Inharmonicity - so what?

Delwin D Fandrich pianobuilders@olynet.com
Wed, 19 Aug 1998 21:44:46 -0700



Ron Nossaman wrote:

> >> . . . . When the
> >> mere act of touching the bridge pin terminating a beating string clears up
> >> the beat, it ain't the soundboard design, or is it?
> >
> >Yes.  You're altering the resonant frequency of the soundboard by touching the
> >bridge pin.  More anon...
>
> *When you then CA the pin, and the beat stops even though you are not
> touching the pin, it's the pin. When you touch the pin NEXT to the pin
> terminating the beater and the beat doesn't stop, it's not the alteration of
> the resonant frequency of the board by touching pins that makes the difference.

Perhaps I should have said a definite "maybe."  By now I should know better than to
respond positively to scenarios in which only part of the information is available.



> >It's not even so much a matter of soundboard system crown.  I'm not convinced
> that within reasonable limits the lack of crown and/or bearing has much of
> anything to do with pins coming loose or staying tight.  It does have to do with
> soundboard springiness.
>
> *Nope, I didn't say anything at all about crown /bearing affecting pin
> tightness.

My mistake.  I thought that was what you were implying.


> >OK.  So, here is the short and sweet version of the principle:
> >
> >If the fundamental resonant frequency of the string loaded soundboard assembly
> >at the point of contact with the affected string is higher than the fundamental
> >frequency of the string, the motion of the bridge tends to follow the motion of
> the
> >string and the string sees both the actual speaking length and some artificially
> >longer speaking length.  False beats will readily develop and will be nearly
> >impossible to control.
> >
> >If the fundamental resonant frequency of the string loaded soundboard assembly
> >at the point of contact with the same string is lower than the fundamental
> >frequency of the string, the motion of the bridge will tend to oppose the motion
> of >the string and the result will be a cleaner, more efficient termination of the
>
> >speaking length of the string.  False beats will show up more rarely and will be
> >easier to treat.
>
> *The fundamental resonant frequency of any area of the soundboard system
> will be dependant on the impedance of that area.

The fundamental resonant frequency of any area of the soundboard is dependent on the
relationship between the mass of the system and the springiness of the system.  As
is impedance.  The resonant frequency is not "dependent" on impedance, nor is
impedance "dependent" on the resonant frequency.


> Less mass and more
> stiffness in the treble, and more mass and flexibility in the bass. That's
> woofers and tweeters. If the killer octave area in a traditional system is
> too low in impedance for the frequency ranges it needs to handle, by being
> too flexible, then it's fundamental resonance frequency is lower than it
> needs to be as well.

Not necessarily.


> By what you outlined above, this area should be
> relatively free of false beats and easier to treat, should any happen to
> arise. That's exactly backward from what I see in pianos - does not compute.

That's what I see in a lot of pianos as well.  But with their newly designed
soundboards and rib systems those same pianos become relatively free of false
beats.  They also pick up sustain in the killer octave region.


> Also, the bridge is just that... a bridge. It's job is to provide string
> termination and convey energy back and forth between the soundboard assembly
> and the string plane. The tenor/treble bridge extends from the lowest
> impedance areas of the board, to the highest. It is highly unlikely that at
> any point along the bridge, the soundboard system impedance measured at the
> string termination point equals that of the soundboard directly beneath. The
> stiffness of the bridge averages impedance loads of both the string plane,
> and the soundboard assembly.

This is all quite correct.  But still the resonant frequency of the
soundboard/rib/bridge/string assembly varies dramatically depending on the driving
point.  It is true that it is unlikely that it will vary dramatically from one
unison to the next, but it will almost certainly vary some.  The variation from two
points 50 to 75 mm apart can be dramatic.


> This should make the killer octave seem
> somewhat less bad than it actually is,

Why?


> ... and maybe it does, but there is still
> some flexibility there, and it is still evident, though blended at the
> boundaries somewhat. The point here is that if the fundamental resonant
> frequency of the soundboard is supporting false beating strings, All the
> strings in a range should beat similarly.

I'm not sure "supporting" would be my choice of words here.  This brief outline of a
principle was not intended be taken as the "cause" of all false beats.  It was
simply an explanation of why one piano can have an abundance of false beats while
some other piano of "lessor" make can be remarkably free of them.  And to point out
that, at least to some extent, this tendency can -- should -- be designed out of the
soundboard system.

My classic example is the 9 foot Julius Bauer that I used to own.  This piano had
its tenor bridge mounted on dowels.  These dowels were about 50 to 60 mm long
through the killer octave region.  The bridge pins were so loose that I could wiggle
them in their holes.  Many of them were easily pulled out using just my fingers.
Conventional wisdom said it should have lots of false beats -- tall, floppy bridges,
loose pins, etc. -- yet there was barely a false beat in the piano.  Even before the
bridge was fixed and it was restrung.  This design had may other problems, but false
beats was not one of them.



> If, for instance, the left hand
> string of A6 beats, and the middle string does not, why not? If it's a
> general problem, the symptoms should not be so specific. When I run into a
> lot of false beating strings in a given grand, I check bearing. The
> beginning and ending limits of the range of false beating strings
> corresponds closely to a range of lower to non-existent bearing readings.

It would be very interesting to hook up a shaker and a signal generator and find out
exactly what is happening to the resonant frequency of the soundboard assembly
through this region.  It doesn't always do exactly what you think it should do.


> I
> assume there was adequate bearing, for the most part, in this area when the
> piano was strung, but it lowers quickly in service. This is the section of
> the board that usually goes flat first, and that's a design problem.

Yes it is.


> Nearly
> all of the beaters clear up with pressure on the pin. Some do not. Why? The
> ones that don't, tend to be a less distinct sounding beat than the loose pin
> beat. I don't see any reason not to blame impedance mismatching and
> resultant fundamental resonance frequency mismatching, at least partially,
> for these. That's a design problem too. That leaves the bulk of the killer
> octave beaters still under the loose bridge pin column for me, at least from
> a service perspective.
>
> >I agree that you have to do whatever you can to attempt to make these things go
> >away.  Just don't beat yourself to death if your best efforts are not all that
> >successful.  It ain't your fault.
>
> *So far, I have steadfastly refused to accept blame for false beats since I
> started in this business. We'll see.

Good for you!

>
>
> >
> >> They'll be using different glues too.
> >
> >What?  Better than CA . . . . ?  How could that be?
>
> *Just you wait. Some day they'll have glues that make pianos better just by
> un-capping them in the vicinity of the ailing instrument. You'll be able to
> glue your fingers together just by reading an ad for the stuff in the
> Journal. I'm lobbying for the name "Resurrectum", but nobody seems
> interested so far. Go figure.
>
> >> Serves you right, troublemaker. Did you get your head working? <Evil Grin>
> >>
>
> >
> >Which "head" are we talking about here, Ron?  If we're talking about the one on
> >the boat, yes.  At least it's working about as well as it's going to work.  If
> we're
> >talking about the one I normally carry around with me -- well, that one hasn't
> been
> >working right for years....
> >
> >Del
>
> Yea, I meant the one in the boat. The portable one seems to work fine except
> for your tendency to go off and leave it running. %-)
> Oh well, my Dad used to yell at me about leaving lights on too.
>
> Tag,
>  Ron

  ------------------------------------------

Sadly, the problem seems more one of getting it to run when I want it too.

Regards,

Del



This PTG archive page provided courtesy of Moy Piano Service, LLC