Reed math, a question?

[ttonon]

Hi Dana,

 

I must apologize for an error I made in my last post. My statement that "any deviation from sinusoidal motion of the reed tongue would necessarily be caused by the excitation of multiple vibrational modes of the tongue" is incorrect, and arose from my own confusion between the time and space dimensions. For my own benefit and for our discussion, I think it's best to keep in mind differences between the time dependent motion (frequency spectrum) of the vibrating reed tongue, the spatial dependency of the tongue's beam mode of deflection, and both the frequency spectrum and spatial dependency of the pressure pulses in the acoustical sound field of the air vibration.

 

I attached one of Cottingham's short papers on the subject, which I think illustrates many of these processes. I haven't used attachments before, and I hope it works. Anyway, note Figure 3, which shows the time dependency of the vibrating tongue at normal blowing amplitude, and at least by eye, illustrates a very smooth sinusoidal behavior. This figure also shows the time dependency of pressure pulses at a point upstream of the tongue, and at a point downstream, in the reed cavity. The point upstream clearly shows distinctive pressure pulses associated with the on-off valve effect of the tongue, and the point downstream illustrates how complex resulting air pressure pulses can become within the reed cavity.

 

The tongue, in its up and down motion through the slot, not only imparts pressure pulses to the acoustic field, but as you recognize, also experiences forces from the resulting complex air motion about the tongue. These aerodynamic forces, in principle, do affect the time dependency of the tongue's motion, and also tend to excite higher modal (spatial) vibration in the tongue. Thus, Figure 4 shows the spectrum of the time dependency of the tongue's motion, for a blowing pressure that is significantly larger than that normally used. This figure indeed shows the presence of higher harmonics in the tongue's time dependent motion, but, keeping in mind that the ordinate is expressed as a log scale, these higher harmonics are confined to only about 10 percent of the tongues motion. It seems to me that such a small alteration of the tongue's time dependent motion would have a minor effect on the main acoustic field indicated in Figure 3 - even when the reed is blown at excess pressures. Also in Figure 4 is shown an even much smaller - three orders less - contribution to the tongue's motion made by the second vibrational mode. A degree of departure from sinusoidal motion obtainable by strong over blowing is also illustrated in Figures 6a and 6b.

 

Thus, for normally blown reeds, sinusoidal time dependency seems to be the rule, and the on-off valve effect defines the origin of the acoustic field. Although it may be true that an extremely loudly blown reed tongue would experience time dependent motion significantly differing (say, at most, up to 20 %) from sinusoidal, the on-off valve effect will still be a major influence on the resulting acoustic field.

 

Best regards,

Tom

[Dana Johnson]

Hi Dana,

 

I must apologize for an error I made in my last post. My statement that "any deviation from sinusoidal motion of the reed tongue would necessarily be caused by the excitation of multiple vibrational modes of the tongue" is incorrect, and arose from my own confusion between the time and space dimensions. For my own benefit and for our discussion, I think it's best to keep in mind differences between the time dependent motion (frequency spectrum) of the vibrating reed tongue, the spatial dependency of the tongue's beam mode of deflection, and both the frequency spectrum and spatial dependency of the pressure pulses in the acoustical sound field of the air vibration.

 

I attached one of Cottingham's short papers on the subject, which I think illustrates many of these processes. I haven't used attachments before, and I hope it works. Anyway, note Figure 3, which shows the time dependency of the vibrating tongue at normal blowing amplitude, and at least by eye, illustrates a very smooth sinusoidal behavior. This figure also shows the time dependency of pressure pulses at a point upstream of the tongue, and at a point downstream, in the reed cavity. The point upstream clearly shows distinctive pressure pulses associated with the on-off valve effect of the tongue, and the point downstream illustrates how complex resulting air pressure pulses can become within the reed cavity.

 

The tongue, in its up and down motion through the slot, not only imparts pressure pulses to the acoustic field, but as you recognize, also experiences forces from the resulting complex air motion about the tongue. These aerodynamic forces, in principle, do affect the time dependency of the tongue's motion, and also tend to excite higher modal (spatial) vibration in the tongue. Thus, Figure 4 shows the spectrum of the time dependency of the tongue's motion, for a blowing pressure that is significantly larger than that normally used. This figure indeed shows the presence of higher harmonics in the tongue's time dependent motion, but, keeping in mind that the ordinate is expressed as a log scale, these higher harmonics are confined to only about 10 percent of the tongues motion. It seems to me that such a small alteration of the tongue's time dependent motion would have a minor effect on the main acoustic field indicated in Figure 3 - even when the reed is blown at excess pressures. Also in Figure 4 is shown an even much smaller - three orders less - contribution to the tongue's motion made by the second vibrational mode. A degree of departure from sinusoidal motion obtainable by strong over blowing is also illustrated in Figures 6a and 6b.

 

Thus, for normally blown reeds, sinusoidal time dependency seems to be the rule, and the on-off valve effect defines the origin of the acoustic field. Although it may be true that an extremely loudly blown reed tongue would experience time dependent motion significantly differing (say, at most, up to 20 %) from sinusoidal, the on-off valve effect will still be a major influence on the resulting acoustic field.

 

Best regards,

Tom

That was an excellent piece of writing and very clear. It made me laugh to see the setup used in the PDF file you attached. It is essentially identical to what I did my first experiments on back in 1995 including the laser vibrometer. The only thing I wish to point out is that the seemingly sinusoidal reed velocity / time waveforms are quite visibly biased toward the sawtooth with the leading and trailing slopes being visibly different angles. This isn't an insignificant deviation with regard to the harmonic content needed to create that change. However the resulting difference between the reed's motion and the effect of that motion on the pressure pulses is clearly orders of magnitude different. That the reed acts as a valve isn't in question, What I feel is significant is the difference in timing of the pressure pulse on the up swing vs. the downswing where a small timing difference in reed motion and velocity has an amplified effect on the pressure pulse depending on the magnitude of the pressure involved. I haven't given this anywhere near enough thought, though it has always seemed to me that the difference between the up pulse and the down pulse helped to explain why we simply didn't perceive the sound as an octave above the fundamental of the reed itself since the valve is closed twice per cycle of the reed. If the pulses were equal as in a air siren the frequency would be simply equal to the number of pulses / sec. where for the air blown free reed it is half that. What I find interesting is that the second harmonic is often not the strongest harmonic. ( In my concertinas it is the third harmonic that dominates after the fundamental. ) Lots of questions that I wish I had more time to pursue, but sadly that sort of experimenting doesn't get concertinas made ( at least in any reasonable time ) and I'll have to leave it in the capable hands of the people who work in situations that support the research. It is always good for those folks doing the experimenting to have a hand in making some instruments since I have found in the process of making concertinas that many assumptions I and others had did not measure up to experience. The proof is in the pudding and you don't ever really find out if your idea is on the right track without actually trying it out. As a maker, I am primarily interested in information I can use to adjust the sound of my instruments. There have been many surprises along the way and more to come I'm sure.

