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From: tpermutt@eng.umd.edu (Thomas Permutt)
Newsgroups: comp.music
Subject: Re: Musical Frequencies
Message-ID: <1990Dec13.182547.512@eng.umd.edu>
Date: 13 Dec 90 18:25:47 GMT
References: <561@ub.d.umn.edu>
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In article <561@ub.d.umn.edu> jbovitz@ub.d.umn.edu (Jeffrey Bovitz) writes:
>A bit ago, someone (from Georgia Tech) wanted a list of the frequencies
>for musical notes.  My brother has a solution.   Chris...?
>
>Thanx Jeff.  The formula is based upon a Middle "A" of 440 Hz.  
>The formula goes:
>
>  
>      440 * ((2)^(1/12)) ^ h
>       
>       (i.e.  440 Hz * (the twelfth root of 2) raised to the h power)
>       where h is the number of half-steps above or below Middle A.
>
>For example, Middle C is 8 half-steps below Middle A, so h=-8, and
>the freq of Middle C is 261.6 Hz.  Remember that there are 12 half-
>steps in an octave, and an octave is defined as doubling of the
>frequency.  BTW, this formula works great on a spreasheet.
>
>Hope this helps.
>
>Chris Bovitz   moonunit@meteor.wisc.edu

This is quite correct, for the "standard" equal-tempered scale.  But that
represents a compromise arising largely from the fact that pipe organs, for
example, take a long time to tune, and need to be played in lots of        
different keys.  If you are going to play in, say, C major, why not
try
C = 261.6                    
G = C * 3/2
F = C * 4/3
E = C * 5/4
D = C * 9/8
B = G * 5/4
I think you will hear a much nicer sound.  And, since your question
suggests that the frequencies are under software control, you can always
reprogram for different keys.