Klarinet Archive - Posting 000888.txt from 1997/05

From: Stephen Froehlich <shorthnd@-----.edu>
Subj: Re: Pitch of tuning notes
Date: Sat, 31 May 1997 10:12:41 -0400

On Sat, 31 May 1997, Jonathan Cohler wrote:

> I believe that your statement here is basically correct. The physical
> reason is that the vibrating element (the string) is not a totally linear
> system. As I recall, the non-linearities are most noticeable in the very
> high-tension strings of the highest notes of the piano (and not very
> noticeable at all down lower). I believe it has to do with the properties
> of the metal strings at very high tension that makes them non-linear (i.e.
> the force of the tension is not always directly proportional to its
> displacement from equilibrium).

Quick note. The linear theory behind string vibration treats
tension as CONSTANT. I believe that this is the most important non-linear
term in the motion of a piano cord. It might also be the sound board,
though. I don't really know beyond the first sentence.

Stephen Froehlich