Fw: Fw: "The Invisible Tool"/beat rates - and where they come from

[Michael Gamble]

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Hello Bob Davis
Thanks for your input. I agree that the frequencies produced by the =
model A aren't mathematically produced but sonically with many reasons =
for their diversions. I'm very glad to get those figures of yours if =
only to be able to listen out for them on my A. I will see (hear) what I =
can hear, analyse what I hear (see) from you and maybe, just maybe, =
there might be some conclusions to be drawn... But I doubt it! Which is =
why we do what we do do (do do do) Dum dum  ;-)
You'll notice I'm having a good session with Isaac OLEG on this subject =
- a subject which is endless ...Yes? And I do indeed do it by ear. ;)
Regards
Michael G (UK)

----- Original Message -----=20
From: BobDavis88@aol.com=20
To: pianotech@ptg.org=20
Sent: Tuesday, October 21, 2003 9:31 AM
Subject: Re: Fw: "The Invisible Tool"/beat rates - and where they come =
from


Michael G sez:


  Yes, I agree. There is no likelihood of the exact science of sound and =
its harmonics being produced text-book fashion in the piano. The =
principle  applies though - and I doubt it's far removed from the "text =
book" version. What say you?



Depends upon what you call far removed, but it's precisely that =
difference that is important to piano tuners. You're right that the =
principle of coincident partials explains where beats come from, but =
it's the  _departure_  from the principle which explains the compromises =
necessitated by inharmonic mismatches, and that is so vital to refined =
tuning. It's still in the textbook; it's just on a different page.

The other day I mentioned some phony figures to help illustrate this =
point. You have a Steinway A, so here are some real measurements, from =
the temperament area of a Steinway A.

If A4 is tuned to 440 Hz.,=20
its 2nd partial vibrates at 880.92
its 4th partial is 1766.4 instead of 1760
(and its 8th partial is 3609.36, instead of 3520)

If A3 is tuned to 220 Hz.,=20
its 2nd partial vibrates @ 440.48 instead of 440
its 4th partial is 882.6, instead of 880
its 8th partial is 1774.8, instead of 1760

This creates significant beating, even though the fundamental of the =
upper note is twice that of the lower. You can see that at the 4:2 =
level, you've got 880.92 versus 882.6, (over a beat and a half per =
second). At the 8:4, it's even worse.

If A3 is then retuned so that its 2nd partial is also 440,
its fundamental will be at 219.76, but the other coincident partials =
will come a little closer to matching.

Fortunately, we do some of this automatically by ear, but it's still =
important to know when to go for smooth and when we are likely to have =
to squeeze it a little to get better results elsewhere in the piano.

Bob Davis
Stockton, California


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