ttonon

Hi Geoff and Stephen, I agree that a certain kind of “bleed” or pressure relief is sometimes required to allow certain high pitched reeds to speak; however, from my own investigations, I would say that the physical mechanism is most surely an acoustical phenomenon, called resonance. The reeds are mounted on cavities, and for certain cavity geometries, resonance can occur at the frequency present in the musical tone. When the cavity is leak proof enough, its resonance can destructively interfere with the self excitation mechanism by which the reed tongue vibrates. The fact that this phenomenon occurs for high pitch reeds is because it’s only those reeds for which the wavelength of the musical tone (or some key harmonic) can become comparable to cavity dimensions. Such an occurrence is partly happenstance, requiring a match between the cavity dimensions and the fundamental (or possibly a first harmonic) wavelength. The bleed is sufficient to leak away acoustic (oscillatory) pressure within the cavity, destroy resonance, and allow the starting mechanism for self excited vibration to occur. For these higher frequencies, the cavity supports most likely either Helmholtz or quarter wave resonance. To view such a phenomenon from the point of view of steady bellows pressure does not include acoustic (unsteady) phenomenon. Concertinas are musical instruments, and the principles by which they operate must inherently be according to the principles of physical acoustics, a fairly well understood science. For a more elaborate explanation of these concepts, including a survey to determine what part of the concertina musical range is susceptible to such choking behavior, and many other acoustical phenomenon involved with concertina operation, please see my article in PICA: http://www.concertina.org/pica/ Best regards, Tom www.bluesbox.biz

Greetings, For those interested, I put up on the web some of my own very first recordings of the BluesBox, when I myself was evaluating two different prototypes, from a musical point of view. The recordings were made on cassette tape around 1997, and while coming across them recently, I realized that technology has evolved to a point where conversion of cassette recordings to digital is now very easily done. I know this group focuses on concertinas, and the instruments played in the recordings were converted piano accordions, but the subject matter is still on topic for the simple reason that the BluesBox technology can theoretically be installed in concertinas. In any event, I hope some here find the sounds interesting. They are unlike any other made by free reed instruments, including the Asian free reeds, and including previous uploads by me. I must add the disclaimer that I'm not a professional musician, so I ask the kinder and seriously interested listeners to please keep this in mind. I never meant these recordings to be regarded as a performance, but rather as a historical technical evaluation of a new musical invention. The recording that uses a bassoon reed with internal mics was made in two sessions, and most of it contains musical explorations of themes around the minor key songs, "Anniversary Waltz," and "Two Guitars," as well as experiments with both slow and fast blues. I really can't explain why I chose the two minor key songs. I suppose they were the first thing to come to mind, and perhaps they also lend themselves easily to the kind of pitch bending experiments I was capable of. I do want to emphasize that I had next to no previous experience with the invention. Thus, I ask the listener to have some patience with my learning curve that transpired as the tape rolled. I think you'd agree, the learning curve is very steep. Even though I do return to familiar themes, new bending experiments occur throughout both tapes, as I found new bending ideas to explore. Thus, I encourage the truly interested listener to bear through the slack periods in order to discover more new and different musical rewards further on. The links are: bassoon reed with internal mics. Minor key melodies, slow and fast blues: http://www.sendspace.com/file/6q7qa9 midrange reed with SM58 acoustic mic. Acoustic blues, with vocal: http://www.sendspace.com/file/rbazm5 Best regards, Tom www.bluesbox.biz

For years? We get a moment now and then when the universe seems to click in our favor, and this, for me, is one of these moments, when I feel community among fellow human beings is at a premium. I do echo your wishes, at least the spirit of them, and I say, lets give it a try. Chris, I’ve been thinking about free reeds for some time now, and one thing I’ve isolated is the possibility that the apparatus involving their construction can be better suited to provide a more predictable and desired sound. I’m also aware that I’m not the only one on this quest, and right now, I think the most competent people for such an undertaking are the makers. Of course, you are welcome to study my PICA article, though I’m sure you understand that this article concerns cavity resonance, and it’s my experience that cavity resonance is detrimental to free reed operation. So it’s a paper on what not to do, rather than what you’d want to do. Nevertheless, the concepts there are fundamental. Concerning cavity designs that can be optimized for musical tone, I cannot offer anything significant from a theoretical point of view, and as I say, I think the makers have a far better grasp on this topic than I do, in a practical sense. I do however have some new ideas and theories that I’ve been playing with, in my daydreams, though these require experimentation for verification in the real world (drat!). I think that this, for me, is indeed a years’ long project, since there are many things on my plate now, though when I get through them, and IF I arrive at worthwhile conclusions, I’ll be sure to let you know. In the meantime, I think interesting topics will pop up now and then on this very interesting discussion group. Best regards, Tom

