ttonon

Probably not for anyone, but I believe you're wrong about the relative effects of shape and volume. It's a general principle of acoustics (and of lasers and other resonant chambers) that the shape is of extreme importance. A bell shape has a very different timbre from a rectangular bar containing the same amount of metal. A rectangular resonant chamber with dimensions 10 cm x 20 cm x 5m has a fundamental frequency 24% lower than a cubic chamber 10 mm on a side, though both have the same volume....(snip) Hi Jim, you have many interesting comments, though I must warn here that one cannot assess the importance of geometric parameters unless one first specifies the mode of acoustic vibration. For instance, Tony's conclusion may indeed be correct if in fact the acoustic cavity mode that is predominate when the reed sounds is when the cavity behaves as a Helmholtz resonator. This is rudimentary acoustic theory at work. In the Helmholtz case, the resonant frequency is given by f = (c/2/pi)*(AL/V)^0.5, where c is the speed of sound, pi the ratio of circle circumference to diameter, A the area of the pallet hole, L the effective length of the air mass vibrating in the pallet hole, and V is the cavity volume. Thus keeping the same pallet hole geometry and changing volume will uniquely change resonant frequency. In all your examples, the cavity dimensions are significant with respect to the wavelength of oscillation, and you are correct in pointing out that cavity shape is very important for those modes that contain boundaries defined by these shapes. For Helmholtz resonance, all cavity dimensions must be much smaller than this wavelength, in which case, cavity shape is immaterial, and only A, L, and V are important. One can study the resonance properties of concertina cavities and conclude that the modes that are most likely to occur over the musical range of the entire concertina family are Helmholtz and quarter wave, with Helmholtz predominating. Thus, it's very possible, if not probable, that many of the cavities Tony has studied exhibit Helmholtz resonance, in which the cavity volume as a whole is the significant feature of the cavity itself. For those cavities that exhibit quarter wave resonance, the cavity length is critical (along with A and L), and cavity width is not as critical. Best regards, Tom www.bluesbox.biz

Greetings and thanks for everyone's reply. Frank, I appreciate your comments, only I'm more curious about variations in sound within a given instrument, and those variations which cannot be so surely explained away. Let's take a brand new instrument, with no obvious construction problems, are there occasional notes that sound particularly "good," or particularly "poor?" I suppose this is not likely in a good instrument, because the maker would probably strive to make the notes even sounding. My query then is directed to the instrument maker. Are there, during construction, certain reeds that sound, as example, particularly resonant, and perhaps so resonant that they stand out too much, and it becomes necessary to alter the cavity, or something else, in order to bring the sound of that note back to the fold? The same question applies to a particularly "poor-" or "weak-sounding" tone. In a sense, I'm looking for a problem to solve, for an unexplained phenomena with significant occurrence. Hi Jim, thanks for your comments. I'm interested in this kind of arrangement because the bulk of the notes on the instrument can serve as a kind of control for exceptional occurrences. If we can single out a note or two, we might then be better able to understand the reasons behind the exceptions, using the rest of the instrument as a control. Best regards, Tom

How many concertina players/makers participating in this group have noticed variations in tone among the notes in his/her instrument? I’m particularly interested in whether an occasionally exceptionally “good” sounding tone is noticed among the separate notes, and whether, if noticed, the player would wish that all the notes would sound similarly. If such exceptional tones are experienced, where do they lie on the keyboard – at the low, mid, or top (pitch) end, and how would you describe this tone? Also, it would be interesting to know whether the instrument contains accordion-type reeds or traditional-type reeds. In similar fashion, how many players/makers notice an occasional weak, or "bad" sounding tone among the separate notes, and if so, where on the keyboard does it occur, how would you describe the tone, and what kind of reeds are in the instrument? Also, if maintenance problems are known to cause such poor tones, please let us know, but I'd be particularly interested in those poor tones that have no obvious explanation. I’d appreciate a sampling of comments on these questions, because I’m wondering how much the general tone of the free reed instrument can be improved, and I think it would be useful if we had an idea of the extremes of tones realizable. We might be able to identify features of instrument construction that influence these tones. Best regards, Tom www.bluesbox.biz

