Newsgroups: comp.speech
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From: ted@nmsu.edu (Ted Dunning)
Subject: Re: Fundamental Frequencies of the Musical Notes
In-Reply-To: rsl11@kuhub.cc.ukans.edu's message of 1 Jan 93 10:54:01 CST
Message-ID: <TED.93Jan1134723@lole.nmsu.edu>
Sender: usenet@nmsu.edu
Reply-To: ted@nmsu.edu
Organization: Computing Research Lab
References: <1993Jan1.105401.46023@kuhub.cc.ukans.edu>
Date: Fri, 1 Jan 1993 20:47:23 GMT
Lines: 59


In article <1993Jan1.105401.46023@kuhub.cc.ukans.edu> rsl11@kuhub.cc.ukans.edu writes:

	   I would like to know what the fundamental frequencies of the musica
   notes are if someone is aware of them. Tha is what frequencies do they
   correspond to the notes

   do, re, mi, fa, sol, la, si, do.
   or
   C, D, E, F, G, A, B, C


the simplest approximation is that middle c has a frequency of 256
hertz and each half step results in change in frequency by a factor of
2^(1/12). 

thus, you can compute a table using bc

> bc -l
f = 256
x = e(l(2)/12)
f
for (i=0;i<12;i++) {
 f *= x;
 f;
}

256.00000000000000000000 < c
271.22255215597958772480 < c#
287.35028436719948324056 < d
304.43702144069659306947 < d#
322.53978877308753016598 < e
341.71900266752879737759 < f
362.03867196751233246895 < f#
383.56661168043046366260 < g
406.37466930385906550010 < g#
430.53896460990184598863 < a
456.14014368785372397602 < a#
483.26364809302707022125 < b
511.99999999999999993134 < c

(i added the labels and separated out the output).

if you note, this scale is pretty close to well tempered, but the
intervals a little bit off so that the fifth:

383.56661168043046366260/256 = 1.49830707687668149868

instead of 1.5 and the fourth

341.71900266752879737759/256 = 1.33483985417003436475

instead of 1.3333...

these discrepancies can make chords sound a little off, but on the
other hand, all the chords can be transposed without changing how they
sound. 

have fun with this.