Best Wishes,

Dana

[ttonon]

I haven't given this anywhere near enough thought, though it has always seemed to me that the difference between the up pulse and the down pulse helped to explain why we simply didn't perceive the sound as an octave above the fundamental of the reed itself since the valve is closed twice per cycle of the reed.

I agree. The misconception that the musical tone has a fundamental frequency twice that of the vibrating tongue surely discounts the sophistication of our ear/brain hearing system. The true state of affairs does however reflect how remarkable our hearing system really is, and even a very slight difference between the two air pulses is detectable by our hearing system. The two pulses would have to be very nearly exact for the ear to detect the multiple frequency. We of course realize that the musical tone originates from two pulses of air per cycle, but the acoustic pressure field that results loses that information. Said another way, there are an infinite number of ways the acoustic pressure field can be synthesized, but there’s only one way to analyze the result in the way our hearing system does it. This method of analysis is that of Fourier, in which the pressure waveform striking our eardrums is mapped onto a frequency/amplitude spectrum (domain), and there’s one unique solution for this. Thus, our hearing system is presented with a waveform without any information how that waveform came about, and it processes it as it does any other wave form. With this method of analysis, the period of oscillation is an important parameter, and once it has been determined, the overall spectrum is defined. Only a very slight difference between the two major air pulses is enough to make known the longer cycle period to our hearing system, and it very accurately identifies the period of oscillation with the vibrating tongue. I’ve satisfied myself of this outcome by taking a sinusoidal wave form, and by means of audio-editing software, changed the sign of the negative part of the wave, thus making it positive, leaving a humped waveform with on-half the period (twice the frequency) of the original. Upon playing this waveform through a computer, I indeed hear a musical tone with twice the frequency of the original tone. However, the sound of the flipped wave does necessarily sound much more complex than a pure tone, because of the infinite amount of overtones such a waveform necessarily contains – according to Fourier. But then I made the same very small change in every other one of the humps on the flipped wave form, thus defining a cycle period twice as long, though equal to that of the original sine wave. The amount of changes required in order to produce the perception of a tone with the same fundamental as the original sine wave was very small. Interestingly, the passage from a sound of double frequency to original frequency was, for lack of a better word, "continuous," a feature made possible because of the large number of harmonics in the mathematically altered waveform. These harmonics greatly confuse just what octave the musical tone actually is.

 

There are indeed other interesting features in the figures of the Cottingham reference. I’m interested by how smooth the pressure waveform above the reed is, in comparison to the one below. It’s my own experience that – quite remarkably - the sound of the musical tune on one side of a free reed is very similar (but not identical) to that on the other side, and this similarity seems to contradict the very different waveforms measured. My conclusion here is that the airflow during the pressure measurement of Fig. 3. is from the bottom up, and that the microphone above the reed is placed inside the exit region of the jet formed when air pulses through the slot. This pressure trace is thus not that of the oscillatory static pressure in the acoustic field, but rather that of the dynamic pressure in the jet region, which serves to very well define the moments in time air flows through the slot.

 

Best regards,

Tom

Edited October 26, 2010 by ttonon

[Dana Johnson]

 

There are indeed other interesting features in the figures of the Cottingham reference. I’m interested by how smooth the pressure waveform above the reed is, in comparison to the one below. It’s my own experience that – quite remarkably - the sound of the musical tune on one side of a free reed is very similar (but not identical) to that on the other side, and this similarity seems to contradict the very different waveforms measured. My conclusion here is that the airflow during the pressure measurement of Fig. 3. is from the bottom up, and that the microphone above the reed is placed inside the exit region of the jet formed when air pulses through the slot. This pressure trace is thus not that of the oscillatory static pressure in the acoustic field, but rather that of the dynamic pressure in the jet region, which serves to very well define the moments in time air flows through the slot.

 

Best regards,

Tom

What a lot of fun this stuff can be! Regarding your the above comment, I'm not sure what to think. It seemed that the mike above the reed is on the positive side of the air flow since this kind of free reed doesn't operate from the neutral position ( unlike the reed in a sheng) so the "flow" will be going down through the reed. The Pressure pulses however probably propagate in both directions when the valve closes. What happens then I haven't a clue except that the acoustic environment inside the chamber vs outside is very different with very different wave impedances. I don't know how that would affect things. A year or so ago I was looking at the airflow through a reed with a smoke stream and a strobe and was interested that even then the reed motion was stopped or made very slow by the strobe, the air flow through the window was remarkably smooth and undisturbed by the presumed passing of the reed. I had mistakenly assumed I'd see some disturbance. At the time I was just curious about what was happening, and I didn't have a clear chamber to see what happened in there so could only observe the air stream above the reed and at the reed window. Partly from that, I am presuming for the time being that the sound propagation is through the airstream superimposed on it. The strobe simply wouldn't pick up the density variations. This all may be obvious to you since I think you have more experience in this sort of area.

Incidentally for what it is worth Arthur Benade ( may his name live forever ) has an interesting discussion of the heterodyne process on the formation of the harmonic series of the air driven reed. ( Fundamentals of Musical Acoustics 14.1 - 14.3 )

Best wishes,

Dana

[ttonon]

Hi Dana,

 

While it’s true that the harmonium, the instrument from which Cottingham’s reed was taken, operates in only one air flow direction, I doubt that the experimenters did their measurements with the reed assembled into the musical instrument itself. My guess is that they built an air delivery system that can be easily and accurately controlled, and this system would necessarily contain some sort of cavity over which the reed is mounted. The mounting of course can be freely chosen, and it’s thus very possible it was chosen such that air flow went from the cavity through the reed. On this subject, I emailed Cottingham my question, but so far I haven’t heard from him.

 

I find your observation on air flow visualization very interesting. It’s very likely that the tip velocity of the vibrating tongue is comparable to the jet velocity of the steady (time average) air stream through the reed slot. This can be easily verified by calculation, and I think others have measured such a result. Thus, when the tongue is moving in the direction of the mean flow, it’s not too surprising that little air flow disturbance is observed when the tongue passes through the slot. In this case, the tongue passes through the slot, generally moving along with the air. When the tongue moves against the steady stream, however and like you, I’d expect quite a bit of disturbance, with much turbulence. As usual, one experiment leads to many more interesting questions, suggesting further experimentation. There are results available from other experimenters on this matter, and hopefully I can look into it a bit more and post here when I have more time to do so.