Dana, the reed tongue vibration is the primary system for vibration. All these air flow considerations we have made are done simply in order to understand the forcing (exciting) mechanism that causes reed vibration. The momentum of the reed itself is very large, compared to any momentum present in the air stream, and it certainly is not a throw away. In the paper, the reed equation of motion is Equation 10. All our discussion involving pressure is represented by the term F1(t) on the right hand side of this equation. The first term of this equation is the force required to accelerate the tongue (Newton’s law), the second term is the force required to generate the acoustic sound field that radiates sound to the surroundings (friction is neglected), and the third term is the restoring force due to the springiness of the reed. This is pretty much the classical vibration equation of motion for a cantilever beam. If my own analysis of the excitory mechanism is correct, and if Ricot is correct in throwing away unsteady terms because they are negligible, you can forget about momentum, because it’s an unsteady effect inherent to fluid motion. Recall that, in the suggestion I made in the previous post concerning the excitory mechanism, I invoke only the steady state Bernoulli equation, and the conclusions were made without any consideration of fluid momentum, as it affects motion outside the steady state Bernoulli equation. I reason that, as the tongue moves upward away from the slot, the pressure force decreases, and I didn’t bother to add in a force that would be necessary to push the fluid out of the way. Because the motion is so (relatively) slow, the fluid is really not rushed enough to produce appreciable force, compared to the forces invoked by the Bernoulli equation. It’s as though, as you are exiting the theater, people are very gentle, and you on your roller skates are able to move along. There’s no bully accelerating himself and pushing everyone else out of the way. I agree with you that the water reed may have peculiarities not present in the air reed, but here, I’ll rely on Ricot’s argument using the Reynold’s number, which appraises the level of inertial forces, mainly because I find myself a little too lazy to go elsewhere. How well does it work without the resonator? Can it produce a sound as loud as the Western free reed? It seems that, in this case, what we have is basically a Western free reed with a relatively thin plate. I’d be surprised if it can provide a very loud tone, since the mean, equilibrium, position of the tongue would move to the other side of the thin slot with a relatively low blowing pressure, and you cannot develop a high blowing pressure without choking the reed. But, as always, I may be wrong. I’d guess the reason for the minimum blowing pressure is so that enough energy can be transmitted to the air column within the tube, enabling a vibration mode in the air column to become established. These sound sources (reeds and edge tones), from an energy point of view, are very inefficient. My guess here is that it must be fairly thin in order for the air column to control its motion, or timing, so that the reed’s vibration can be made to line up with how the air column wants to vibrate. We have a co-operative system here, much like that in a reed organ pipe, the sounding frequency of which is slightly above the natural vibration frequency of the reed. The reed in this case is a beating reed and not a free reed, but I think the physical principles have similarities. As an aside, the beating reed in clarinets is very supple, and the musical tone, coinciding with vibrational modes of the air column, is well below the natural vibrational frequency of the reed itself. The reed can couple with the air column in this case because the player’s lips introduce a lot of damping, which greatly widens the resonance response curve of the thin reed. With brass instruments, the players lips vibrate at frequencies close to the musical tone, and here, the damping is relatively small. I guess this is a bit off topic, but I find it enormously interesting. Do you have a sheng, or a bawu? I’ve been toying with the idea of getting some of these instruments.

