Piano acoustics

[Richard Brekne]

Richard Moody wrote:

> | -------- Original Message --------
> | Subject: Re: Piano acoustics
> | Date: Tue, 29 Jan 2002 11:40:46 -0500 (EST)
> | From: Gabriel Weinreich <weinreic@umich.edu>
> | To: Richard Brekne <Richard.Brekne@grieg.uib.no>
> |
> | Dear Mr. Brekne, in this case the simplest process -- transverse motion
> | of  the soundboard -- is also the dominant one. ....... I think you can
> | understand it better as the bridge giving rise to standing waves in the
> | soundboard which are, in fact, what are called modes of vibration of the
> | soundboard.
> |
> - GW
>
>     I take transverse motion to be the simple up and down movement of the
> soundboard rather like the back and forth movement of a loud speaker cone
> or headphone diaphram.

I think the Askenfelt contribution pointed to a little more complex then my
understanding of the loud speaker analogy. And I am still pondering it and
wondering about a few things relating to it.

>
>     I wish "standing waves" would be better defined, but the interesting
> concept is that the soundboard "vibrates in modes".

I agree a whole lot with both these statements.

> Modes I take to be
> what acousticians call the segments of vibrating string that we call
> "partials" to differentiate them from "harmonics".... harmonics being a
> tone resulting from a fundamental with "overtones" (harmonics) of perfect
> ratios.

More or less, but the string is a so called one dimensional system... with
modes following the length of the string so to speak, where as the soundboard
is a so called two dimensional system with modes showing themselves both
lengthwise and widthwise as it were. The soundboard modes are not "harmonics"
in the same sense, but now that you mention it, I need to re-read what is said
about exactly this point.

> Because the string is stiff, we are told, the partials are sharp
> from  perfect and this sharpness is called inharmonicity.   Now if the
> soundboard is vibrating in modes and it is conceivably stiff therefore
> shouldn't it have its own inharmonicity?

As said... I am sure the SB modes are not related really to string
inharmonicity.... other then the fact that they both represent natural
resonances for each of these differing media. I am sure Weinreich covers this
in his contribution to the 5 lectures tho.

> So,  does the SB somehow
> reproduce the frequency of the string's partials (inharmonicity), or does
> the SB vibrating in modes with its own stiffness determine (more or less)
> the  inharmonicity of the piano?   ---ric

Now THIS is an interesting question. And I think I have to suspect that this
is sort of involved in the para inharmonicity question, and why folks like Jim
Coleman suspect that said "para" is caused by bridge/soundboard impedance
concerns. Otherwise I am also trying to turn over in my mind how the
soundboards natural frequencies and the forced frequencies the strings place
on the board result in the seemingly relatively true replication and
"enlargement" (to avoid the use of "amplification") of the strings "sound".
The enlargement or "amplification" in that sense I am ok with... but the
strings multi-frequencies moving in a billion different directions at once...
delivered to the bridge/SB which developes bending waves where the speed of
these are frequency dependent... such that the higher the frequency the faster
the wave speed... troubles me.  This would seem to present a situation where
essentially the higher the string partial, the quicker the corresponding
soundboard wave runs through the SB system... which my unschooled  mind wants
to jump at wondering why I dont hear the high frequencies before I hear the
fundementals.... to put a point on it.



--
Richard Brekne
RPT, N.P.T.F.
Bergen, Norway
mailto:rbrekne@broadpark.no
http://home.broadpark.no/~rbrekne/ricmain.html