 

I certainly share your respect for Arthur Benade and read with great interest the book you mentioned. I myself strongly recommend this book to anyone who experiences any enjoyment for understanding how musical sounds work. In this book, Benade has written a rigorous, basic, and comprehensive description of musical acoustics, with very little recourse to mathematics, focusing primarily on basic physics and intuitive understanding – a much desired method of teaching, particularly for engineers and those with a “hands-on” feel.

 

It’s my understanding that the heterodyne frequencies generated in waveform overtones are inherently associated with non linear effects – effects that are not only present in many musical instruments, but also in our own hearing apparatus. Benade gives a good description on the miraculous capability of our hearing system in this regard. I believe in the last couple decades or so, much progress has been made in understanding these non linear effects in musical instruments; e.g., I think only recently has it been firmly established that the “brassiness” sound associated with brass instruments played at loud volume is associated with a nonlinear coupling of the air column with the coupled reed (lips of the musician). Nonlinear coupling between the beating reed and the air column of the clarinet has also been shown to have significant effect on the instrument's regimes of operation - that particular set of harmonic structure that defines the musical tone. Concerning free reeds, however, I see little reason for such nonlinear effects in the tongue vibration to have much of a role in the musical tone, and I say this mainly because we do not hear directly the tongue vibration itself, but rather a chopped airflow produced by this vibration. Here again we see how unique the free reed instrument is, comparing it to other reed instruments. The Cottingham results do seem to support this view, in illustrating indeed how small nonlinearities affect the tongue vibration (non-sinusoidal vibration). I can of course be making an oversight here, but for the moment at least, I can’t see that the coupling between the non-sinusoidal aspects of the vibrating reed and the acoustic field is strong enough to allow such nonlinearities to have very significant affect to the musical tone. Of course, I’m not implying that you are suggesting this, and Benade’s discussion is of course fascinating and well worth reading on its own terms, for its underlying physical understanding.

 

Best regards,

Tom

Edited October 28, 2010 by ttonon

[Dana Johnson]

Hi Dana,

 

While it’s true that the harmonium, the instrument from which Cottingham’s reed was taken, operates in only one air flow direction, I doubt that the experimenters did their measurements with the reed assembled into the musical instrument itself. My guess is that they built an air delivery system that can be easily and accurately controlled, and this system would necessarily contain some sort of cavity over which the reed is mounted. The mounting of course can be freely chosen, and it’s thus very possible it was chosen such that air flow went from the cavity through the reed. On this subject, I emailed Cottingham my question, but so far I haven’t heard from him.

 

The Harmonium reed like Concertina and Accordion reeds operate in one direction not because that is the way they are mounted, (though obviously with the back side valve they are restricted to this operation ) but because they simply will not start in the other direction or if manually started will not continue to work. In the Chinese Sheng, where the reed is cut from the reed plate and has zero set, the strong coupling to it's resonator tube allows it to operate either on the suck or blow ( this is a mouth played instrument resembling a cross between a teapot and a squid and about 3000 years old with brass reed/plates ). Without the resonator tube, the "modern" western style free reed relies on the extra kick it gets with the airflow under the tip on the down swing to maintain it's oscillation. That kind of reed will only work with one direction of air flow. You can place a chamber around and over a reed ( like the draw side of a regular concertina), but what is depicted in the apparatus is the equivalent of the press side of a concertina with the chamber underneath the reed.

 

Given that I first read The Fundamentals of Musical Acoustics in the 1970's I'd be mightily surprised if we hadn't learned a thing or two in the interim. The weight ( about 50 lbs.) of my first wave analyzer compared to my current one ( a small portion of a CD Rom ) is an example. I'll defer to your greater knowledge of the current state of affairs regarding sound character In that regard, I'd consider the substantially audible effect of tight reed clearances (.001 or less per side ) on the " crispness" of the tone. In Benade's example, he adds a curved ramp to create the difference between the up swing ( no ramp once above center ) and the ramped down swing after center. In an air driven reed, a similar effect is created by the retarding effect of the airflow on the down swing. The mass of the reed has an averaging effect on the reed's response to this. Considering however that the nature of the reed's passage through the closed part of the window is one of the chief ways the varying tonal effects of different stops that are achieved in reed organs, I think there is likely to be something more potent going on here directly comparable to the nonlinear coupling of the " valves" of brass and single reed instruments. There is also a pronounced effect on a reed that is played with too much pressure that strongly affects it's tone, but I haven't figured out whether this is due to the limiting effects of a now too small pad hole, or the pressure limitations of the reed itself. Cottingnham's reed didn't have the variations of tip design to separate the effect of the short time the reed is closing off or partially closing the window from the rest of it's cycle. This is one place where having an old reed organ manufacturer on hand might shed some light on things and give ideas for good directions to go.

Best,

Dana

[ttonon]

Hi Dana,

 

Yes, I understand the operation of the Asian free reed and its differences with the Western reed, and I agree that your reference to Fig. 1 in Cottingham's paper is a good argument for concluding the air direction to be as you say, and I can very well accept that to be the case, since typical harmoniums do mount reeds this way, with their reeds excited only by vacuum air. I didn’t give as much weight to this figure as I should have, focusing mainly on an explanation for one of the things that puzzles me about Fig. 3. But if I might mention another observation about that figure, the magnitude of the pressure oscillations within the cavity is, from the numbers shown, about 136 dB, which of course is quite a loud sound and surprising, at least to me. It’s unfortunate though that the Authors presented the magnitude of the pressure trace above the reed in “arbitrary units,” without explanation, so we really can’t compare pressure magnitudes inside and outside the cavity.

 

Nonlinear effects play a relatively minor role in the operation of string instruments, enabling their effects to be more or less tagged on to a linear analysis. This of course does not mean that their effects cannot be noticed; the stretched scales in a piano being one example. For woodwinds and brasses, however, nonlinear effects are important in understanding just what “regime of oscillation” defines the musical tone. "Regime of oscillation" only means that particular set of harmonics in the air column that make up the tone. For these latter instruments, much of the nonlinearity comes in through the relation between air flow velocity and pressure difference across the reed, showing up as higher harmonics in the pressure response. The air column in the body of these instruments, however, still behaves linearly. This linear response contains a very large number of possible harmonic modes of vibration, much like that of the vibrating string. The reed of a clarinet is further supple enough – operating at a frequency well below its own resonance frequency of vibration – to respond to many of the higher harmonics originating in the mouthpiece, and thus, both the reed and the air column can respond to these higher harmonics. The players lips in the brass instruments respond much less to these higher harmonics, however, the air column can and does. Thus, with these instruments, the presence of a large number of possible (linear) modes of vibration in the air column allows the nonlinearity of the mouthpiece to participate in the regime of oscillation for the playable tone.

