By Gobel R., Hill P., Liebert W. (eds.)
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Extra resources for Abelian Group Theory and Related Topics
Whether there will then be guarter tones, eighth, third, or (as Busonir thinks) sixth tones, or whether we will move directly to a tJ-tone scalethat Dr. Robert Neumann has calculated,2we cannot foretell. However that may be, attempts to compose in quarter or third tones, as are being undertaken here and there, seem senseless,as long as there are too few instruments available that can play them. Probably, whenever the ear and imagination * Perhapsthat also explainswhy there were church modes:The effectof a fundamentaltone was felt, but sinceno one knew which tone it was,all of them were tried, And the accidentals areperhapsaccidents in the modechosen,but not in the natural, the basicone.
In the overtone seriesr*which is one of the most remarkable properties of the tone, there appear after some strongersounding overtones a number of weaker-sounding ones. Without a doubt the former are more familiar to the ear, while the latter, hardly perceptible, are rather strange. In other words: the overtones closer to the fundamental seem to contribute more or more perceptibly to the total phenomenon of the tone tone acceptedas euphonious, suitable for art - while the more distant seem to contribute less or lessperceptibly.
The value of such a method of composition cannot be overlooked, even by those who do not believe it is indispensableto all composition whatsoever. Thus, for example, not every biography has to begin with the birth of the hero, or indeed farther back with his ancestors,nor end with his death. Such completenessis not indispensableand may be forthwith discardedif one has some other aim, say, to present a certain characteristic period in the life of the hero. It is likewise doubtful whether the aggregate of eventsin a pieceof music must inevitably refer to the fundamentalpostulate,to the fundamental chord, just because- as I have said - such reference assures good results through formal completenessand agreeswith the simplest attributes of the material.
Abelian Group Theory and Related Topics by Gobel R., Hill P., Liebert W. (eds.)