'Perhaps mistakenly, the ancient Greeks attributed to the association of music and numbers a predominant place in the philosophy of of the cosmos. Perhaps equally mistakenly, some composers of the Forties and Fifties tried to build music entirely by numbers. But regardless of the rights and wrongs of such beliefs, there are incontrovertible mathematical facts which must be outlined, however briefly.
Other numerical data less closely associated with musical reality, but forming a basis for modern composition, are also worth a mention, even though they only demonstrate man`s subconcious awareness that there is beauty in numbers, and that they in turn can make beauty of out chaos.'
Introduction to chapter 6; 'Numbers' of The New Music: The Avant Garde since 1945 by Reginald Smith Brindle.
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