Hi Dans, Thanks for your insightful observations. Dana, reading through your descriptions here gives me opportunity to recall how efficient mathematical descriptions are. If a picture can save a thousand words, how many can an equation solve? I’m very pleased to have such an opportunity to think about these things, and in focusing on these details, I’ve finally come up with my own, hopefully realistic, description of how the reed works. I’m not 100% sure it’s correct yet or even that it’s the mechanism Ricot uncovers, but it is simple enough to intuitively understand, once certain physical concepts are understood. But before I go into that explanation, let me comment on your paragraph above. Remember that Ricot invoked the Reynolds Number in order to argue that the water flow field is similar to the air flow field, in reality, for working reeds. I thus would not try to look for a Reynolds Number in his model. For actual operation of actual reeds, as you point out, the width of the slot comes into play for large swings of the tongue. Thus, without any reference to any theoretical model, the choice of slot width as characteristic length, to me, seems reasonable, and I share at least some of your criticism when Ricot throws out the operation of the tip region, which incorporates this dimension. However, as I explained previously, I don’t make an issue about it. In addition, even in Ricot’s model, the slot width IS a key parameter, and it arises because it defines the extent of the flow region above the reed. This parameter, h, appears in their Equation 8, and physically it incorporates the importance of the width of the tongue, which is essentially the width of the slot. The larger the value of h, the more flow is diverted into the variable area gaps. I think this reason alone should somewhat temper your objection here. In addition, I don’t think Ricot’s formulation includes the case where the tongue vibration amplitude is large enough to send the tongue through to the other side of the slot. How can it do so if indeed the tip region is eliminated from the mathematical solution? I think we have to accept that their solution applies only to small amplitude motion. Okay, in order to understand the way I think the reed works, first consider a flow of air striking normally to a wall. Fig. 5 in the paper can suffice for this, but you’d have to first eliminate the gaps and picture a wall of infinite extent. The streamlines of flow will be similar to those drawn near the axis in the figure, with the flow being smoothly diverted, eventually becoming parallel to the wall. The streamline right on the axis is unique. It intersects the wall perpendicularly, and the fluid in this streamline hits the wall and stays there (though it takes an infinite amount of time to get there). The pressure at this normal point of intersection is equal to the “stagnation” pressure in the fluid. This stagnation pressure, Po, is the maximum pressure in the flow field and equal to the pressure that is attained when any part of the flow field is decelerated and brought to rest, without any loss in energy (as from friction). Po is also the pressure that is used to accelerate the fluid to the velocity it has attained anywhere else in the flow field. All this can be expressed by the equation Po = P + rho*V^2/2, where P is the static pressure at any point in the field, rho is fluid density, and V the magnitude of the velocity at the corresponding point. This is the Bernoulli equation for steady, incompressible flow, which is derived from the Euler equation, which in turn is derived from the principles of Conservation of Mass and Momentum. Since we are not including heat and temperature effects, this equation is also the Energy Equation for the motion. It reflects the law of Conservation of Mechanical Energy, with P representing the local potential energy, and with the V-squared term representing local kinetic energy. Po is the maximum pressure in the system (analogous to the largest height or most extended spring position). It is a conservative system (no losses) and at all points in the system, the sum of total energy (potential + kinetic) is constant (and equal to Po). Thus, the maximum velocity in the system must be Vo = (2*Po/rho)^0.5. Thus, everywhere in the system, P is less than or, at most, equal to Po. Now go back to Figure 5, as it’s drawn in the paper, with the gaps. Using the above concepts, we see immediately that the average pressure on the top of the reed tongue is less than Po. Only the stagnation point has Po, and everywhere else has less pressure. Furthermore, as the flow velocity increases above the tongue, the pressure of the air that touches the top of the tongue becomes lower. This is a direct result of Bernoulli (above) – the higher the velocity, the lower the static pressure, P. Keep in mind also that Po is the pressure in the bellows, away from any air motion. We call this simply bellows pressure, or driving pressure. A second important concept arises from the ASSUMPTION that the pressure on the bottom side of the tongue is everywhere constant and equal to atmospheric pressure (outside the accordion). With these two concepts, we might understand how the reed works. Assume periodic motion and imagine the tongue moving downward, approaching the slot. At any moment, there’s an average pressure, P1, on the top side of the tongue and atmospheric pressure Pa on the bottom, with net pressure (P1 – Pa) pushing the tongue towards the slot. As the tongue gets closer to the slot, the gap circumventing the tongue gets smaller, causing the average air velocity above the tongue to decrease. From Bernoulli, this causes an INCREASE of the average pressure, P2, acting on the top side of the tongue. Thus, (P2 – Pa) > (P1 – Pa), which means that the force pushing down the tongue increases as the tongue approaches the entrance to the slot. Conversely, as the tongue moves upward away from the slot, it experiences a lessening force. If the tongue/slot fit were perfect, when the tongue enters the slot, all air flow stops, in which case the pressure forces on the tongue are the maximum possible, and equal to (Po – Pa). (Dana, keep in mind that steady state – actually quasi-steady – is assumed. With such sudden stoppage, there would