lastly it is altered again and becomes, by the power of 3 once more, F#,#, and serves in four keys. But this carries us beyond the horizon of our musical world of twelve keys; for in B#, the top of the tonic E, we have reached our twelfth fifth, and it here coalesces with C of the seventh octave, and closes the circle. This is the way that all notes become alternately altered, either by commas and sharps in the upward genesis of scales, or by commas and flats in the downward genesis, by the alternate powers of 3 and 5. In the upward genesis in this illustration, notes by the power of 5 serve in three keys, and those by the power of 3 serve in four keys. In the minors it is just the inverse on this by the Law of Duality. But no note serves for more than either three or four keys, as the case may be.

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DEFINITIONS.
Subdominant - The fifth below the tonic in a key.
Tonic - The middle fifth in a key.
Dominant - The fifth above the tonic in a key.
Affinity - The genetic relation of notes.
Position - The relative place of chords in a key.
Partials - Harmonics, so called because they are the parts of a sound.
Modulation - Change of key.
Tetrachord - From tetra, four, and chord. It does not mean a four-note chord, but four notes such as our C, D, E, F.