By Ernst Levy, Siegmund Levarie
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Extra info for A theory of harmony
Page 1 1 Tone Structure The Oneness was considered by the Pythagoreans to be the beginning of everything. They say that out of the Oneness sprang the Indefinite Twoness. The first, they say, is cause and motivation, the latter, effect or matter. Out of the Oneness and Twoness sprang the numbers. Diogenes Laërtius Page 3 The raw material of theories are facts. The raw material of musical theory is music. '' It is something that, first and last, happens in the soul. To an inner, spiritual something corresponds an outer, physical something: tone.
Beside theoretical considerations, recent developments in the aesthetics and techniques of composition seem to suggest that there exists a limit beyond which the norms are no more recognizable. " In those days, logically enough, the triad was ostracized. Soon, however, the feeling began to prevail that one had gone too far, for it developed that artificial norms threatened to drive music into becoming a secret language evolved from a code system. Subsequently the rich discoveries that had been made in those years of frantic experimenting were incorporated into styles of writing that did not draw their principles from a mere feeling of revolt against inherent natural norms.
A tone, however, is a being, an individual. Relation between tones is fixed, characteristic. Now it would not at all be true to assume that the discovery of a tone is a gradual process leading from becoming to being, from glissando to fixed pitch. On the contrary, everywhere we first perceive and deal with separate units, individuals, discrete quantities. Mathematically speaking, whole numbers were discoveredor inventedlong before the "infinitely small" began to be apprehended. Thus it is but natural that we should choose the series of digits for our guiding principle.