be some kind of “water hammer” effect, but apparently, Ricot’s work showed them to be negligible, compared to other forces at play.) Let’s step back now and look at a simple property of all vibrating systems, consisting of a spring and a mass, being excited by a periodic force. When the mass is near the center of its motion, it’s displacement is near zero, which means its spring force is near zero, and its velocity is near max. Importantly, at resonance, the periodic force causing the motion is also at a maximum. Said simply, the periodic force causing motion is IN PHASE with the Velocity. This means, and it can be shown mathematically, that the work done by the pressure forces goes directly into maintaining the motion against all friction and losses in the system. We have thus see the mechanism by which the pressure forces acting on the tongue are made to time their action so that these forces are in phase with the oscillatory tongue velocity. For me, at least for the moment, I think I understand this, and furthermore, I perhaps also understand Ricot’s conclusions – but I’m still not 100% sure, and here’s why. First of all, it looks to me that his excitation force arises simply from the steady flow Bernoulli equation and that his more general, unsteady, analysis for the flow field above the tongue simply produced the numbers he needed to justify throwing out unsteady effects. I’m still confused, however, by his explanation in the paragraph after Equation 8. He says that the “pressure fluctuations associated with volume flux fluctuations due to the reed aperture variations” do not transfer energy to reed motion, because they are in phase with the displacement (and out of phase with the velocity). I guess I don’t know what he means by the effects of “reed aperture variations.” In my reasoning above, it looks to me like these variations do indeed produce a force out of phase with displacement and in phase with velocity. Lastly, I’m not sure if the mechanism I propose can explain the start transient. Perhaps for this, we would need to incorporate unsteady effects, such as a “water hammer” or some other inertial effect. I think we take on too much difficulty by mixing the start transient and periodic motion into the same physical explanation for how the reed works. I do indeed suspect that some unsteady effects would be necessary to explain the start transient, but apparently, these effects are not, and do not account for the periodic motion. One interesting experiment would be to very closely observe the tongue tip during start up, with some kind of flow visualization to see if any jets are formed, or if there’s any flow separation from a boundary. If not, then my guess would be that unsteady effects are important. I would guess this is the case, simply because, during start up, velocities are very small, and particle stay times (as I described in my previous post) may indeed be comparable to the period of oscillation – a dead giv-a-way for unsteady effects. I certainly believe that you can build reeds with 0.01 mm (0.0004 inch) clearance, at least in some areas of the gap. I have a Baldoni accordion with “handmade” reeds, and on the East Coast, in Winter, I often have to slowly aspirate air through the instrument in order to warm up the reeds. Until I do, they are often so cold from the night before that most of them buzz, presumably because the tongue hits the sides of the gap, and this is a reasonable assumption because Aluminum plates have such a higher coefficient of thermal expansion than steel tongues. Calculations certainly bear this out, when you are talking about clearances near the tip end that are less than a thousandth of an inch. As I mentioned before, I love the sound of the bawu. You can find some good examples on YouTube. In the literature, and according to Fletcher’s notation, the Western free reed is classified as a closing/opening, or (-,+) reed. In this notation, the first symbol denotes how air flow changes with increasing pressure from the front side of the reed, and the second symbol from the back of the reed. The clarinet (beating) reed is (-,+). The trumpet (lip) reed is either (-,-), or (+,-). The Asian free reed is (+,+). It’s not surprising that there could be two different operating regimes here, but in most normal use, as you say, the Asian tongue is blown entirely downstream of the slot. As you know, a resonating air column is required for this mode of operation. Interestingly enough, the Western free reed can, and does, also operate in this configuration, though not with accordions and concertinas. With harmonicas, however, the vocal tract of the musician does provide the required resonator, and indeed, Steve Levy became famous for his master of his “overblowing” technique. Incidentally, Ricot is aware of all this issues, and this explains his statement at the beginning of the paper, “However, in the instrument, the accordion reed only operates in its blown-closed configuration…” I point this out only to answer one of your original comments, calling into question whether Ricot realizes that the Western free reed can “only” be operated this way. “Only” isn’t true, as in the case of the harmonica, and Ricot merely accounted for that possibility. Dana, I have enjoyed very much this discussion, and I know that there are at least a few other areas where we could find much interest in sharing experience on musical instruments. In these days, I’ve had extra time on my hands, as I’m between jobs – rather, I hope I’m between jobs. I’m not sure why I have such interest in free reeds. It’s true my grandfather, father, uncles, etc. played accordion, but my own siblings think I’m a bit weird for it. It does give me both musical, social, and intellectual outlet. Since studying them, I’ve learned about other musical instruments, and it’s interesting to see how different features among different kinds of instruments vary. No instrument is “perfect” from any point of view, and most of the difficult features simply provide challenges for the makers, many of whom are extremely skilled and competent individuals, who have done much to elucidate and even extend the fundamental principles by which the instruments work. I certainly concur with your aside to Chris. Best regards, Tom

