impedance and empericism

[Marc Damashek]

Empiricists:

Distractions abound. 

The original question went something like "Don't we have to worry about all
sorts of extraneous influences before we can discuss tuning optimization?"

Let's focus for a minute, friends );o) . It is irrelevant to that question
whether the *pitch* of some string changes, for whatever reason, so long as
its partials all change by the same multiplicative factor -- regardless of
whether those partials are harmonic or inharmonic. The main issue is not
whether the partial frequencies of a string have changed, but whether their
relative frequencies, their ratios to one another (and NOT their amplitudes)
have changed.

Example: if the temperature rises by 30 deg and RH by 80 pct and the relative
frequencies of the first four (wildly stretched!) harmonics of some string all
increase by 10% from 440*[1, 2.5, 3.8, 5.3] to 440*[1.10, 2.75, 4.18, and
5.83], I can still bring the string back to its original state by dropping the
tension by the right amount (1/1.21) -- the square of the desired pitch
change. If the frequencies implausibly change by different (relative,
fractional, percentage, NOT absolute) amounts when the piano structure swells
and raises the tension, then all bets are off.

After this week's discussion, the stability of the frequency ratios on any
string still seems to be a viable, or at least testable, hypothesis. The
tuning proposal on the table is that once the actual distribution of partials
has been measured on each of a set of strings, one can find a numerical
solution that will minimize any error criterion that is based on the relative
frequencies of those partials (NOT drive the error to zero, just find the best
-- least -- practical value). That solution should not be sensitive to effects
that merely change the string tension. They may be sensitive to effects that
change the termination points on the string itself, but again, we have to
determine whether that is a practical concern; maybe it is. Likewise, drastic
changes in the relative amplitudes of partials WILL have an effect on the
final sound, because the tuning technique will have been primed with the
initially measured set of amplitudes. If things are that bad, remeasure the
piano. 

Choosing and trying various error criteria is a matter of experiment,
experience, taste, and who knows what else, but that's what we're already
doing, both aurally and with ETDs -- it's not black magic.

Cheers,

Marc Damashek
Hampstead, MD

"Delwin D Fandrich" <pianobuilders@olynet.com> wrote:
> 
> ----- Original Message -----
> From: Conrad Hoffsommer <hoffsoco@martin.luther.edu>
> To: <pianotech@ptg.org>
> Sent: June 15, 2000 8:10 AM
> Subject: Re: impedance and empericism
> 
> 
> > Jimrpt,
> >
> > At 09:52 06/15/2000 EDT, you wrote:
> >
> > > ,...... If a source of pitch/tone were such that it gave off a
> > >'measured'/'perceived' pitch of 440 hz at  70F , 10% RH and 22 mb AP
> would
> > >the 'perceived' pitch/tone be the same 440hz at 100F,  90% RH 26mb AP ?
> And
> > >the 'measured'?
> >
> >
> > Gut feeling:
> >
> > Yes.
> >
> > You have not changed the source, only the speed at which the vibrations
> > travel between source and receptor.  If the receptor were moving relative
> > to the source, I could see where there might be a difference in
> perception.
> > (Hello, Dr Doppler, etc.)
> 
> ---------------------------------------
> 
> Well, but we do change the source.
> 
> We tend to think of the bridge as a fixed termination point for the
speaking
> portion of the string.  It is not.  It moves in response to the vibrations
> at the end of the string in a complex fashion.  That is, it moves, but it
is
> not always in phase with the force at the end of the string.  Without doing
> a whole lot of thinking or analysis on this, I suspect that this could have
> the effect of making the string act as if it were either very slightly
> longer or shorter than it actually is depending on whether the bridge were
> moving in phase with the end of the string or 180º out of phase with the
> string.
> 
> Del


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