 

With the Western free reed, there’s no analogy to the air column, and thus, nonlinearities (higher harmonics) associated with reed tongue vibration have very little outlet to the musical tone. I can see only a limited outlet for these higher harmonics in the way they influence the opening and closing of the “siren” mechanism, and as found by Cottingham and others, this influence appears small. With Asian free reeds, there is an associated air column, and I believe this is the chief reason why the Asian free reeds sound more interesting to me. In fact, the sound of the Bawu to me is reminiscent of the clarinet, and not surprisingly, since the air column is essentially a tube closed at one end. Perhaps in the future someone will experiment with making a keyboard instrument with an Asian free reed.

 

There is also a pronounced effect on a reed that is played with too much pressure that strongly affects it's tone, but I haven't figured out whether this is due to the limiting effects of a now too small pad hole, or the pressure limitations of the reed itself.

 

I also observe that a very large bellows pressure can seriously affect tone. My first guess at a mechanism here would be the fact that, in that part of the cycle in which the tongue emerges from the slot, the overall motion is damped. This arises only because of the nature of the valve-like tongue response to a pressure difference, and in this part of the cycle, the reed becomes an “opening” reed. In other parts of the cycle, the tongue behaves as a “closing” reed, and oscillation is supported (admittance coefficient is negative). There are complications of course involving phase differences, and we do know that harmonica reeds can be forced to support oscillation while acting as opening reeds. My further guess is, however, that accordion and concertina reeds cannot be made to operate in this way. In any event, an implication from my prolific guessing is that thicker reed plates would produce less susceptibility to large bellows pressure and thus support louder musical tones. Does this concur with your experience?

 

Best regards,

Tom

www.bluesbox.biz

Edited November 2, 2010 by ttonon

[Chris Ghent]

In any event, an implication from my prolific guessing is that thicker reed plates would produce less susceptibility to large bellows pressure and thus support louder musical tones. Does this concur with your experience?

 

The prospect of greater bellows pressure introducing a different sound by limiting the upward travel of the reed and also limiting the volume (though volume might be compensated for by the complementary increase in downswing?)makes sense in a non-scientific way, (that is, it sounds right to me!) but I'm not sure about the issue of the thickness of the reed plate. The term reed plate is relevant more to accordions, and perhaps you were thinking of these reeds. In accordion reeds the wind slot under the reed tends towards the vertical. In this instance depth or thickness is more relevant as the reed will be fighting almost the full power of the air at a much earlier point than in a concertina reed. While the amount varies, concertina reeds have the underside of the slot relieved, meaning they are tight at the very top and nowhere else. This allows the air to go somewhere else and lowers the pressure on the upswinging reed until the moment it broaches the aperture.

 

Please do not allow this to impede your discussion which I cannot understand much of, or should I say, I cannot understand enough of.

 

Best

 

Chris

 

This post was edited for stupidity, my own, at least in the amount I could detect it.

Edited November 3, 2010 by Chris Ghent

[malcolm clapp]

 

....Sheng...resembling a cross between a teapot and a squid....

 

 

Another mouthful of coffee over my keyboard!

[Dana Johnson]

In any event, an implication from my prolific guessing is that thicker reed plates would produce less susceptibility to large bellows pressure and thus support louder musical tones. Does this concur with your experience?

 

The prospect of greater bellows pressure introducing a different sound by limiting the upward travel of the reed and also limiting the volume (though volume might be compensated for by the complementary increase in downswing?)makes sense in a non-scientific way, (that is, it sounds right to me!) but I'm not sure about the issue of the thickness of the reed plate. The term reed plate is relevant more to accordions, and perhaps you were thinking of these reeds. In accordion reeds the wind slot under the reed tends towards the vertical. In this instance depth or thickness is more relevant as the reed will be fighting almost the full power of the air at a much earlier point than in a concertina reed. While the amount varies, concertina reeds have the underside of the slot relieved, meaning they are tight at the very top and nowhere else. This allows the air to go somewhere else and lowers the pressure on the upswinging reed until the moment it broaches the aperture.

 

Please do not allow this to impede your discussion which I cannot understand much of, or should I say, I cannot understand enough of.

 

Best

 

Chris

I do find that in concertina reeds at any rate, thicker reeds will support higher pressures and reach higher volumes, but as to the plates (or depth of the reed window ) I have found that a plate has to be quite thin before it reduces volume noticeably ( if not perhaps measurably ). I wondered about this at one point and increased the thickness of my lower reed shoes ( low C on a C/G concertina to C two octaves above that ) to 1 1/2 times their original thickness with no noticeable result other than an increase in weight. I later changed back to my current thickness for all my shoes of .063" which is about .010 " thinner than normal wheatstone shoes. I think there is a minimum window depth that is proportional to reed length (as evidenced by the very deep cast plates of bass accordion reeds that are nearly 1/2 inch deep. The controlling factor I think is the depth where the arc of the reed swings away enough from the end of the window to dump sufficient air to the point where the air flow no longer counters the increasing tension of the reed on the down swing. As Chris mentions Accordion reed windows being vertical or nearly so may behave a little differently than concertina reeds with their varying back relief angle.

The sound difference I was thinking of is one that also results with too small a pad hole ( the proportion of which seems to vary with other factors I haven't been able to understand yet. ) (The point at which the effect doesn't occur is how I now choose my pad hole sizes with an interesting improvement in tone when the hole is just big enough. ) I also wonder if the greater pressure on the reed on the part of the upswing before it rises substantially above the top of the reed plate doesn't make the upswing slower than the down swing with the pressure working in the same direction and that this difference is amplified at higher pressures effectively flattening the reed pitch as well as amplifying the difference between down swing and up swing and the resulting harmonic content of the pressure curves.

The problem I always run into is that too many of the parameters of the acoustic path seem interconnected in such a way that conducting experiments on any part of the set up can give misleading results when we think that one thing is happening and don't realize it is an artifact caused by an interaction with another part of the system. AS an example, I changed my tuning apparatus at one point and noticed ( without associating it to the change ) that my reeds around G-G# above middle C especially around two octaves above middle C were slow to start and required more pressure than I'd remembered. At A and above or F and Below, they seemed to be normal again. Not having changed my reed profiles I was at a loss as to what was going on, especially since I didn't notice any trouble in the instruments when assembled. I finally figured out that my new tuning set up had a resonance between G and G# that was sucking energy out of the reeds at that frequency range.

Things like the powerful effect of a chamber on a reed, position of the pad hole, thicknesses of the different parts and the material they are made of etc. all feed back to the reed in ways that interact, making isolation of any factor quite difficult. AS a result I've found myself limited to saying things like " when I do this, this seems to happen" and any attempt at explaining it ends up being little more than conjecture.

I'm not willing to accept Chris's remark about his editing of his reply. I know him well enough to know that he is a very sharp guy who I've learned a great deal of valuable stuff from over the years. That he takes the time to reevaluate his thoughts as he puts them down and can see flaws in his reasoning is a mark of this, and I'd much rather he allow his thinking some freedom from "correctness ". More than once, it has led us to interesting discoveries.