Hi Rich, I think we’re rapidly reaching diminishing returns in our discussion, and I find myself without the time and energy to continue in the minutest detail, though I offer the following. I appreciate your forthcoming, and your situation, which became evident to me early on, is perhaps unfortunate, because physical and mathematical principles can indeed assist one in understanding how these little vibrators work. Your practical experience, however, is very valuable input to the general progress of free reed instruments, and I hope we together can make meaningful contributions. I’m aware of the three threads you mention. I myself participated in them. I’ve read three of Cottingham’s publications regarding free reeds ("The motion of air-driven free reeds," "Theoretical and experimental investigation of the air-driven free reed," and "Variation of frequency with blowing pressure for an air-driven free reed"), and I’m not aware of others. None of these three, however, deal with the interaction between the free reed and a resonator. I’ve read Benade’s wonderful book, and recommend it to anyone who would like a deep, intuitive feel of how musical instruments work. The man is a physicist, and his intuitive approach is based on sound physical principles. Unfortunately, nowhere in the book is there a treatment of free reeds. Any other treatment of free reeds, that I'm aware of, does not treat a reed that is acoustically coupled to its cavity used as a resonator. One of Wheatstone' patents treats only huge resonators. Benade’s book, however, contains relevant information to our discussion. In Section 13.7 of the 1990 Edition, titled, “A Loudness Experiment Comparing Two Saxophone Tones," Benade explains a method to produce a “louder and more penetrating tone” for saxophones. The discussion is relevant here because the method produces (by a change in mouthpiece) a new musical tone with enhanced overtones, which is precisely what my calculations in Resonant cavity design models predicts. In more detail, please look at Benade, page 245, Fig. 13.8., which shows that the fundamental of the new musical tone is 50% lower than in the original tone, and despite this drop in the fundamental sound pressure level, the enhanced overtones result in a musical tone that is roughly 1.33 times louder than the orginal tone, or, alternatively, the new tone in the altered sax is as loud as 2.6 saxophones playing with the original tone. It appears no one has quantified any effect reed cavities (can) have on the operation (sound) of free reeds. Until this is done, we can only speculate on the magnitude of such an effect; however, the calculations in Benade certainly at least give promise to the idea. I regret that you haven’t been able to understand my arguments. But that's okay; perhaps in another thread we can take this up further. In the meantime, for a more elaborate discussion on how modification of inertial terms (acceleration) is used to tune plates, check out Benade, Section 9.4, “Adjustment of Frequency Relations by Variations of Thickness,” and for the tuning of a clarinet, see Section 2.3, “Adjustments of Natural Frequencies by Means of Small Changes in Air Column Shape.” Benade’s approach is almost all intuitive, explaining physical concepts with a minimum of mathematics, and I highly recommend this book. Hi Theo, For a theoretical treatment of this effect, see the third Cottingham paper mentioned above. In the paper, this effect is attributed to “aerodynamic” effects, which is acoustician terminology that describes viscous friction, eddys, jets, and other departures from Potential (Irrotational, Inviscid) Flow. In the realm of Small Perturbation Solutions in Fluid Dynamics, at least some of these effects can probably be captured in the mean flow terms, if one who is clever enough to formulate and solve the governing differential equations. (It’s not likely anyone will ever do this.) In any event, the paper explains that, for blowing pressures often encountered in normal playing, the frequency of oscillation of the reed decreases in an approximately linear fashion with increasing blowing pressure, and as the blowing pressure is increased well above normal playing levels, the frequency levels off and eventually rises. Has anyone here noticed this latter effect? I should point out that these statements are not derived in the cited paper from first principles, but rather, experimental values of growth/damping coefficient (aerodynamic effects) are inserted into a theoretical framework, and the stated influence of pitch on blowing pressure is produced, giving some credence to the entire approach. Hi Alan, This is an interesting conjecture, and to substantiate it, we’d have to know whether the elastic properties of the valve are affected enough by humidity. Perhaps humidity softens the leather, in which case, I’d guess the pitch of the reed would increase very slightly. We should realize here that a shift of only a couple cents in musical tone would, in most cases, go unnoticed during a session. Many other instruments experience inaccuracies in tone production, either because of (sometimes unavoidable) instrument construction, or because of player skill, even beyond a couple cents. As Theo points out, the human ear is capable of accurate measurement, if the conditions are right. For pure sinusoidal tones played at concert levels (60 – 90 dB) and under ideal listening conditions, the Just Noticeable Difference (JND) is a constant 1 hz up to about 1 KHz, and beyond 5 KHz, rises rapidly. (It’s no accident that the piano keyboard stops at 4186 Hz.) However, for many situations involving complex musical tones, with rapid and simultaneous notes being played, a couple cents inaccuracy is not serious offense. In fact, it’s an extremely rare free reed instrument that has all its notes tuned within 2 cents of exact. If it exists, it will soon change. Even better, many electronic tuners that are used for such tuning are themselves off by this much. Best regards, Tom www.bluesbox.biz

