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distribution of primes between 2^N and 2^(N+1)

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  • danterosati
    Hi- I am a musician studying properties of the overtone, or harmonic series, and the question of the appearance of prime numbered partials in each octave of
    Message 1 of 1 , Oct 10, 2006
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      Hi-

      I am a musician studying properties of the overtone, or harmonic
      series, and the question of the appearance of prime numbered partials
      in each octave of the series is of interest. So I was wondering if
      anyone could give me any pointers to information on the question of
      prime distribution between successive powers of 2, which represent the
      octaves in the overtone series.

      Another thing we talk about in tuning theory is "prime limit" which is
      the largest prime factor in a given ratio. For example, the musical
      ratio that represents the major third is 5/4 and we call this a
      5-limit interval, while an interval like 9/8 would be a 3-limit
      interval. I could see this as a question in number theory regarding
      the pattern made by prime distribution plus the highest prime factor
      of each composite number. Would there be any information about this as
      well?

      looking forward to any replies

      Dante Rosati
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