The Art of Music, which is music on its spiritual and inspirational side, has been carried to a wonderful perfection of development; while the Science of Music, which is music on its intellectual and logical side, has been left far behind. Works on the Science of Music have been a failure, not because music has not a scientific basis, but, and for the most part, because Mathematicians have dealt only with the law of Ratios, ignorant of other laws which play an important part in music's scientific basis and build. They have carried the law of ratios beyond its legitimate sphere, and so their conclusions do not represent the method of Nature truthfully.
Nature's own art, not man's device, enables us to realize and represent all the harmonic progressions that belong to music. It has been nature's self to the practical and inspired musician. By the division of the octave into twelve semitones, he is emancipated from the restrictions and jargon which arise from misapplied mathematics. The mathematicians say that such and such things are wrong; the great masters in music inspirationally do these very things.