Reynolds number, which can range from zero to well over millions, is the ratio of inertial forces (usually in steady state) to viscous forces. For large Reynolds Number, viscosity plays little effect, and for very small Reynolds number, viscosity cannot be ignored, and may dominate the motion. Numerical values of Re have different significance in different types of flow problems. For internal flows, as in a pipe, it’s most likely that the flow will be laminar for Re less than about 2400 and turbulent for higher values. For external flows, as for flows around an airfoil, Re can be very large, and different flow regimes are encountered throughout. Complications arise when the flow becomes supersonic (shocks). For subsonic flows, viscosity can be neglected except for a very small region near the boundary of the foil, known as the boundary layer. I hope you don’t mind my digressions. Re = UL/v, where U is the “characteristic” velocity, and L the “characteristic length, and v the kinematic viscosity of the fluid (which is equal to the dynamic viscosity divided by the fluid density). In their problem, they choose the width of the reed slot as the characteristic length, and I would agree with this choice. The velocity to use in this evaluation is also straightforward, being that which the fluid attains when, in steady flow passes through the slot. I am, however, uneasy at simply looking at the Re and concluding that the air flow and water flow cases are similar, because of the oscillatory nature of the flow. But I’m not going to object. In this game, unless you have something concrete to show, or a better analysis to present, it’s best to first see what the results are. Until I can come up with something better, I look to this paper as a milestone. I think you have valid points concerning the start transient of the motion, but again, I say that the start transient is not relevant to this paper. Ricot simply uses his formulations to calculate a periodic motion that is (presumably) independent of any kind of start transient. I agree with you that, for all we know, the start transient might contain physical processes not necessarily present in the periodic vibration. Let me ask, can you explain just how it is that the reed can start vibrating, from rest? After thinking about it myself, I still have some questions, and I haven’t yet found any explanation that I consider adequate. This might shed some light on the issue. Take a plate that has a perforation (aperture), the left side of which contains air at constant pressure P1, which is greater than that constant pressure P2 on the right side, which also contains air at the same temperature. Let’s look at the steady state; i.e., long after the motion started. When the air leaves the aperture and enters the right side, it must form a jet. This is not opinion. It must be the case, according to the laws of Physics, and I can go through the verbal proof, if you’re interested. But to save time, I’ll pass on this here in order to explain something a bit more complicated. Let’s say P1 is greater than P2 by 3 inches of water column. This will give a jet velocity of 116 feet/sec, as calculated using the so-called “Bernoulli Equation,” which is valid for incompressible, steady state conditions. Let’s say also that the aperture is a round hole with a diameter of ¼ inch. Now look at a molecule of air as it passes through the hole. (You can imagine yourself trying to get out of a theater in a crowd, through a single set of doors.) It’s velocity isn’t much – it takes you forever - until it gets very close to the hole, say within ¼ inch – the same distance as that which spans the aperture. In a blink, the molecule is accelerated to 116 ft/sec, whips through the aperture, and once it’s another ¼ inch or so downstream of the aperture, it completely forgets that there was an aperture to start with. In a time span of about (1/4*2)/(116*12) = 0.00036 seconds, the molecule completes its experience of the aperture. Now let’s say that, just when the molecule gets within ¼ inch to the left of the hole, you increase P1 to twice it’s value, and you took 0.001 seconds to do it. Will the molecule feel the change? Not much, because it’s long gone before the pressure P1 is significantly increased. If, however, you increased P1 in 0.0002 second, the molecule will definitely experience the change, because information of this change will travel to the molecule at the speed of sound (1030 ft/s), and the increased value of P1 will impart an increased velocity to the molecule during its passage through the aperture. One conclusion from this is that, if you change P1 at a frequency less than about 1/0.001 = 1000 Hz, the air motion can be considered steady, and you can use the Bernoulli Equation for each value of the pressure, even though the pressure is changing. Another conclusion is that, if you change P1 at higher frequencies, the steady flow equations become increasingly inaccurate, and at frequencies above around 1/0.0002 = 5,000 Hz, time changes in the flow field become very important. In these