Dana

[ttonon]

The problem I always run into is that too many of the parameters of the acoustic path seem interconnected in such a way that conducting experiments on any part of the set up can give misleading results when we think that one thing is happening and don't realize it is an artifact caused by an interaction with another part of the system......

 

...AS a result I've found myself limited to saying things like " when I do this, this seems to happen" and any attempt at explaining it ends up being little more than conjecture.

 

Dana, I appreciate your honesty and candidness. I myself find the operation of the free reed very puzzling, and I’m at a loss to explain the physical details by which it operates during it’s full cycle of vibration. I’m aware of the explanations you can find on the web, which typically allude to a “Bernoulli Force,” but nowhere have I found a description that I think is satisfactory. Any adequate physical explanation must necessarily include fluid dynamical principles, but invoking the name “Bernoulli” for only a part of the cycle for me isn’t sufficient.

 

In the scientific literature, there has been some progress at physical understanding, and I think it will continue; however, as you might expect, such progress has heretofore been made with sacrifice to the most simplifying assumptions. For me anyway, it thus remains to be seen how solid this apparent progress really is. One of the most rigorous and fundamental of studies to date is presented in a 2004 paper by Ricot, Causse, and Misdariis, in which the stated intention is precisely to identify the self exciting forces that maintain the vibration, as well as to explain the mechanism for conversion of the vibratory pressure pulses to a musical tone. Furthermore, theoretical and calculated results are compared with experimental measurements, and the agreement is quite good. For me, however, I have not yet satisfied myself on just how well the study does explain the self exciting forces – during the complete cycle - and this may be simply because of my own confusion on the terminology used in the paper, but even worse and from my own point of view, I find some of the explanation in this paper apparently self contradictory. The language in the paper is a mix of that of an acoustician and that of a fluid dynamicist. I’m more comfortable with fluid dynamical approaches and so I’m not too surprised by the confusion I come away with.

 

I don’t think it’s necessary to discuss all the details of this paper here, but I do think it useful to state what I think is one of it’s main conclusions; i.e., that the typical “Bernoulli” force present in so many models of reed motion cannot – and does not - sustain the free reed tongue vibration, but rather, certain “inertial” terms present in a more general formulation of the fluid dynamical momentum equation can and do. This conclusion is backed by reasonable agreement with experiment. For anyone curious about such scientific studies of their beloved free reed music maker, I attach this paper, below.

 

Another reason for attaching this paper is that it presents pictures of a flow visualization, which serve as some justification of the model assumed for the mathematical analysis. I note this at least for Dana, because of his interest and previous experiments with smoke visualization. In the paper, however, the authors power the reed by water flow, which is perhaps easier to visualize. One interesting thing about their pictures is that the leaking gap between the tongue and the sides of the slot admit substantial water flow, preventing a complete shut-off when the tongue is passing back up through the slot. I draw attention to this as a possible explanation why Dana did not see an obviously intermittent flow of smoke as the tongue passes in and out of the slot.

 

The authors of the paper use the results from the water reed to justify their assumption that jets are formed as air escapes around the tongue and into the slot. Such an assumption allows a great simplification of the governing flow equations, allowing you to say that the pressure on the underside of the tongue is equal to the static pressure under the reed. From my own experience, such a conclusion can be valid only if the residence time of the air passing around the reed and into the slot is small compared to the period of oscillation. In other words, for certain frequencies below a maximum, this assumption will be valid, but for reeds operating at higher frequencies, it would not be a good assumption. In these latter cases, the flow field is inherently unsteady, and a “quasi-steady” application of the Bernoulli Equation (jet formation) is not permissible. I’m very surprised that the authors did not present an order of magnitude analysis that would indicate at least approximately where this critical frequency lies. The reed for their analysis does of course have a relatively low vibrating frequency.

 

Chris, during the short time that your discussion group for concertina builders had life, I presented my own order of magnitude analysis for the existence of jet motion, and if I remember correctly, I concluded that the dividing frequency is around a thousand Hertz. This of course cannot be a precise number, but it does lead me to suspect that both flow regimes (jets and no-jets) exist within the concertina range of musical tone.

 

Dana, if it is indeed true that both regimes can be found, I’d expect that there could be something different in the operation of higher frequency reeds from the lower frequency reeds. I’d guess further that the effect of the angled sides on the slot (vent) could show up in this regard. For the low frequency reeds, I’d guess that angling has little effect, because the jet really wouldn’t know it’s there (the flow separates from the wall). For the high frequency reeds, however, with no jet, the angled slot causes the unsteady pulse of air to flare out, inducing more air vibration downstream of the slot. Even though, it’s still not clear what you might observe, even if all this guessing is valid. For instance, the additional air vibration may only add to the effective mass of the vibrating tongue, causing only a lower frequency of vibration than otherwise. Thus, you would then simply tune out the effect and never be aware of it. It's already widely accepted that free reeds operate at a frequency slightly lower than their plucked, or truly "free" vibration, and the main reason for this is the inertial loading, caused by the vibrating air mass. On the other hand, the flare could possibly affect the frequency spectrum of the musical tone. Thus, should you find yourself with nothing else to do, you can compare two high pitched reeds, identical except that one has a slot flare and the other does not. I am being facetious here, since I’m well aware of the time such experimentation eats up.

 

Dana, concerning the effect of the mean air flow on reed operation, particularly when such flow is very high, I again must plead ignorance. From Fig. 6b in the Cottingham paper, there is indeed verified an influence on the tongue vibration itself, apart from any effect due to pad holes. In this figure, nonlinear motion (higher harmonics) of the tongue increases, and the mean (equilibrium) position of the vibration moves downward, in the direction of the air flow. In fact, it looks to me that the upward movement of the tongue, counter to the air flow direction is squashed. I’d venture a guess that any free reed would choke with sufficient air flow, and it would not be difficult to explore the issue experimentally.

 

Along with Dana, my experience has led me to understand that Chris has, in addition to acute physical insight, exceptional virtues of curiosity, open mindedness, and the ability to encourage cooperation among people with very different perspectives. All these qualities add very much to my experience while reading from this group.

 

Tom

www.bluesbox.biz

[Dana Johnson]

I just downloaded the paper and will spend a while with it before I say much more. A couple thoughts though. First regarding "choking" of reeds, I think you are likely right that reeds should choke given enough pressure unless something else comes into play, and it may simply be the case that in concertinas once a reed has a certain amount of strength, the choking range simply goes beyond the pressures we can generate without bursting the bellows or reaches some self limiting flow rate below choking range. Since for "normal range " reeds, "set" can determine whether a reed will or won't choke under any playing pressure, there seems to be a relationship between the bias of the reed and the reed "gain" as it were. If the bias is high enough they don't choke ( at least anywhere near as easily )

 

The other thought I have on the spot is that while I think it is very cool to have a water driven reed, water and air have very different physical properties especially acoustically, not just relating to density, but to compressibility. I am not sure if there are many conclusions you can really dare carry over from one model to the other. But I still have a lot of reading and pondering to do.

