and semitonic progression are usually found together. [Scientific Basis and Build of Music, page 68]