S&S D Duplex

[Sarah Fox]

Hi Phil,

> 3.  If longitudinal vibrations can pass the bridge, it seems to me that
they
> can just as easily pass the aliquot.  So the aliquot position is
irrelevant.
> The plate pin becomes the relevant thing. In order to actually tune this
> portion of the string for longitudinal vibrations you would need to have a
> movable plate pin.  This feature has not been incorporated into any piano
that
> I have seen.

Actually every contact point would be a sound reflection point, resulting
from an abrupt impedance differential.  If we're talking about compression
waves in the string, which it appears is the implication, the free resonant
frequency between any two contact points would be half of the speed of sound
through spring steel (not through air), divided by distance.  It would be
*incredibly* high (bat frequencies and beyond, not dog frequencies), and it
would only be tunable by moving contact points (assuming the spring constant
is indeed constant -- or approximately so).  You suggest the sound would
stop at the hitch pin.  It would not.  That is only another contact point.
It would travel into the plate and beyond.  It would also have a difficult
time coupling into the bridge, except by rocking it.

Personally, the importance of longitudinal vibrations doesn't seem very
probable to me.  It is easy enough to see how transverse vibrations are
coupled into duplex strings from vibrations in the bridge, irrespective of
what Mr. Steinway might have claimed to the contrary.  Why invoke mysterious
ultrasonic longitudinal vibrations?  Just because Mr. Steinway got a patent
doesn't mean he understood the acoustics of his invention.

In the end, could it be that the biggest benefit of a tuned duplex scale is
the "freeing up" of the vibrations of the strings and bridge by eliminating
the need to mute the strings on the far side of the bridge?  After all,
mutes of any kind work through frictional dissipation of vibrational energy.
Isn't it reasonable to expect that muting adversely affects a note's
sustain?  If the purpose of muting is to kill objectionable ringing in
nonspeaking string segments at inappropriate frequencies, isn't an alternate
solution to tune those frequencies to where they are appropriate and
therefore not objectionable?

I am reminded of a closed field speaker system I once designed for my
research. (Think of a tiny speaker in a very long, sealed tube.)  The
objective was to make it flat (+/- 1 dB) from 100 Hz to 15 kHz and make it
efficient enough to deliver 120 dB SPL to the end of the tube with minimal
distortion products (-60 dB or better).  I first attempted this by muffling
the ends of the tube in order to avoid resonance peaks about every 120 Hz.
(Think in terms of "muting" inappropriate frequencies.)  I kept muffling and
muffling until I had to deliver so much power to the speaker driver as to
toast the voice coil.  (We're talking about an EV1202 ferofluid driver!)
Eventually I learned to work *with* the resonances instead of against them.
I removed almost all the muffling and filled the tube with smaller
open-ended tubes that were tuned to a variety of other frequencies.  The
idea was to "resonate at all (or many) frequencies."  I achieved enough
efficiency to deliver 120 dB SPL at 1000 Hz using only a half watt of input
power!  I was up to several watts at 15 kHz, but not nearly enough to blow
the voice coil.  In the end, my system achieved the flatness I desired,
along with far more efficiency than I had ever hoped for.  It was sort of a
"Bose" solution.  Hopefully the parallels to the duplex scale are obvious
here.  Where possible, it seems best to correct the tuning, rather than to
kill the sound.

Peace,
Sarah