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

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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
Message 1 of 1 , Oct 10, 2006
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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