Negative crown

[Doug Richards]

Ron,
Very well put.  I think we are talking the same language.  The only
difference I have is my dislike for the word "impedance".  In my line of
work, the only people that talk of impedance is them electrical guys (you
know, the ones that need scopes to see what they are doing).  I am much more
comfortable talking about mode shapes, resonant frequencies, dynamic
coupling and the like and leave the impedance to the EE's.  

The reason I replied to your thread in the first place is reflecting on
previous threads about Killer Octaves.  Seems like there should be someone
that optimized the impedance so that the Killer Octaves died.  Maybe we
haven't figured out the best way to kill it yet...  (or more likely, another
manufacturing problem or reliability issue comes up again).

Anyway,  thanks for the reply.  And YES, we are having fun!
doug

> -----Original Message-----
> From:	Ron Nossaman [SMTP:nossaman@SOUTHWIND.NET]
> Sent:	Tuesday, December 29, 1998 11:48 AM
> To:	pianotech@ptg.org
> Subject:	RE: Negative crown
> 
> At 10:03 AM 12/29/98 -0800, you wrote:
> >Ron,
> >I have a question for you.  You said that when the crowned soundboard is
> >loaded by the strings, the impedance goes up.  I would agree with that.
> The
> >question is from the string perspective.  The piano has strings with
> >frequencies ranging from ~50 Hz to ~4kHz and the I imagine the soundboard
> >has 30-50 natural modeshapes in that range.  So my question is: with such
> a
> >broad range of soundboard and string frequencies, what is the soundboard
> >impedance "matching"?
> >
> >I don't really have an answer to this either...
> >
> >
> >doug richards
> >San Jose, CA
> >
> 
> 
> Doug,
> 
> Well, 'matching' is probably too definite a word here, but the soundboard
> impedance should change along the scale to accommodate the impedance of
> the
> string plane at a given point. The individual strings have their own
> impedance value, which changes drastically from low bass to high treble,
> but
> it's not linear with frequency, although frequency is a factor. That would
> make it way too easy and everyone could be making well designed
> soundboards.
> (I didn't mean it Del, I slipped) In theory, it's a matter of tailoring
> the
> soundboard stiffness/mass to receive string energy at the proper rate,
> relative to the rate at which the string supplies it. Assume a given point
> in a given string scale. A soundboard assembly with a too low impedance in
> that area will have more volume and, in the extreme, a tendency to
> 'splatter' on the attack, and short sustain. A board with too high an
> impedance will be quieter, thinner sounding, and have a much longer
> sustain.
> Both of these conditions can, and often do, exist in the same soundboard
> in
> different areas of the scale. The trick is to arrange the proper balance
> of
> mass and stiffness in any particular portion of the soundboard assembly to
> reasonably accommodate the impedance levels of the string plane in the
> same
> area to get the overall sound we're after, while still having the overall
> strength to support the string bearing load over a long period of time.
> Are
> we having fun yet? The assembly needs to be quite stiff in the treble, and
> much more flexible in the bass. In practice, there are about a billion
> variables to factor in, and it still comes down to best guess on some of
> the
> factors involved. Del pointed out that, unlike an individual doing a
> one-off
> redesign in the shop, a manufacturer can have the luxury of making small
> incremental changes to fine tune the assembly. Even then, what seems to be
> a
> short term gain could end up being a long term detriment as the design
> ages
> in the piano. Throw in the nearly infinite variations of density and
> stiffness in the materials used, the possible configurations of size, case
> shape, rib scale, crowning method, grain angle, bridge construction and
> position, string bearing and load distribution, and the fact that no two
> practitioners of the soundboard design, installation, maintenance, and
> repair art seem to agree on what they all are looking at, and we are most
> definitely having fun.       
> 
> Is that what you asked?
> 
> Regards, 
>  Ron