Inside Beats

[Richard Moody]

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----- Original Message -----
From: <A440A@AOL.COM>
To: <pianotech@ptg.org>
Sent: Wednesday, January 10, 2001 8:47 AM
Subject: Re: Inside Beats


Virgil is quoted as writing:
"IF A3 has a fundamental frequency of 220hz., then F3 sounding at
176 hz. would produce a pure major 3rd at an exact 5:4 ratio.
True so far, it would then seem that, in order to expand the
F3-A3 3rd by 7bps, F3 should be lowered by 7 beats to 169 hz."


Greetings
.
   In Virgil's example, the   F3, with a fundmental of 176 Hz, has its fifth
partial at 880 Hz, as does the A  with a fundamental of 220
    If you drop the F by 7 Hz to 169, its fifth partial becomes 845 Hz,  so
you create a beat rate of 35 Hz.  However,  Virgil has written that you drop
the F by 7 *BEATS*, not cycles.
By using the word "beats", a requirement is created for something to
compare,
since beats come from two differing frequencies.  Does he mean that the F3
would be dropped until it beats at 7 bps with its original pitch? Vague and
ambiguous writing, I believe.
Ed  Foote

What ever, the 169 is incorrect.
 He should say "to expand the F3-A3 3rd by 7 beats,  lower the  5th partial
of F3  by 7 "beats" (from 880 to 873).

873 divided by 5 then gives a fundamental of 174.6.  This is F3 in ET.
The confusion occurs because he did not give the arithmetic, so the reader
has to do the calculations on their own time to figure out if a mistake
actually occured.   For further clarity, perhaps a reminder that the
coincident partials (which cause the beats) of a  major 3rd are the 5th
partial of the lower note and the 4th partial of the top note, (hence the
5:4 ratio). Still the reader has to know how the frequency of a partial is
gotten, and enough music theory to know what a major 3rd is.      ---ric