A correction of one of the, unforntunately, frequent typos in postings of late. rh There is a reasonable analogy to drawn between the flexural, bodily, behavior of the tines of the fork and the transduction of this to a cyclic vibration or stress wave passing through the(STEM )(corrected version) and the flexural, standing waves on the string which are transduced similarly by the terminations at the bridge/board and agraffe/capo interface. Robin Hufford wrote: > Hello Sarah, > The "pseudo-longitudinal wave" is, in fact, a true longitudinal wave but it > is a forced vibration and contains the frequencies of the forcing function. It > is the normal mechanical wave or density fluctuation passing through a medium > as the particles of the medium oscillate around their equilibrium positions in > the waveguide which, in this case, is mostly the continuing portion of the > string threaded across the bridge, the bridge itself, the bridge pins, or the > part of the wire passing through the agraffe, along with the agraffe, Capo bar > and plate. This is not a variation in tension but, rather, again, a density > fluctuation passing through the medium with a wave velocity which is a function > of the inertial and elastic properties of the medium itself, imposed upon this > is the frequency and extent or lack of periodicity. > This can be viewed in another way and that is as a state of cyclic stress > passing through the medium. > Not to be too repetitive on the list as this has been thoroughly explored > in the threads referred to earlier, although vehemently disagreed with by others > here on the list: this can be easily comprehend by considering the behavior of > a tuning fork. The tines oscillate back in forth at a right angle with regard > to the stem. Their flexural, oscillating, bodily behavior is mechanically > transduced to a cyclic stress, strain, or density fluctuation, as you will, > which is a forced vibration passing along the bass and stem of the fork. When > placed in contact with the bridge, and it matters little where, this vibration > then passes into the bridge and board where reflexion, superposition and its > attendant interference, both positive and negative create distortional and > dilational waves in the board itself; momentum is then radiated away as acoustic > radiation. Precisely the same thing happens with the vibrating string itself: > the standing waves are enabled by the, essentially, rigid termination > mechanisms which transduce the strain energy associated with the standing wave > behavior in the wire into forced longitudinal vibrations at the terminations. > There is a reasonable analogy to drawn between the flexural, bodily, > behavior of the tines of the fork and the transduction of this to a cyclic > vibration or stress wave passing through the tines and the flexural, standing > waves on the string which are transduced similarly by the terminations at the > bridge/board and agraffe/capo interface. > The longitudinal wave energy, at the frequency of the forcing function, > passes into the bridge with out need of flexion, although I have never argued > that flexion is completely absent for several reasons, and, crosses the bridge > and continues along the duplex where again, reflexion and superposition create > audible, tunable vibration. > I don't know whether these segments increase sustain or not, although, I > have no doubt that, in some cases, the difference in total sound, as I said in > the previous post, increases the perceptibility of the note produced by the > speaking length, possibly in a kind of gestalt/figure interaction. This would > be very difficult to pin down, accurately. > This view, which is rather unpopular here, requires a subtle distinction to > be drawn between the flexural, bodily behavior of the vibrating portion of some > object or structure, and the nature of wave motion, or, again, localized > density fluctuations which pass through a medium and do not require actual > bodilty motion of the medium itself for their propagation. These are just the > normal, ordinary mechanical waves encountered everywhere. The function of the > soundboard and bridge stabilize the endpoints of the string and allow the > transduction through mode conversion of strain energy of the standing waves > which are of course, primary, but, in another sense secondary phenomena. > Regards, Robin Hufford > > Sarah Fox wrote: > > > My other attempted post, accidentally directed to Robin Hufford in > > private... > > > > ----- Original Message ----- > > From: "Sarah Fox" <sarah@gendernet.org> > > To: "Robin Hufford" <hufford1@airmail.net> > > Sent: Monday, November 18, 2002 3:35 AM > > Subject: Re: S&S D Duplex > > > > > Hi Robin, > > > > > > OK, thanks for explaining the "longitudinal" wave to me (i.e. which isn't > > > really a longitudinal/compression wave at all). Steinway's "longitudinal" > > > wave, if I understand you, is little more than the variation in tension of > > > the wire as it vibrates, resulting in lateral forces (in direction from > > > tuning pin to hitch pin) across the bridge. Correct? I would think there > > > must also be some transverse (e.g. vertical) vibration in order for > > cyclical > > > tensional variations to result in any sort of string vibration. Really I > > > view the pseudolongitudinal wave (as you explain it) as yet another aspect > > > of a transverse wave. Of course I'd need to think about it... and my > > brain > > > doesn't work all to great at this time of night. <yawn> > > > > > > I suppose I would still echo Del's concern: Does a pseudo-longitudinal > > wave > > > travel to the duplex segment through the wire or through the bridge? I > > > would argue that unless the string slips freely on the bridge pins, which > > it > > > clearly doesn't, that the bridge would have to move in order for > > vibrations > > > to pass into the duplex segment. I don't think there's anything magical > > > about it. On either side of the bridge, we're still talking about > > > garden-variety transverse waves, which are tunable in every sense to which > > > we have grown accustomed. > > > > > > As I see it, the fundamental questions are still: > > > > > > (1a) Does an unmuted duplex segment increase sustain? (1b) Does the > > tuning > > > of an unmuted duplex segment affect sustain? > > > > > > (2a) Are the tonal effects of a duplex segment desirable? (2b) How does > > > this differ between tuned and untuned? > > > > > > The first question can be answered quantitatively. The second is a > > > subjective matter, not unlike the age-old argument as to whether a large, > > > echoing concert hall sounds better than an "anechoic" chamber -- or vice > > > versa -- or some compromise inbetween. Different strokes for different > > > folks. > > > > > > Anyway, thanks for explaining what is really meant by this "longitudinal > > > wave" thing. It makes much more sense now. > > > > > > Peace, > > > Sarah > > > > > > > > > ----- Original Message ----- > > > From: "Robin Hufford" <hufford1@airmail.net> > > > To: "Sarah Fox" <sarah@gendernet.org>; "Pianotech" <pianotech@ptg.org> > > > Sent: Monday, November 18, 2002 3:35 AM > > > Subject: Re: S&S D Duplex > > > > > > > > > > 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 > > > > > > > > > > > > > > > _______________________________________________ > > pianotech list info: https://www.moypiano.com/resources/#archives > > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives
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