sexual note in the scales of G major and E minor are the two A's; in D major and B minor, the two E's; in A major and F# minor, the two B's; in E major and C# minor, the two F's; in B major and G# minor, the two C's; and in F# major and D# minor, the two G's. These two last scales being the beginning of a second cycle of twelve scales when the scales are written half in flats and half in sharps, as we have done them in this case. Turning to the other half of our circle, those which we have, and which usually in music books are, written in flats, in F major and D minor the sexual notes are the two G's; in B? and G, the two C's, in E? and C, the two F's; in A? and F, the two B's; in D? and B?, the two E's; and in G? and E?, the two A's.
In a musical air or harmony, i.e., when once a key has been instituted in the ear, all the various notes and chords seem animated and imbued with tendency and motion; and the center of attraction and repose is the tonic, i.e., the key-note or key-chord. The moving notes have certain leanings or attractions to other notes. These leanings are from two causes, local proximity and native affinity. The attraction of native affinity arises from the birth and kindred of the notes as seen in the six-octave genesis, and pertains to their harmonic combinations. The attraction of local proximity arises from the way the notes are marshalled compactly in the octave scale which appears at the head of the genesis, and pertains to their melodic succession. In this last scale the proximities are diverse; the 53 commas of the octave being so divided as to give larger and lesser distances between the notes; and of course the attraction of proximity is strongest between the nearest; a note will prefer to move 5 commas rather than 8 or 9 commas to find rest. Thus far PROXIMITY.
By affinity the notes group in chords. The tonic is the center chord, the key of the harmony; the dominant is the fifth above it and the subdominant the fifth below it, and these two are balanced on the center chord as the scales on a balance beam. The dominant chord is vigorous and active, tending to soar; the subdominant is solemn, soft, and grave, tending to sink; the tonic is melodious and restful, and in it the harmony finds equilibrium. This far AFFINITY. [Scientific Basis and Build of Music, page 91]
See Also
factoring
Ramsay - Rationale of the Limit of Musical Mathematical Primes