latter cases, the steady flow Bernoulli Equation is not valid, and more complicated unsteady flow equations must be used (e.g., Equation 3 in the paper). These latter equations contain time derivatives that account for the forces needed to time-accelerate fluid. This kind of acceleration should not be confused with the convective acceleration in steady flow. An example of this latter effect can be seen in the example of the theater exit. When you get near the doors, other people push on you, overcoming your inertia, increasing your velocity. You don’t need your own muscles for this. If you were on roller skates, you would be simply convectively accelerated out the door. An example of time acceleration would be a short sprint, accelerating yourself from a standing start. I don’t entirely understand your question involving the vacuum aspirator, but let me simply say that the Bernoulli Equation doesn’t cause suction on the reed. I know you can find this term used in some web explanations on how reeds work, but it’s not accurate. Pressure pushes against things, moves them in the direction of lesser pressure. The lower pressure area doesn’t “pull.” As I understand Ricot’s analysis, he sets the pressure underneath the reed tongue to a constant value, equal to the pressure under the reed (on the back side of the plexiglass). The justification is that, since jets are formed, this pressure boundary condition must be satisfied. An interesting complication here is the difference between the flow going into the reed and that exiting, in the form of jets. In the paper, Ricot treats the exit flow as (quasi)steady, while he writes unsteady equations for the entrance flow. The reasoning here is not obvious to me. First off, you might think that, if the exit region is steady, then why not the entrance region? The fact that Ricot, after finishing the analysis, throws away unsteady terms suggests that the simple question may be valid. This is one aspect of the paper I need to spend more time on. Are you saying that smoke streamed through the tiny gaps circumventing the tongue? If so, then I presume that your smoke experiment and Ricot’s water experiment agree? The only way I can understand a “plug” effect, causing a vacuum is by invoking some kind of unsteady phenomenon. With the presence of jets, I can’t see a way to incorporate such phenomena. I’m having difficulty understanding all you’re saying here. Perhaps my paragraphs above can supply some common terminology for us. In any event, I totally agree with your first sentence here. It seems to me that Ricot finds all his physical mechanisms in the flow above the reed. If I had to make a wild guess from my understanding so far, I’d say that the only term he says is important for the excitation of the reed is the usual V^2 term present in the steady flow Bernoulli equation. If so, the actual situation is much simpler than the way he formulated it. I suppose it’s useful to first make a more general (unsteady) formulation, then trim it down, according to the results you get. I really can’t make much sensible comment on your points. I also have many intuitive kind of questions. I would like to do my own analysis on this, and this is maybe one reason why I’m motivated to discuss the paper with such interest. The fluid on the back side of the tongue does contact the tongue and does have an effect. It transmits its static pressure to the back side. They are not saying that, just because the flow avoids that area, being swept in a jet, there is a vacuum there. The pressure there is equal to the pressure on the bottom side of the plexiglass. (This statement neglects presumably small pressure fluctuations due to turbulence and eddies.) Although you may be correct, I see no need – without proof - to allude to extra mechanisms for a so-called “real reed.” I can accept that they built a free reed, and I can assume that this reed behaves as other (but maybe not all) free reeds. I agree that there are many complications that further study can focus on. As usual with early investigations, much credit can be earned if you can put the problem in as simple a way as possible, eliminating all complications that might cloud the fundamentals, then succeed in nailing down something real and not understood before. Not all attempts are successful. This study is recorded in the literature and future researchers with take it apart, piece by piece. If there is a concern about how realistic their choice for side gap clearance, my guess is that the theoretical calculations can be very simply performed by setting this gap to zero. The theoretical calculations don’t have to worry about the tongue sticking in the slot! In fact, maybe they did this calculation, and if they did, I hope to think that they’d report if such a gap has such a prominent role in reed operation. I don’t know, apart from the obvous problem of scraping, is it possible for a free reed to operate with zero clearance? Is the marble/copper mixture applied with the copper in a molten state? How do you mean, “overblown?” Best regards, Tom

