[impedance]

[Roger Jolly]

>the point along the decay curve at which the measurement is taken.  If we
>are to prove anything about voicing affecting inharmonicity independently
>from its effect on volume, then we would have to find a way to play the
>note, regardless of its voicing, so that it has the same volume level
>during the inharmonicity measurement.
>
>-Robert Scott
> Real-Time Specialties

Hi Robert,
               I have developed a key striking device that has reproducible
results within 10% of both inharmonicity and sustain, over 10 strikes. I
can vary both velocity (height) and mass (loaded with copper shot)
Nick named the "Jolly thumper".  It can be rigidly clamped to the key bed
and has very low friction, (phosphor bronze bearings, on travel system) It
is also trigger operated. 
For any test to be meaningful a complete touch weight analysis has to be
done when comparing the spectrums of two notes, to ensure that the
frictions are very similar.  The regulation and string mating also has to
be fastidiously done to make a comparison. Centre pinning has to be 4gms
friction for hammer flange and wippen flange.  The key strike point can
also cause a variance, and this I have reproducible to within 1/2mm.
I have done several test with virgin (untreated & un needled hammers) cups
only filed out to mate to string and control phasing.
Hammers were weighed before installation and were within 0.01gm.
You are correct in saying increased, velocity will alter the harmonic
spectrum ratios. Preliminary results seem to indicate that the harder the
blow, the greater the ratio, plus the shorter the sustain as you go up
harmonic series.
Don is also correct in saying that humidity has an effect, is it the boards
effect, or the elasticity of the hammer, or even the friction changing?
Good questions, When you start looking at the complexities of the partial
differential equations for mechanical impedance of solids, coupled with
theoretical inharmonicity vs real time measurements.  It's going to take a
better brain that mine to figure out.
Harold Conklin, who in my humble opinion, was one of the finest researchers
into piano acoustics of the 20th century, stated that he did not understand
sound board impedance, was probably correct in finding the subject
extremely complex. So many variables, and no real money to fund adequate
research. 
The only thing that my personal quest has proven, is that how little I
know, and to be very leery of so say impedance and inharmonicity experts,
that have simple algebraic solutions.
When I collect enough reproducable data, that can be used  I will publish
the results in the Journal.
More questions seem to surface, than answers, I'm afraid. 
Warm regards Roger




Roger Jolly
Saskatoon, Canada.
306-665-0213
Fax 652-0505