More later.

Dana

[Michael Marino]

Wonderful discussion and very fertile ground for thought and experimentation. Good news news is I have found a source that is affordable in small batches of PB102 Bronze which is one of the forms of vocal bronze (referred by some as bell metal bronze, though it is not the only type used for that art/science). Bad news is PB103 or 104 requires orders in the half metric ton minimum unless you buy from a stockist and if they have it and you can count on the price going up by over 100% and still having to buy a rather large volume. have found some wonderful texts dealing with frequency and vibration from the engineering side of things and will move forward there.

 

 

Mr. Benade is most definitely a place to start. Though he does admit that further research is needed in his writings; the sad part is that it is only in the last 10 yrs that research has really started to take off and there is still large sections that are poorly understood. As both of you gentleman have pointed out so well in this discussion. I know there are going to be a few who look at the fact that I am using Bronze and not brass and say too brittle. Before doing so go look up the properties of PB102 and you might be surprised. Other progress is getting 80% done with cutting out one of the designs I have done for fretwork and realizing that I really don't like the way it sets and that being so have set about reworking sections, which now done waits for me to finish client work to start cutting again.

 

On the reed front have been mapping the shapes and frequencies of accordion reeds and think I have found the type of vocal steel they are using (there is more than one of those as well) and will be able to look at what type of density i will need for the harmonica reeds and who knows I might type putting a tongue in a few of the old empty shoes that I have though finding a way to insure that the clamp will hold after loosened to remove the last bit of broken reed is going to be interesting.

 

Have a Veterans/Remembrance/Armistice Day and take a moment to reflect on what we owe those who gave their lives for our societies, better yet think on how we can make society a little bit better as a tribute to them.

 

Michael J. Marino, DC Sgt USAR Retired

[Dana Johnson]

I've been through the paper once and am getting ready for the second round. (Take heart, Chris, the difficulty in understanding it is not your fault. perhaps people who are used to this format manage it better, but it lacks so much in explanation there is very little that is really clear.) So far it seems like there are a lot of assumptions that I don't feel they should make. They seem to not understand from what I can see that the reed will only operate with the flow in one direction though they say that in accordions they are only used that way. This alone makes me feel they have missed something very important. No mention of reed set and it's effects and the requirement for it. No analysis of the transient starting motion, only steady state operation which tells you little about what initiates the motion. The Dye streams are at the sides of the reed, and the tip where motion is greatest and the air flow is greatest is avoided to eliminate any 3D effects simply because they are too hard to handle. How they can draw any conclusions about the driving forces without taking that into account I don't understand. You can't discount something simply because it it too hard to calculate. That their model produces results that are a simplified approximate match for actual accordion reeds might tell you that they have a reasonable approximation of an oscillator that produces similar results, but it doesn't explain much. In astrophysics they usually think data is in agreement with theory if it is within a few orders of magnitude of predictions, but for reeds, just being within the same order of magnitude needs to be more refined. Water being a much denser medium containing a lot more power, may be able to drive reeds in ways that air cannot. My experience shows that reeds are actually quite sensitive to their surroundings, and are not at all effectively driven in the more or less chamberless manner they show. The impedances the reed has to deal with on the input and output sides can determine if the reed will or won't start at all. Water driven reeds might be overpowered into running in less ideal conditions where air driven reeds simply won't start or if manually set in motion won't continue. I don't want to discount the work which raises interesting ideas, but I hardly think they should say they have solved things yet.

Dana

[Ken_Coles]

In astrophysics they usually think data is in agreement with theory if it is within a few orders of magnitude of predictions, but for reeds, just being within the same order of magnitude needs to be more refined.

 

That's why my job is easy! All I have to do is know how to point the telescope at the right star.

 

Ken

(astronomy teacher)

 

Good luck with this topic gents, you should be academics, all of you.

[JimLucas]

In astrophysics they usually think data is in agreement with theory if it is within a few orders of magnitude of predictions, but for reeds, just being within the same order of magnitude needs to be more refined.

That's why my job is easy! All I have to do is know how to point the telescope at the right star.

 

Ken

(astronomy teacher)

 

Good luck with this topic gents, you should be academics, all of you.

Oh no, they're much too smart to be "academics"!

[ttonon]

Hi Dana,

 

Thanks for your very detailed observations, which go much further than what I even hoped for, and I can see that you have a very good physical intuition for mechanical systems and the free reed in particular. You do indeed point out many confusing parts to this paper, as it’s written, though the many problems you see with the assumptions and modeling to me aren’t what I myself find very confusing, and I’m willing to go along with their general approach, out of curiosity to see how well it agrees with experiment. Although I would like to take up your comments, let me say first that my own main point of confusion is the nature of the V^2 term they find to dominate the motion. They attribute this term to “upstream inertial loading,” and that “the delay in the variation of upstream fluid velocity due to the inertia leads to a velocity fluctuation in the reed opening.” They incorporate all inertial effects in the general formulation, then (as I understand), eliminate all inertial terms in the Bernoulli (Momentum) equation because they prove to be very small. I suspect they are using the term “inertia” for the usual (time) acceleration force, as well as for convective (spatial) acceleration. As I mentioned before, acoustician and fluid dynamicist terminology can be quite different, even when describing the same phenomenon. I think my next move for understanding my problem is to fully understand just what his manipulations of the Momentum equation imply, which I haven’t done yet.

 

I fully understand your objections, and they raise good questions. Let me say, however, and as you realize, this paper is written for a community of people that have seen many of these concepts over and over again. Thus, once you’ve gone through an understanding of a particular kind of assumption, you need not go through it again, and, when you read the assumption again in the next paper, you simply accept it. Let me give you some of my own thoughts on the points you raise. And Dana, I realize that, in your second reading, many more things will become clear to you, and you will probably come away from it with a different set of questions. But let me address what we have so far.

 

I agree with you that water behaves as an incompressible fluid in this application, but so does air. This is one assumption that’s very easily understood, and can be stated simply, as, “The compressible effects of air are confined to terms with magnitude of Mach Number squared, when the largest terms are normalized to magnitude of order unity.” This statement is not an assumption, it follows directly from the equations of motion. Thus, let’s say that M^2 is about ten or fifteen percent, then, without loosing too much accuracy, we can throw away those compressible terms, compared to unity. Since M is defined as the ratio of local fluid velocity to the local speed of sound, we are imposing that (v/c)^2 is around 0.1, or that v/c is around 0.3. Since, for atmospheric air, c is around 1000 ft/s, this means that air motion involving velocities less than about 300 ft/s can be considered incompressible; i.e., that changes of density can be, to first order, ignored. When the air is forced through the reed, forming a jet, it’s a simple matter to calculate the maximum air velocity possible in the jet, regardless of how complicated the reed motion is. If the bellows pressure is about a half inch of water column, this means that there’s only sufficient potential energy in the compressed air to accelerate the air jet velocity to at maximum about 47 ft/s (from the steady state Bernoulli equation, which is really the momentum equation, and for this mechanical system, equivalent to conservation of energy equation). We see that this velocity is entirely within the incompressible flow regime.

