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branch of study which bears the name of Harmonic is to be regarded as one of the several divisions or special sciences embraced by the general science that concerns itself with Melody. Among these special sciences Harmonic occupies a primary and fundamental position; its subject matter consists of the fundamental principles—all that relates to the theory of scales and keys; and this once mastered, our knowledge of the science fulfils every just requirement, because it is in such a mastery that its aim consists. In advancing to the profounder speculations which confront us when scales and keys are enlisted in the service of poetry, we pass from the study under consideration to the all-embracing science of music, of which Harmonic is but one part among many. The possession of this greater science constitutes the musician.

The early students of Harmonic contented themselves, as a matter of fact, with being students of Harmonic in the literal sense of the term; for they investigated the enharmonic scale alone, without devoting any consideration to the other genera. This may be inferred from the fact that the tables of scales presented by them are always of enharmonic scales, never in one solitary instance of diatonic or chromatic; and that too, although these very tables in which they 165