A complete view of Acoustical Science & its bearings on music, for musicians & music students.

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" The subject has been treated here at such length in order to show that a right view of the cause of consonance and dissonance leads to rules for relations which previous theories of harmony could not contain. The propositions we have enunciated agree, however, with the practice of the best composers, of those, I mean, who studied vocal music principally, before the great development of instrumental music necessitated the general introduction of tempered intonation, as anyone may easily convince himself by examining those compositions which aimed at producing an impression of perfect harmony. Mozart is certainly the composer who had the surest instinct for the delicacies of his art. Among his vocal compositions the Ave verum corpus is particularly celebrated for its wonderfully pure and smooth harmonies. On examining this little piece as one of the most suitable examples for our purpose we find in its first clause, which has an extremely soft and sweet effect, none but Major chords, and chords of the dominant Seventh. All these Major chords belong to those which we have noted as having the more perfect positions. Position 2 occurs most frequently, and then 8, 10, 1, and 9. It is not till we come to the final modulation of this first clause that we meet with two minor chords, and a major chord in an unfavourable position. It is very striking, by way of comparison, to find that the second clause of the same piece, which is more veiled, longing, and mystical, and laboriously modulates through bolder transitions and harsher dissonances, has many more minor chords, which, as well as the major chords scattered among them, are for the most part brought into unfavourable positions, until the final chord again restores perfect harmony.
" Precisely similar observations may be made on those choral pieces of Palestrina, and of his contemporaries and successors, which have simple harmonic construction without any involved polyphony. In transforming the Eoman Church music, which was Palestrina's task, the principal weight was laid on harmonious effect, in contrast to the harsh and unintelligible polyphony of the older Dutch system, and Palestrina and his school have really solved the problem in the most perfect manner. Here also we find an almost uninterrupted flow of consonant chords, with dominant Sevenths, or dissonant passing notes, charily interspersed. Here also the consonant chords wholly, or almost wholly, consist of those major and minor chords which we have noted as being in the more perfect positions. But in the final cadence of a few clauses, on the contrary, in the midst of more powerful and more frequent