Ryan said:

> "Higher" frequency, lower pitch.  Just like when you pluck a 
> string, then shorten the string by a half, the note will sound 
> an octave higher.  Or, so said Pythagoras.  And just the same, 
> cutting the frequency in half raises the pitch an octave.  So, 
> 880 Hz would be the A above middle C, and 440 Hz would be the 
> A an octave higher than the 880 A.

Whoa!  Sorry to be pedantic here, but we're tripping over 
definitions.  "Pitch" is not identical to "frequency", but is 
certainly not the inverse!  :-)  Pitch is the quantity used by 
musicians to describe the ear's *perception* of a higher or lower 
frequency.  With a simple sine or square wave (e.g.), the pitch 
and frequency correspond very nicely, that is, twice the frequency 
is one octave *higher* in pitch.  But that's half the period, of 
course, which is what happens when you shorten a vibrating string. :-)

And since middle C is approximately 256 Hz, 440 Hz is the definition 
of A above middle C, and is in fact an international standard.

Just trying to keep things straight (and looking forward to going 
home and compiling this code on my IIci to test it out!)

-- 
| Greg Dunn                        | "Talking about music is like   |
| GregDunn@aol.com                 | dancing about architecture."   |
| gregdunn@indy.net                |                 Frank Zappa    |
| http://members.aol.com/gregdunn/ |    (quoting Thelonious Monk)   |