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iv It is from this point of view that the present volume has been written. The rules herein given, though in no degree inconsistent with the theoretical system expounded, are founded, not upon that, nor on any other abstract system, but upon the actual practice of the great masters; so that even those musicians who may differ most widely from the author's theoretical views may still be disposed to admit the force of practical rules supported by the authority of Bach, Beethoven, or Schumann.

The system of theory propounded in the present volume is founded upon the dictum of Helmholtz, quoted in Chapter II. of this work (§ 42), that "the system of Scales, Modes, and Harmonic Tissues does not rest solely upon unalterable natural laws, but is at least partly also the result of sesthetical principles, which have already changed, and will still further change with the progressive development of humanity." While, therefore, the author follows Day and Ouseley in taking the harmonic series as the basis of his calculations, he claims the right to make his own selection, on aesthetic grounds, from these harmonics, and to use only such of them as appear needful to explain the practice of the great masters. Day's derivation of the chords in a key from the tonic, dominant, and supertonic is adhered to, but in other respects his system is extensively modified, its purely physical basis being entirely abandoned. It will be seen in Chapter II. (§ 44) that by rejecting altogether the eleventh and thirteenth notes of the harmonic series, and taking in their place other notes produced among the secondary harmonics, the chief objection made by the opponents of all scientific derivation of harmony—that two of the most important notes of the scale, the fourth and the sixth, are much out of tune—has been fully met. In the vexed question of the minor tonic chord, Helmholtz is followed to a considerable extent; but Ouseley's explanation of the harmonic origin of the minor third is adopted.

Truth is many sided; and no writer on harmony is justified in saying that his views are the only correct ones, and that all others are wrong. No such claim is made for the system herein set forth; but it is hoped that it will at least be found to be intelligible, perfectly consistent with itself, and sufficiently comprehensive to explain the progressions of the advanced modern school of composers.

It has been thought desirable to separate as far as possible the practical from the theoretical portions of this work. The latter are therefore printed in smaller type; and it will be found