Alan and David on F3/A4

[Alan Barnard]

Glad to help, but please post this slightly corrected version. I got out
the ol' Coleman Beat Locator cards and found a couple of corrections to
make:
 
When you tune with a fork, electronic or otherwise, you are tuning A4 to
the fundamental of that fork, i.e., 440 bps.
 
F2 works for the test because the 5th partial of F2 is A4, where it
coincides with the fundamental of the fork.
 
B1 works because the 7th partial of B1 is A4, where it likewise coincides
with the fundamental of the fork.
 
F3 is a poor choice because it has no partial at A4! It has a 5th partial
that coincides with A5 which is, of course the 2nd partial of A4.
 
So if F3 is used, the beats that you are counting are at A440 (the fork)
and A880+, i.e., the inharmonic 2nd partial of A4.
 
Therefore, if you very accurately match the beat rates of F3-Fork and
F3-A4, you will tune A4 sharp every single time! 
 
The Yamaha example doesn't really bear on this discussion because they are
talking about an altogether different approach (and shouldn't the #1
example be tuning A49 instead of A47?). F3 is only mentioned in relation to
the 3rd-10th test of the octave, which is only to ensure that you have the
A3-A4 octave expanded, or at least not contracted, which has nothing to do
with the dead-on-ness of A4 at 440 bps.
 
Here is another logical way of seeing this. When we tune an interval 5th,
we are comparing a 3rd partial to a 2nd partial. Likewise, when tuning an
interval 4th, we are comparing a 4th partial to a 3rd partial. In the case
of setting A4 to the fork, we are tuning a UNISON where the interval ration
is 1:1 and we must, therefore, compare beat rates arising from the exact
same partial. Because the fork is only sounding (for all practical
purposes) at its fundamental, we must use comparison intervals that have a
coincident partial at A4. Hence B1 or F2.
 
But not F3; it has no coincident partial at A4.
 
Alan Barnard
Salem, Missouri


> [Original Message]
> From: <ed440@mindspring.com>
> To: <pianotech@ptg.org>
> Date: 01/09/2006 6:58:13 AM
> Subject: Alan and David on F3/A4
>
> Alan Barnard and David Renaud:
>
> Your posts on this topic are beautifully written.
> Thank you.
> I hope you don't mind if I repost them to ExamPrep.
>
> Ed Sutton
> _______________________________________________
> pianotech list info: https://www.moypiano.com/resources/#archives