 

Dana:

They seem to not understand from what I can see that the reed will only operate with the flow in one direction though they say that in accordions they are only used that way. This alone makes me feel they have missed something very important.

 

 

I think they understand very well the construction and operation of the Western free reed, and there are many subtle ways this understanding comes out. It’s in the first paragraph of the Introduction, and inherent in the terminology, classifying the type of reed to be (-,+). In the first paragraph, they say also, “However, in the instrument, the accordion reed only operates in its blown-closed configuration…”

 

Dana:

No mention of reed set and it's effects and the requirement for it. No analysis of the transient starting motion, only steady state operation which tells you little about what initiates the motion.

 

In the first paragraph, they say, “There is a rectangular slot in the support plate immediately beneath the reed.” In the paragraph just below Fig. 1, they state that the offset distance depends greatly on the stationary profile of the reed, and that, for them, it’s less than 0.4 mm. This gap is labeled in Fig. 3. In the paragraph under “B. Application of the Model,” they explain that they set the initial conditions for calculation with the reed position equal to the reed offset. In their calculated results, Fig. 9., the equilibrium position of the vibration looks to be about the same as the equilibrium position for the experimental measurements in Fig. 7.

 

Their analysis involves a numerical method of solution, which proceeds from initial conditions, converging to a steady-state (periodic) oscillation. It is this periodic condition that they are interested in, and for this, the start transient is irrelevant. In other words, the start transient is not unique, but the final, periodic state is unique (which can be proved from mathematical theory), and their goal is to explain how the self excitory process supports only the periodic motion.

 

Dana:

The Dye streams are at the sides of the reed, and the tip where motion is greatest and the air flow is greatest is avoided to eliminate any 3D effects simply because they are too hard to handle.

 

Yes, for the calculations, they chose a part of the reed that is removed from the influence of the tip, which as you say, contributes substantiably to reed operation, but which contains complicated 3-D flow patterns. But is there really any difference in the operation of their region of calculation from that of the tip? Do you expect that a different kind of physics, with different governing equations operate there? I myself don’t think so, and I can accept their simplification as a clever choice in seeking out only the fundamental features. Why complicate the issue with 3-D effects? These 3-D effects might not even be very important in the operation. Said another way, the width of the tip region might be interpreted as a simple extension of the side regions that are calculated.

 

Dana:

How they can draw any conclusions about the driving forces without taking that into account I don't understand.

 

You seem to be assuming that this region contains a different kind of physics than what appears in the model. I don’t think it does.

 

I do, however, share your somewhat irritation on such maneuvers. But after reflection, I think in my case it’s only jealousy – “Now, why didn’t I think of that?” It’s often said that the people who make the biggest strides on seemingly intractable engineering problems, and perhaps any problems, are the ones who see through to the heart of a phenomenon and throw away everything else. I do think this to be often the case.

 

Dana:

You can't discount something simply because it it too hard to calculate.

 

I agree, but in this case, I think the justification is that there’s nothing new going on in the tip area, other than topological effects. Such effects, in other problems, many times prove to affect constants, scaling, and only confined regions, without giving any further physical insight. Yet, it’s also true, that geometry, in other cases, proves to be most intimately linked to the fundamentals. Here’s where intuition comes in, and you’re entitled to what you think.

 

Dana:

In astrophysics they usually think data is in agreement with theory if it is within a few orders of magnitude of predictions, but for reeds, just being within the same order of magnitude needs to be more refined.

 

I think the acceptable level of agreement between theory and experiment depends greatly on the problem at hand, and wouldn’t care to generalize too much. Their calculated results for aerodynamic pressure (Fig. 9b) is spot on - excellent agreement. I don’t see much problem with the fact that their calculated acoustic pressure (Fig. 9c) is orders of magnitude higher than the measured pressure, simply because such a quantity is enormously dependent upon location. For me, it’s agreement among wave forms that is impressive, because they intimately describe the timing of forces, which is a key focus of the paper. No one else, to my knowledge, has done as well, for the free reed, and although it’s not as close as in other analyses involving other musical instruments, I’m well impressed. But as I said, I still fail to come away with a truly intuitive, physical feel for what’s going on. I of course reserve the possibility that the agreement I see is erroneous, or happenstance, but as I say, I do accept that I have more homework to do.

 

Dana:

Water being a much denser medium containing a lot more power, may be able to drive reeds in ways that air cannot.

 

The authors justify the water reed by stating that the Reynolds numbers for both water and air operation are not far off. The Reynolds number is indeed a key scaling parameter in these kinds of flow – a statement backed by an entire culture of investigators. There’s at least one more parameter involving density, but again, if you realize that the flow regimes are both incompressible, this parameter isn’t important. Here’s where sometimes an order of magnitude agreement is valid. The Reynold’s Number experiences extremely large variation among different flow regimes. Sometimes flow with Re around 100 is very similar to flow around 1000. So for me, the fact that the Re numbers are within a hundred percent of each other allows me to pass on their approach, rather than challenging it with an analysis of my own.

 

Concerning your remaining comments, Dana, the effects of surroundings, cavity, start transients, etc., I think that they are all important issues that should be part of an attempt at complete understanding of the free reed. But I think we ought to go easy on these guys. The problem is difficult enough, and if by their cleverness are able to extract an answer to one of the most puzzling aspects of the free reed, then I’d want to encourage them. Even if they fail, their attempt, to me, it’s very respectable. As a hint, let’s say that other work substantiates their results. We are then in a position to study these other issues, such as, for instance, the operation of a free reed mounted over a cavity. Doesn’t “without acoustic coupling” in the title suggest that they might go further with it? My guess is that they may move on to the Asian free reed.

 

By the way and as I'm sure you realize, you are free to contact the authors and tell them what you think. Some authors print their email addresses on their papers, but all list their affiliations. Speaking in general, my guess is that many of them would be very curious what an instrument maker thinks about his/her work, and perhaps would have many questions to ask you. Incidentally, I did try to contact Ricoh a few years ago, but he didn’t get back to me.

