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. . . It is nonsense to believe
that the idea of the
“imitation of nature” according to scientific laws was
consciously manifested
by the first harmonists. Their use of perfect triads was not dictated by
mathematical and physical considerations, but was imposed by
practical
laws of musical composition. How else can we explain the use of minor
and diminished chords, which occupy four degrees of the scale (when major
chords occupy only three) and which do not constitute an acoustically exact
reproduction of the structure of the world of sound? It is a matter of
skill, of practical convenience, which ignores scientific considerations
and obeys only the laws of composition.
Furthermore, tonal harmony, from its beginnings, is not satisfied with perfect triads alone. Other aggregations were inherited from the modal system by the tonal system. One of them is at least as important as the perfect triad: the seventh chord—the one which consists of a minor third superimposed on a major triad—is also a perfect imitation of nature, since a certain seventh appears shortly after the third in the overtone series; but, here again, this is only a single chord of the scale (V), while harmonic usage reproduces this type on all degrees of the scale. The use of seventh chords is no more dictated by scientific considerations than the use of triads—rather, it is the product of compositional necessity.
René Leibowitz
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