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

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

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. 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

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

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

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

Hi Dana, Thanks for sharing your extensive experience and understanding on free reed operation. I do, however, believe you make an error with the above statement, which, upon close examination, is self contradictory. Assuming I'm not misunderstanding your statement, any deviation from sinusoidal motion of the reed tongue would necessarily be caused by the excitation of multiple vibrational modes of the tongue. Cottingham at Coe College has measured the time dependence of the vibrating reed tongue and found it to be virtually sinusoidal, but with a very small, albeit measurable, departure, due primarily to the first overtone. I doubt any researcher would attribute the rich harmonic structure of the musical tone to this very slight departure from sinusoidal motion. Thus, the first part of your statement does agree with scientific consensus, with only the second part being in error. The rich harmonic structure of the musical tone is rather due primarily to the sharp pressure pulses caused by the tongue passing back and forth through the slot, with significant modification of these pulses by acoustic interaction with surrounding structures - most significantly the reed cavity. In other words, a perfectly sinusoidal motion of the reed tongue is entirely capable of producing a musical tone with the rich harmonic structure we hear. Best regards, Tom www.bluesbox.biz

Greetings all, There will be a free reed musical instrument session, with talks and performances, at this year's meeting by the Acoustical Society of America (part of the American Institute of Physics, http://asa.aip.org/), next week at the Sheridan Hilton, San Antonio. I'll be delivering a paper on reed vibration and cavity resonance, with application to pitch bending, at 2:30 PM, and there will be a demonstration afterward, by Kenny Kotwitz (BluesBox), Don Mopsick (bass), and Kyle Keening (drums). There are, of course, many other very interesting presentations about free reed instruments scheduled. Tom www.bluesbox.biz

Hi Dana, I’m not sure what you’re trying to explain. By “porous absorber effect” I’m referring to the suggested dissipation of acoustic energy by means of “a thin piece of fabric or leather - or just roughing up the chamber walls” as the original Poster asked, and the conclusion I come to is that the required material thicknesses are quite large, compared to most chamber dimensions. Your suggestion to consider resonance in the chamber and the resulting vibration of the chamber walls seems to be a theoretical explanation to a different approach. Perhaps Harold tried such a method? Or perhaps you mean to say that a fabric lining can somehow make its effect known through this wall flexing? In any event, considering the number of partials in the sound from just one reed, and considering the total number of reeds in an instrument, chamber resonance is not a very common occurrence, so I don’t see how it can explain a general mellowing out of tone for a group of reed/chamber pairs. I invite you to take a look at the calculations I made at http://www.concertina.org/pica/index.htm, which illustrates the discrete nature of the resonance phenomenon in concertina chambers. I’m also not sure what you mean by “hard surfaces… …have higher frequency resonances…” Are you looking at the flexing of chamber walls caused by impinging sound waves, without the global resonance of the chamber, and suggesting that this kind of flexing might be a mechanism for dissipation in unlined chambers? This is very confusing. Every acoustic phenomenon has a wavelength dependency, including the chamber resonance and flexing wall mechanisms you mention. Though I think you are right to suggest that a plausible mechanism should work over an entire range of frequencies. This is precisely what the porous absorber is capable of: it is effective for all frequencies above a certain minimum, as I explained in my previous posts. Perhaps it would be useful if Harold would care to explain what he did and the effects he observed.

Did you mean to say that the wavelength of 4 kHz is 0.25 FEET, or 3 inches? Sound travels at about one foot per millisecond, so 1,000 Hz has a wavelength of 1 foot. This jibes with teh lengths of organ pipes. Still, it seems intuitive that even 1/16" of soft material would absorb some high frequencies of sound. But I also agree that it's better to bring up the middle and low range of a box, than to deaden the upper region. Most boxes I've played (very few) have weak upper notes anyway. --Mike K. Hi Mike, Thanks for the correction. Silly me for the gross error. When I first read the suggestion to take out harsh tones by means of porous absorption, I was skeptical, then, deciding to do the calculation, I was going between metric and English units and confused myself, being influenced by the apparent practical convenience the numbers showed. Looking at this fresh now, the 1/16" soft material would theoretically be useful to damp frequencies above 48,000 Hz, but basically useless for frequencies in the range of most human capability. For frequencies above about 14,000 Hz (about the limit of my own hearing), one would need a thickness of at least about 0.1 inch (for 1/10 wavelength thickness). But this would of course offer no effect with my hearing. For the original 4,000 Hz and above partials, we'd need thicknesses at least around 0.35 inches. Such may be difficult to incorporate into actual instruments, without causing problems. Perhaps there are very porous reticulated foams that one could try. As I mentioned before, the pores should be interconnected and distributed throughout the material. Best regards, Tom

In Acoustics, the technique you refer to is called porous absorption of sound, and to be effective, the porous material should have interconnected pores and be thick enough to cause significant attenuation for frequencies above a given frequency. As a rule of thumb, thickness should be at least a tenth of the wavelength of the sound you want to attenuate, but ideally, it should be more like a quarter of a wavelength. This is because the porous material dissipates energy by air friction, which requires air motion, and air motion is at a maximum a quarter wavelength away from a rigid surface. Let's take a conservative example and say you want to attenuate sounds with frequencies around 4,000 Hz and above. In other words, let's say you want to diminish partials of some offending notes that have frequencies at and above 4,000 Hz. The wavelength at 4,000 Hz is about 0.25 inches, and so the porous absorber should be at least about 0.025 inches, and much better, about 1/16 inch, in thickness. To attenuate frequencies lower than 4,000 Hz, you would need greater thicknesses, and for frequencies higher than 4,000 Hz, you can do with thinner materials. Best regards, Tom

