[impedance]

[Marc Damashek]

Don:

Thanks -- my persistence is not obstinacy, I hope -- I'm trying to understand
what the physical processes might be, in order to eventually model and allow
for them. Let me please ask for a little further clarification...

Clearly, as the humidity and pressure change, the physical size of the support
structure changes, as does the coupling of the strings to the soundboard, and
perhaps bearing angles change at the bridges and agraffes. If the only thing
that changed were the tension on each string, I'd expect all partials on any
given string, whether harmonically spaced or not, to be multiplied by the same
factor (which could even vary from string to string). This would mean that the
*ratios* of higher partial frequencies to the fundamental on each string would
remain unchanged. I hear you saying -- not surprisingly -- that the absolute
frequencies change with weather, rather than the ratios of partial frequencies
to their respective fundamentals. If the ratios themselves were to change, I
would find it very perplexing. The tuning technique I've been discussing
relies directly on those ratios, and if they are stable over time then they'd
only need to be measured very infrequently.

If the news is bad (at least to the extent that the whole piano needs to be
measured in order to do the job), I'd be very interested in trying to
understand why those frequency ratios might be changing, rather than just the
relative amplitudes of the partials. (This is also the only change I'd expect
from voicing -- a change in hammer shape should alter the relative amplitudes
of the partials, but not their frequencies [Morse and Ingard is a good
reference here].) I've assumed the ratios -- the detailed inharmonicity of
each string -- are basically determined by two factors: the stiffness of the
wire (the systematic stretching effect, smoothly changing over the keyboard),
and inhomogeneities of the wire (random deviations from that smooth
progression). What else might lead to anomalous changes in the ratios as a
result of dimensional changes, like the ones produced by weather? Is there
really something else going on? I don't yet own RCT, and haven't gotten my own
analysis code cranked up to the point of doing the detailed measurements, but
I'd genuinely like to find out how much of this is real and how much is
folklore. As you point out, the tools have only recently become available, so
there's not a vast literature to fall back on.

Cheers,

Marc Damashek
Hampstead, MD


Don <drose@dlcwest.com> wrote:
> Hi Marc,
> 
> With todays technology it is *already* possible to prove that the frequence
> of the partials change with voicing and also with the changes in the
> humidity content of the sound board. We can minize such changes with
> humidity control--but unfortunately we can't control the barometric
> pressure which affects the partial pressure of the water content of the
> wood. Sorry to rain on your parade. It affects the octave widths as well so
> the change is on all partials from the bottom up. Remember Marc, we can
> hear very tiny changes in frequence as tuners probably on the order of
> 0.025 hertz at A4 partial one. 
> 
> At 08:52 AM 06/13/2000 EDT, you wrote:
> >Don:
> >
> >Ouch -- yes, if the string coupling to the soundboard changes
significantly,
> >then the *amplitudes* of the various partials will change also. I doubt
that
> >their *frequencies* would change significantly (apart from second-order
> >loading effects that change resonant frequencies due to changes in
damping),
> >because the frequencies of the partials are essentially determined by the
> >string itself -- normal small-amplitude vibrations of the soundboard are
not
> >big enough to give rise to spurious frequency components
> Regards,
> Don Rose, B.Mus., A.M.U.S., A.MUS., R.M.T., R.P.T.
> 
> Tuner for the Saskatchewan Centre of the Arts
> 
> drose@dlcwest.com
> http://donrose.htmlplanet.com/
> 
> 3004 Grant Rd.
> REGINA, SK
> S4S 5G7
> 306-352-3620 or 1-888-29t-uner


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