Inharmonicity - so what?

[Ron Nossaman]

Hi Del, more stuph.

>
>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.
>

I'm not trying to blast the idea out of the water here because I think you
are right. Your blanket statement covered a lot of real estate and I'm just
trying to connect it into my reality where I can get it to fit. For me,
that's going to take a little conceptual whittling. 



>
>> *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.


Yea, you're right, bad wording. I didn't mean to say that one was the result
of the other, but rather that both the fundamental resonant frequency and
impedance of the soundboard system react similarly to changes in mass or
stiffness. They will both go up, for instance, with increased stiffness,
though not necessarily to the same degree, or at the same rate. On second
thought though, an increase in mass will raise impedance and lower
fundamental resonant frequency wouldn't it? Hmmm, needs more thought.



>
>> 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.


OK, I got it now. Yes, that makes sense.




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

The stiffness of the bridge would spread the driving point out along it's
length to become a less defined driving area. This would tend to blend local
anomalies in both impedance and fundamental resonant frequencies a bit.
Since you won't ever hear the piano without the bridge, you probably can't
know exactly to what degree this is happening, but it is happening. Moot
point, but that's what I meant. It's self-averaging to some degree like
string bearing load distribution.    



>
> 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.

Granted, point taken. My point originally was that a new piano, with
adequate bearing through the killer octave area and minimal evidence of
false beating will develop false beats in this area as bearing decreases
with loss of crown. I still think that bearing angle has a whole lot to do
with it and, while a new soundboard design can have a better impedance match
and fundamental resonant frequency relationship through that area, it will
also have good crown and bearing that should be more likely to stay that way
than the original design. So the new board design minimizes the false beat
problem, but not necessarily entirely for the reason stated. 



>
>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.


How was the bearing in the killer octave? My contention is that loose pins
aren't a big problem with adequate bearing. It's just when the friction of
the string on the bridge surface is low enough as a result of inadequate
bearing to allow the flagpoling of the pin to generate the beats.



>
>> 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.


You bet it would. It seems I'm going to have to plan on accumulating a few toys.


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

Well, mine's still locked up tight (sinus). Guess I'll try to get a couple
hours sleep before I go tuning. Maybe I'll get lucky and nobody will expect
me to make sense at them. Then again, what's unusual about that?

Best,
 Ron