 

Best regards,

Tom

Edited November 12, 2010 by ttonon

[Dana Johnson]

Thanks tom for the great reply. You made a lot of stuff clear that probably would be to those the paper was written for. One question I have is when they are referring to reynolds number, what aspects are they applying that to? The window? the gap at neutral, (that varies from zero at the root of the reed to .4 mm at the tip,) or the gaps between the reed and the window as the reed enters which is typically around .019-.025mm. Presumably if they are interested in starting forces then the reed hasn't reached that point yet. But my experience with reeds is that they do not begin with a complete cycle, but build over a period of 20 or 30 partial cycles depending on the pitch of the reed in a decidedly non linear fashion, starting with very small oscillations that increase gradually to a point and then jump dramatically in power / travel at the point where the main harmonics begin to become visible in the sound output. This doesn't seem the sort of thing you would see if a I am curious about this jump where it seems the forces acting on the reed increase in effectiveness if not in amount as well. This would suggest to me that aspects of the geometry that are not reached initially as the reed begins to oscillate have important effects that can't easily be shown by a static flow of dye.

 

I get the compressibility bit now thanks to your explanation. One question about the jets I might have since I think they have amply demonstrated their shape, is whether they contribute to a reduced pressure under the reed by the same mechanism as a vacuum aspirator. No large scale vortex under the reed is needed for that to occur. In the initial stages of oscillation, the only flow is through the jets since the rest of the area is effectively blocked. As the amplitude increases though the shape if not the nature of the flow under the reed I would expect to be changing greatly throughout the cycle. Perhaps they have dealt with this, but I have't been able to decode it.

 

I'd actually be inclined to mostly discount any Bernoulli effects ( as microscopic an understanding of them I have ) in comparison with the entrainment of the fluid beneath the reed by the stream of fluid running through the reed window. When I did the small experiment using smoke instead of dye, there was no tendency for the smoke to flow under the surface of the reed beyond the edge of the opening. Instead, it simply "poured" through the windowing the same manner you's expect air to flow into the end of an open pipe with a large part of the flow coming perpendicular to the window opening. If enough motion was imparted to the fluid beneath the reed by the jets or larger scale flow at higher amplitudes, the momentum of that "plug" might be significant enough to create a substantial vacuum when the flow is blocked as the reed enters the tight portion of the window and flow is effectively cut off. They seem to address something similar to this by having the downstream side of the reed in free air while the upstream side is still water. While this seems to slam the door shut, I wonder if it doesn't simply introduce it's inverse with the lack of inertia of the lower water mass to counter the momentum of the upper mass.

 

The action of the mass of air above the reed is confusing to me regardless. I am not sure to what part of the flow they are ascribing bernoulli sorts of interaction. I can easily imagine the following of the water behind the reed on the down stroke as well as some deflecting sideways over the reed to go around through the gaps, but while the pressure easily can force the reed into the opening, since it is equal in all directions in the + side of the chamber, as the reed moves forward, I'd see most of the water entering the gaps coming from the side since it has no direction change to fuss with. When the water changes direction over the reed as shown in their diagram, whatever change in pressure due to the horizontal part of the flow over the surface would seem to be countered by the need to dump the forward momentum into the reed . Visualizations like mine are easily misled by ideas we grow up with that are often wrong, so I'm only musing here. The Sketch in Fig 5 they have here is a bit misleading since the scale factor is way off for the gap by the reed. The fit of a normal accordion reed is very tight as mentioned above and they show the gap in the vertical and horizontal being about equal when they are really about 20:1 almost all of it being in the vertical until the reed rises to an appreciable height during operation. Since they seem to be driving the reed at or near it's starting pressure at very low amplitude, I'm presuming that the gap doesn't much more than double, which doesn't change things much.

 

I can see the water flowing around the reed, as it resists the pressure, but as it swings back up on the reverse side of the cycle, the idea of it pushing back a huge mass of water in a plug seems essentially impossible if we are dealing with incompressible fluids, where with air it wouldn't be a big issue. That probably isn't what they are suggesting, but I am confused about what's momentum they are talking about. The Jets obviously have considerable momentum in proportion to their size, but the flow over the reed's surface is pretty darn slow in comparison, and only a small portion of that will actually make it into the jets compared to the amount entering from the side direction extending along the surface of the reed plate a little ways. The inertia of the water above the reed seems like a pretty big thing, and I can see a lot of influence on the reed there ( among which they mention the pitch reduction ), but that doesn't seem to be what they thing is driving things anyway. As far as I can see (and I may be missing their point here) the only place they find something that can drive the oscillation is in the out of phase velocity fluctuations and inertial forces being out of phase

 

I am beginning to see I think that they are concentrating on the jets which is after all where the flow ends up for the most part. One thing about what they say that troubles me is that they say that because there is no contact with the lower side of the reed by the upstream water that there is no effect of the water (or air ) on the back side of the reed. Are they suggesting some sort of cavitation occurs? I don't' see the water or air on the back side of the reed detaching from the reed, so it will move with it's own inertia, velocity etc.

 

I also noticed that while they use an accordion reed, they don't use the reed plate ( mounting the reed over a clear plastic window) and their side gaps may in fact be to the scale they have drawn. A normal accordion reed would have to have very high pressure air to operate with that much gap. I also notice that in their picture of the jets, the tip jet is much larger than the side jets even though it represents such a short length in comparison. If a lot more water is moving here, might that be an indication that it might be more important than the side jets and possibly the source of a much larger percentage of the pressure variation readings? But as you say, is it different in kind than the sides? Perhaps, since the physical results are so much different, there is more than one thing at work here.

 

I understand your point about the agreement of their model output with measurements, which does suggest to me that they have latched onto something worthwhile here. This doesn't feel like problem solved yet. The starting transient I mention at the beginning ( which may be different for really gappy reeds compared to musically useful reeds), The difference between tip and side jets, and the fact that efficient reeds are tight reeds, and a lot of changes are made at the tip of reeds (arching, twisting, corner cutting etc )to change the reed's motion at the time it is entering the window, makes me think that it should be looked at to see what is going on. Your point probably would be that while the amounts might be different between the sides and the tip area, the mechanism is likely to be essentially the same for the purpose of determining the driving mechanism. Lots to think about, and thanks for your insight and willingness to translate so well the more difficult parts for my more of a practical and less academic education.

Best Wishes,

Dana

 

PS. the Sheng reed is really cool being made integral with it's reed plate, very flared window walls ( from the cutter used to incise the reed's backside ) zero set, +/- operation and near zero gap. They use a paste of marble dust and copper to fill any gap from the cutting of the reed and break the reed loose creating a close to perfect fit. Another Chinese reed is in the Bawu a reed flute with a reed similarly cut from the plate, but with a set and varying from quite a taper with square tip to a triangular reed with a point at the tip. It only operates in the overblown mode needed to dominate the reed's inherent strength and force it to vibrate in sync with the flute's resonances.