Hi Rich, Thanks for the opportunity to discuss these interesting issues. RM: I think of "airflow dynamic" as being the path the air takes and the things in that path which make the airflow change (constrictions due to the smaller pan slots, valve location and properties, path surface friction, pad operation...) and "pressure dynamics" as being the amount of air in that path (caused by bellows movement/time). TT: Let me try to interpret what your thoughts are from a scientific point of view, involving fluid dynamics and acoustics. It first becomes evident that you’re attempting to explain the dynamics of an acoustic phenomena, which is inherently “unsteady” in nature, from a purely steady state point of view. By “unsteady,” we mean that time derivatives in the governing differential equations are significant and cannot be neglected. “Steady state” analyses set all time derivative terms to zero, and in many other phenomena, this gives good results. The steady state view, however, cannot be expected to provide understanding of the acoustic phenomena. Even with steady state phenomena, it’s often unfruitful, or even incorrect, to regard “airflow dynamic” and “pressure dynamics” separately. In truth, they are part of the same phenomena. The steady state governing equations are often adequately described by Conservation of Mass (Continuity) and Conservation of Momentum, which, in effect, becomes the Law of Conservation of Mechanical Energy. In cases where the fluid can be considered incompressible, as in the case here, this latter equation is known by the name of Bernoulli. Thus, potential energy (pressure) and kinetic energy (velocity) are converted back and forth, and at any moment, their sum is constant. Rich, in my attempt to understand your approach, I tried to conceive of a situation where (steady) airstream direction might give us interesting effects, and the best I could come up with at the moment was the one you quote below. But, as I say, this effect is negligible in the case at hand, because the dynamic pressure (total energy) of the airstream through the cavity is very much equal to the (static) pressure. In other free reed situations, such as the harmonica, during upward note bending, using the technique called “overblowing” (the mechanism of which is much different than the mechanism behind overblowing in wind instruments) the direction of airflow is important, I believe, because of the formation of jets. TT (previous)When the reed is mounted over a cavity, the airstream approaching the reed (in the case of opening bellows) and the airstream leaving the reed (in the case of closing bellows) is directed roughly normal to the airstream direction through the reed slot. With the reed operating without the cavity, these airstream directions are different, being much more in the direction of airflow through the slot. RM: What is "normal"? TT: "Perpendicular," and I thank Jim for making this more clear. RM: I don't think that the direction of the flow by itself is cause for the altered pitch, but the reduction of the flow (caused by restrictions of/in the airflow path. TT: Could you please explain what restrictions you refer to? I also see a "restriction," and this causes increased oscillatory velocity amplitude, but I think the physics here is much different than the steady state "restriction" you refer to. For completeness, we might want to introduce viscosity (friction) into our discussion and this complicates the problem, and again, this doesn't appear to explain why the old and new valves behave differently. I will note though, in principle, as explained by the solution of the Spring/Mass/Damper system in harmonic motion, friction will lower the natural frequency of the system. With the reed, there are “aerodynamical” effects, and here, friction can play a role (eddies, etc.). But again, the issue is to compare the reed pitch with simply a change of leather, and it’s unlikely that this change would significantly alter the (small) effects of friction. RM: There has been a lot of investigation and debate about this issue. Personally I think that there is no significant Helmholtzian propensities in concertina construction. The frequency, physical chamber sizes, and math just don't coincide. The discrepancy is HUGE. TT: I would appreciate very much if you could direct me to at least some of these investigations, associating reed cavities with resonators. I haven’t been able to find any. With the issue at hand, you must realize that we're talking about extremely small changes in reed behavior. One cent of pitch variation corresponds to about 0.0005 parts, or 0.05 % variation in fundamental frequency. Think of it! What a marvelous apparatus we have to hear with? And instruments to measure with! I think it’s entirely reasonable to allow for the possibility of a resonator-coupled interaction with the reed. Many experimenters and theoreticians have been fooled by the subtleties of musical instruments. When you say that the “descrepancy is huge,” I think you’re referring to the comparison of cavity resonant frequency to the pitch of the reed. In some cases, it’s not so huge, and when one considers overtones in the musical tone, the overlap can be significant. But again to the main point, a resonator tuned far away from the pitch of the reed can at least minutely affect the pitch of the reed. RM: Not necessarily. I can install new valves which will raise or lower the pitch. TT: At the risk of sounding redundant, if the new leather raises the pitch, I'd predict that the new leather bends farther away from the slot. RM: Following that argument would mean that any increase in air velocity would lower the pitch of the reed. And to only a VERY small degree does it. Consider the pitch difference between playing very softly and very loudly which is many times the air velocity (flow) difference yet the pitch is altered very little (which is one of the great things about free-reed instruments!). Now consider the same setup but with a more restrictive (secured in place or "tougher" new) valve. The valve's restrictions will make a much larger pitch difference than the pressure difference will. TT: Rich, you're pointing out the fact that the steady state (more properly now called "mean flow") plays secondary role in the oscillatory (unsteady) motion, and unwittingly I believe, illustrating the point I make at the outset of this reply, that unsteady behavior cannot be understood properly by addressing only steady state formulations. In the area of mathematical physics called "small perturbation theory," we take a steady flow situation and "perturb" it by mathematically introducing a small oscillation, then solving for the oscillatory motion. The steady state motion, also called "mean motion" is many times inconsequential, and often serves as merely a means to conveniently nondimensionalize the oscillatory results. In my previous post, I refer to the “velocity of the vibrating air,” and I apologize for not being clearer by stating instead, “amplitude of the oscillatory air motion.” So as a result, you’ve confused oscillatory motion with “mean” motion. On the other hand, you are correct in noting that the mean motion has little effect on pitch. In mathematical physics, this effect is called “second order,” and it occurs because of nonlinear aspects to the reed motion, which are of higher order when oscillatory amplitudes are sufficiently small (acoustic regime). I should point out, however, that, in some problems, and using certain methods of asymptotic expansions, one can capture nonlinear behavior in the "first order" (acoustic) results, the complete solution of which can be obtained only by recourse to second order formulations. It would thus not be correct to say that these nonlinear effects are always negligible at vanishingly small oscillatory amplitudes. In any musical instrument, if one changes the geometry in such a way that the oscillitory velocity amplitude is increased near a velocity antinode, as in the case here, inertial loading will be increased and the pitch of the vibration mode governing that motion will decrease. This fact is used to tune cymbals, bells, and woodwinds. For instance, certain modes of vibration are altered in woodwinds by either adding or taking away material inside the bore, at a place where the air vibration is large. Adding material decreases the cross section, causing increased velocity amplitude and lowered pitch. Taking away material increases cross section, decreasing velocity amplitude, raising pitch. An even better example concerns the design of finger pads in wind instruments. Much theoretical work has been done on this topic, and I can give you references if you like. The reasons why pitch is lowered when the finger pad is brought closer to the tone hole are well understood, and are precisely the reasons I have explained here. Finally, and perhaps most relevant to the experimenters among us, I have just done this simple experiment (tonight) in my home shop on the free reed. I can assure you that, if you set a reed vibrating with a steady flow of air and take a small screwdriver and gently move the leather valve closer to the slot, the pitch will drop, and if you move the valve further from the slot, the pitch will increase - by just the amount you have indicated. I welcome you to try it and would be interested to know if you can reproduce my results. Best regards, Tom www.bluesbox.biz

