Klarinet Archive - Posting 000812.txt from 1996/02

From: "Edwin V. Lacy" <el2@-----.EDU>
Subj: Re: String tuning
Date: Tue, 27 Feb 1996 13:11:32 -0500

On Mon, 26 Feb 1996, Gary Bisaga wrote:

> I have recently started on what will hopefully become a part-time
> career in piano repair and tuning. There, you learn the technique of
> "scale stretching," tuning the octaves towards the top of the keyboard
> sharp and the ones towards the bottom flat. The reason, as I
> understand it, is that strings are not perfect tank resonators as
> described in sophomore physics. They always have a resistance
> component, and this component tends to make the harmonics sharper than
> where they should occur. (I haven't done the math but books and the
> piano techs I work with assure me this is so.) So, if you play middle
> C and the C two octaves above, the 4C needs to be tuned sharper than
> 4x the frequency of 2C.
>
> Might the resistance of all other real resonators cause the same
> phenomenon, causing the "tendancy" of "humans ... to want to play high
> pitches sharp?"

The phenomenon you are describing is called "inharmonicity." That is,
the frequency of an upper partial in the harmonic spectrum of a pitch is
not an exact multiple of the frequency of the fundamental. It is well
known and documented that this exists on the piano, and it has been
described with regard to other instruments, but the research seems to be
very sketchy.

I once did a research project which seemed to indicate that the overtones
in the spectrum of bassoon tone might not be harmonic, but as that was
not the primary purpose of the experiment, I didn't pursue it. I have
since been told by a manufacturer of bassoons that no one knows for sure
what the facts are about the bassoon in this regard, but that the
information would be very useful to manufacturers. My experiment was
completed in the mid-1970's, and the equipment available was very
primitive by today's standards. Now, it would be a relatively easy task,
if the equipment were available to someone. I have always thought it
would make an excellent dissertation topic for someone, perhaps on the
clarinet as well as other wind instruments.

Ed Lacy
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Dr. Edwin Lacy University of Evansville
Professor of Music 1800 Lincoln Avenue
Evansville, IN 47722
el2@-----.edu (812)479-2754
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