For a lengthly discussion on some of the theory behind your question, you can read my article, "Reed Cavity Design and Resonance," in PICA, Volume 2, at: http://www.concertina.org/pica/index.htm Best regards, Tom www.bluesbox.biz

Thanks for making these very interesting photos available. How much effort have you put into learning how to play these instruments? Particularly with the bawu, do you play western music with them? It seems you also play pipes. How would you compare playing the bawu with playing the pipe cantor? Best regards, Tom

Hi Mike, A small concern is that the moisture in your breath might cause some rusting on the reed tongues. In any event, good luck with the rig, and I hope it serves you well. Best regards, Tom

Hi Dana, I also find the Asian free reeds fascinating. I particularly like the sound of the bawu, though I hadn’t realized that its reed has a set. The instrument is also interesting in that the shape of the tongue is triangular, and like a flute and clarinet, its tube is cylindrical. But since the reed is mounted near the closed end, it’s not surprising that its sound is reminiscent of the clarinet. Yet, I think it also can sound flute-like. I think the free reed used in this way – with a resonator - can be more expressive, with much more sound complexity, than the way we westerners use it in our instruments. The tubes of the sheng are conical in the region where the reed is mounted, and no doubt this feature helps explain it’s characteristic sounds – quite sophisticated for an instrument that goes back, they say, 3,000 years, and is, perhaps, the first, real, musical instrument. There are numerous videos on Youtube that one can enjoy, and the following two are very interesting. The first is that of a sheng solo, and the second is that of a bawu, with poignant interest in particular to those of you in England, and in general to all westerners. http://www.youtube.com/watch?v=GndoDa0nBl0 Best regards, Tom

Hi ragtimer, Having the movable side makes it easy to accommodate reeds of different lengths. The way you did it, though, adds some cavity volume, and this can cause some problems with impedance matching. True, the movable wall affects the resonant frequency of the cavity, but I can see some possible conflicts in where the wall should be placed; i.e., to accommodate a reed of certain length, or to eliminate an unwanted resonance. I see the need for a cavity when you want to control the airflow through the reed, as with a pallet in a musical instrument. But for some tuning boxes such as yours, where you blow or suck on the box with your lungs, it may be more trouble than what it's worth. Best regards, Tom

Hi Chris, I totally agree with your statements, and I can just add more detail. I think it's safe to say that it's not possible to tune all the cavities of a concertina to the FUNDAMENTAL of their corresponding reeds - even for an English, in which each cavity accommodates two reeds of the same pitch. It may be possible, however, to tune most of the cavities to some overtone of the associated reeds, but for the lower notes, the reachable overtones might be too high in pitch to be heard very well. In any event, one might argue that the "hissing" heard in the quoted claim is due to the cavities emphasizing some range of overtones. But I doubt even this is the case. Another complication is the fact that cavity tuning can be attempted by altering several geometric parameters, not just cavity length or volume. So, I guess one might argue that there are many tuning features that cannot be seen in the pictures. I still doubt this is the case, and my feelings are that such a uniformly tuned instrument would be no small accomplishment. Subsequent cavity tuning for other (similar) instruments would be much easier, though such instruments appear to be quite rare. Finally, in my experience, a cavity tuned to the fundamental would probably choke the reed, preventing it from speaking. As I mention in the related paper that I wrote, there may be advantages to tuning cavities to certain overtones, but the rewards at this time do not appear to justify the necessary work. Best regards, Tom

Hi Dana, I think you mean the opposite; i.e., that the impedance of the box needs to be small. Since impedance is defined as (complex) pressure divided by (complex) velocity, the idea here is that you want pressure oscillations in the box, and thus at the opening between the box and the cavity, small. In this way, the cavity (and reed) doesn't know the box is there. I'm also not so sure about the need - in general - for a cavity in a tuning rig, which needs to accommodate reeds of all pitch. If the cavity and everything else can be made the same as the acoustic geometries that the reed experiences in the actual instrument, then this would be ideal, and there would be no need to check the tuning once the reed is put back into the instrument. But such an arrangement is usually not practical, and tuning needs to be accomplished in an iterative fashion. With accordions, one can tune the reeds while mounted in their working cavities by fitting the entire reed block to the tuning rig. But even here, iterative tuning is hard to avoid because of the complex geometries associated with ports, the proximity of the pallets, the fact that bellows surround the blocks, etc. I understand that for your concertina construction a cavity may work better than no cavity, but it may not be true for all applications. Perhaps others can share their experiences on these points. Best regards, Tom

Hi Ragtimer, I can't locate the springs for return key motion. Are they visible in the photos? Best regards, Tom