Hello Sarah,
Distinctions should be drawn on the subject of string/bridge/soundboard
behaviors which take into account not only the difference between transverse
waves on the string and the possiblity of longitudinal waves there also, but,
additionally, the mechanical function of the soundboard/bridge and string
interaction and the nature of relevant forcing functions themselves.
The standing waves on the string itself do not move across the wire, nor,
in my opinion, do they "rock" the bridge up and down significantly. Rocking is
not necessary to transfer energy into the bridge or past it to the duplex
segments, bridge, soundboard, agraffes, plate or whatever. Another mechanism,
which I called "stress transduction" in a very intense, controversial discussion
of this same subject earlier this year will easily account for this and,
although it seems to be well understood by only a few, is available on the
archives under the subject lines "The behavior of soundboards" "Rocking
bridges" and others which escape me at the moment.
Briefly, at the terminations of the string the wire itself is subjected to
a periodic stress induced in it by the cycling standing waves occuring on the
speaking length segment and their interaction with the bridge/soundboard.
These are separate from the traveling waves developed on the wire by the hammer
which superimpose to create the cyclic standing waves on the string. . The
resultant of the excursions made by the standing waves is along the equilibrium
point of the wire and, at the terminations, a periodic stress is experienced by
the, essentially, immobile wire segments there, held down there as they are by
the vastly greater forces of the other strings, the downbearing, etc. This is
not a free vibration of the wire but, rather, a periodic, mechanical stress wave
which passes easily across the terminations whether bridge pin or agraffe.
Touching a tuning fork to the bridge results in essentially the same kind of
stress transduction.
In the context of the duplex segments, which, in my experience are not
necessary for a great sounding instrument, witness some Chickerings, but which
may well exist on one, it is important to understand that the energy passing the
terminations is a forced vibration; that is a periodic state of stress is
imposed which has the frequencies contained in the string, and not a free
longitudinal vibration. I think Steinway grasped this distinction only poorly
but refers, albeit clumsily, to it with the term longitudinal vibration. As
you point out, the frequency of a true longitudinal vibration in the duplex is
dependant on the lengths and wave speed of the medium, and this produces
frequencies far too high to be much relevant to normal piano sound.
The distinction between a kind of pseudo-longitudinal forcing function
which describes a state of stress and the ordinary, longitudinal wave is
critical, I think, to understanding the intended value of the duplex. Speaking
as a pianist, I never know whether a piano has a duplex or not unless there is
sufficient whistling and jangling to draw attention. If a piano is like this,
usually, there are so many other things wrong with it that these imperfections
are merely a few of many and the connection with the instrument is lessened.
However, many times while tuning I have looked down at the front duplex segment,
silenced it with the touch of a finger, and immediately noted a kind of drier,
dull, sound.
The stress wave, or pseudo-longitudinal state of forcing, passes the
terminations or bridge into the duplex segments where a similar reflexion and
recurrency of effect as occured in the superpositions of the traveling wave in
the speaking length occurs, resulting again in a transverse set of standing
waves which, of course, are greatly attenuated. This can be tuned by moving the
duplex.
Additionally, the transfer of energy into the bridge is easily accomplished
both by refraction and mode conversion of the wave type.
Although it is heresy to some to claim such, in actuality, approximately
the same amount of energy leaves both ends of the wire at the speaking length
terminations - the difference in acoustic effect of the stress wave or
condition passing into the plate on the one hand, and into the bridge/
soundboard on the other, being, fundamentally, the flexural rigidity or bending
modulus which is the product of the modulus of elasticity and the section
modulus of the material, in conjunction with the degree of reflectivity and
size and shape of the medium.
I believe the utility of the duplex in essence, is, exactly, what the
patentee claimed, and that is the tuning of the segments to harmonics of the
fundamental of the speaking length and the effect of this on the sensibility of
the notes, particularly, those of the treble which need some means of becoming
more perceptible than the more instrusive tenor and bass. That the companies no
longer take the trouble to tune them is no surprise to me, given the long
decline of piano building. Numerous other examples exist of features abandoned
or in use in name only. This is characteristic of the industry itself.
However, I do think, judging from what he says, that Ron Overs may be on to
something with regard to his method of altering the tuning of the front duplex,
that may, indeed be new, in this regard, although I have no personal experience
of this.
Regards, Robin Hufford
Sarah Fox wrote:
> 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
>
> _______________________________________________
> pianotech list info: https://www.moypiano.com/resources/#archives
This PTG archive page provided courtesy of Moy Piano Service, LLC