A-428 Tuning Question

[Susan Kline]

> I can now go to 442 without the aid of a
>calculator! :-)
>
>-Gina Carter, Charlotte NC


Gina, list --

There are those of us who don't use these marvelous gadgets. I admit
they would be very handy at times, such as being asked for A=428, or
tuning two identical model 9 foot grands to each other ... however, 
we still are not totally helpless. 

When I have tuned two long grands to A=440, and checked individual 
notes, they were close enough that I couldn't tell the difference.
As long as listeners and customers don't have ears sharper than mine
(which so far has been the case) I'll be all right.

For A=442, I have a fork.
 
For A = 428, one assumes that a musician bringing a pianoforte and
asking for historic pitch has some form of pitch reference, a fork
or one of the Korg tuners, probably. I would ask to borrow it for
the tuning. If I repeatedly had to tune this low, I'd get myself a
fork, probably, or the Korg.

If that wouldn't work, and it was all up to me, I'd have to figure
it out by brute awkwardness. (Technical wizards, are there any gross 
errors in the following?)

For A=428, knowing that I needed to end up 47.-somthing cents 
low, I could calculate beat rates: from McFerrin, G#4 = 415.31 Hz. 
Subtracting from 428, I would get 12.69 beats. Subtracting 428 from 
A = 440, I would get 12 beats. This is reasonable since what I need 
is almost exactly 1/4 tone below modern pitch. (Just 3 cents off ...)

Assuming that a fortepiano brought in for a concert would probably 
already be at A = 428, the pitch adjustment in the temperament octave 
would probably be minimal. However, if the pianoforte were found to be 
at 440, one would have to assume the piano would rebound roughly 1/4 
of the pitch lowering. I could then try tuning the A# slightly sharp 
(7 or 8 beats sharp) of 440, setting the temperament from that 
and seeing what I ended up with. 

I could check results by testing A# against the A (440) fork, wanting 
it roughly 13 beats sharp, then testing A against the A fork, wanting 
it exactly 12 beats flat. While not able to _count_ 12 or 13 beats 
against a watch, it would be easy enough to see if the A# beat rate 
(against the 440 fork) was just a trace faster than the A (also 
against the 440 fork.) Then I could test A against my A = 435 fork, 
and see if it were 7 beats flat. The A beating against the 435 fork, 
giving 7 beats, is close to the F-A beat rate memorized for my normal
temperament, so that wouldn't be too hard to tell with fair accuracy. 
If it passed all of these, it would certainly be close enough for a 
solo concert, and probably easily within tolerances for any instruments 
that might be used.

Calculating technicians, is this on target or out to lunch? 

Regards,

Susan

Susan Kline
P.O. Box 1651
Philomath, OR 97370
skline@proaxis.com

"By using your intelligence, you can sometimes make your problems twice as
complicated."
			-- Ashleigh Brilliant