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on which music is based, and which constitute the science that furnishes the materials wherewith the artist works. Some of the very many proofs are advanced (Sects. 26, 27, and 100) of the broad discrepancy between any two keys thus apparently connected, and the conventional terms "relative major" and "relative minor" that are in common use to define the connexion are here denounced as misleading and consequently dangerous to the composer. Modulation is an art wholly distinct from that of partwriting, and its study should be quite as separate; let complete mastery be obtained of all that is possible in any one key, and the transfer of this to any or to every other key is an easy process; but to curb one's thoughts within a chosen tonality, as much as within an appointed melodic compass, is more difficult and so wants greater practice.

Contrary to the method of some teachers, it is here recommended to work each Species of Counterpoint successively in two, in three, in four, and perhaps in five parts, before entering on the practice of a next Species. This plan is dictated by observation of the very far greater clearness of each speciality to a student if considered in various complexities of part-writing, than if the whole series of Five Species be practised in two parts, without exemplification of how each may be effected by less or more fulness of harmony.

Further, the student is urged to distinguish between the several Species, and to keep them ever distinct. Truly in composition, invention is free as to the choice of few or many, and of longer or shorter notes, also of concords or discords; but to draw all the good from an exercise which it is capable of yielding, a writer must restrict himself to the purport of each exercise, save where impossible to escape its infraction. The term dissolute is not too strong to describe the laxity of aim which relinquishes a purpose when its accomplishment is difficult, and moral and mental training are both advanced by the increase of perseverance with the increase of obstacles.

For Subjects upon which to construct exercises, the student may use any of those given in the models, or may take from other works wherein available themes are collected, or may compose such theses for his own elaboration; in the two latter alternatives he is advised to take or to make music that keeps to one major or minor key, and to shun the difficulties and delusions of the Ecclesiastical Modes, the treatment of which and its study stand apart from the general rules of music. In the composition of a Subject for contrapuntal exercise, the rules of melody and of cadence must be regarded which are herein enunciated, and the writer's honesty to himself and his purpose will be evinced by his considering each as a Fixed Song and not as a Flexible Song that may be bent under any difficulty of treatment.

An endeavour is made to systematise the appropriation of contrapuntal principles to the phraseology, or idiom, of melodic and harmonic figures now in use. Avowedly this is incomplete, and so is insufficient; but some good may be effected if the indication be received that what is, is an enlargement of what was, a necessary outgrowth and not a revolution, save only in the sense that the world revolves, and that the hemisphere is now under the sun which a while since was in darkness, and that the buds, the flowers, and the fruit it bears are the expansion of the germs that once were hidden but never lifeless.

April, 1879.

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