Rich, can you please explain in more detail what you refer to as “airflow dynamic” and “pressure dynamics?” When the reed is mounted over a cavity, the airstream approaching the reed (in the case of opening bellows) and the airstream leaving the reed (in the case of closing bellows) is directed roughly normal to the airstream direction through the reed slot. With the reed operating without the cavity, these airstream directions are different, being much more in the direction of airflow through the slot. It’s not likely, however, that such an airflow effect is the cause for the altered pitch. A more likely explanation is that air in the cavity acoustically couples with the air being set into vibration by the reed tongue. The cavity air provides a spring-like effect (capacitance) that feeds back on the piston (inertia) effect of the air vibrating in and about the reed slot, and the system acoustically "loads" the vibration more so than when the cavity is absent. This is typically what happens with a Helmholtz resonator, and is well understood among Physicists. The leather valve significantly alters the vibration of the air in the vicinity of the slot. Thus, new leather valves, for instance, will probably not bend away from the slot in precisely the same way as the old leather valves. Since the typical result is that the pitch is lowered with new valves, my guess is that the new valves do not bend away from the slot as much as the old valves. This greater proximity to the slot acts as an airflow restrictor, causing an increase in velocity of the vibrating air, which in turn increases it’s inertial effect, consequentially causing even greater acoustic load on the vibration, thus lowering the pitch. Best regards, Tom www.bluesbox.biz

