Helmholtz and Steinway

[Ron Nossaman]

>Are you aware of harold Conklin's research in this area?
>
>Stephen

Some. Mostly from his "Design and Tone in the mechanistic piano, Part III.
Piano strings and scale design". He puts the first longitudinal mode of
plain steel strings at roughly 2500/L, with L being the speaking length in
meters. Speaking lengths between 0.05-2M produce approximate longitudinal
frequencies of 1.25-50 kHz. This is just a tad beyond the frequencies of
the shortest rear duplex scale ratio to speaking length you might find. He
limits the phenomenon to the speaking length too, rather than to the
overall string length. Did he publish later material that obsoletes this?
I'd sure like to get a look at it if he did.

Ok Stephen and JD, if that trick of plucking the front duplex segment and
getting a fundamental tone from the speaking length is the result of
longitudinal mode vibrations going over the capo (rather than transverse
vibrations and a levering rocking motion at the capo, which the Steinway
patent mentioned without specifically naming as lowering string breakage
incidence), and if these longitudinal vibrations pass so easily directly
across the bridge that they excite the rear duplex, then you should be able
to pluck the rear duplex segment and get a fundamental tone from the
speaking length of that same string. When I try it, I get the pitch of the
duplex segment from what appears to be the general surrounding area, rather
than the speaking length (and not at the fundamental at that) of that
specific string. This does not compute with the longitudinal bleed through
model, but does as a secondary effect produced by general bridge movement.
Perhaps I'm wrong here, but it seems reasonable to me for the two duplexes
that are both claimed to be working by the same mechanism, to work the same
way. They don't, at least on my piano. Everything I've seen and done along
these lines still indicates to me that the front duplex is driven by a
transverse vibration, leverage and capo pivoting action (why would
deflection angle alter the effect when it doesn't at the bridge if they are
both longitudinal effects?), and the rear duplex is driven by general
bridge movement.

Ron N