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by Mildbill on November 23rd, 2007

Mildbill

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Is music infinite or will there come a time when it has all been done?

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  • by James Klein on April 7th, 2008

    James Klein

    Music is infinite in the sense that there are an infinite number of different songs/melodies, each of finite length. Proof: Consider writing a melody for each of the following infinite number of songs with the following words:
    1. "I sing song number 1."
    2. "I sing song number 2."
    3. "I sing song number 3."
    etc. etc.
    Writing the melody for each of the above songs is mechanically done as follows: Choose any 4 notes for the first 4 words (keep it the same for all songs), but then change the next note(s) according to the digits encountered by mapping, say, 0 to A (440 hz.), 1 to A#, 2 to B, 3 to C, etc. The tune for each song is unique because each integer is unique. The number of songs is countably infinite because they are obviously in one-to-one correspondence with the integers. QED. (Admittedly, none of these tunes is great music - but then neither is all intentional music.) -- James D. Klein, Walla Walla University

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