Interesting idea. Today's developments in material's science bring to mind even more materials, such as composites (graphite, etc.) and liquid (amorphous)metals. Perhaps someone with expertise in these areas can pass comment. Best regards, Tom www.bluesbox.biz

I don't know off hand, though I suggest the following approach in order to find such a material. The frequency of vibration of a bar of metal mounted as a cantilever depends upon its geometry and the ratio of Young's Modulus to material density. The speed of sound in the material also depends upon this ratio. No other material property affects this frequency and speed, and this ratio thus uniquely determines not only the frequency of the vibrating bar, but also its shape. A material that has the same value of this ratio as does brass will vibrate in the same way brass vibrates. There's another criterion, however, that you should require, since you indicate that brass is too fragile, or weak; namely, that the material's yield strength be greater than that of brass. Many tables can be found that list the physical and mechanical properties of pure metals and alloys. There remains to conduct this search with the above criteria. Incidentally, there's nothing here that limits the search to metals, and some polymers may also prove interesting. Good luck, and sorry I couldn't be more helpful. Best regards, Tom www.bluesbox.biz

Rich, I'd be very interested in seeing this diagram. They were approximately around A3 (about 220 hz). As I'm sure you can appreciate, it would take a fair amount of time and effort to explore the full range of frequencies. As explained in the patent, the furcated idea can be executed in a multitude of ways, with a considerable number of design parameters, and at the present time, I'm not able to adequately explore this technology. Perhaps in the future I can do it justice. Best regards, Tom http://www.bluesbox.biz

Rich, do the reeds you refer to work in conjunction with one-way valves, or is there a double-acting feature designed within the reeds themselves? Can you please explain more detail, or provide a picture? I have a patent for a very simple reed design, what I call a "furcated reed." I don't have a picture of this design on my web page, but those interested can go to www.uspto.gov and do a simple search for Patent Number 6,143,968, with title: Method and Apparatus for the Vibration of Reeds. (Inserting the given number into the simple search box will work, then click on the "images" button.) I will also attach a Word file with some images, but I don't know for sure if this will work. I can explain verbally how this reed works as follows. As most of us realize, the tip of the Western free reed tongue rests in an offset position, slightly out of its slot. Air must pass through the slot from the tongue side in order to start vibration. The furcated reed tongue has two tips, with each tip connecting to a common metal strip that's riveted to the reed plate. One of these tips lies on one side of the slot, and the other lies on the other side of the slot. Thus, air from either direction can start the reed. I've also extended this idea to include multi-furcations (along with bi-furcated, tri-furcated, etc.) in the reed tongue. Along with the obvious features of bi-directional airflow, the elimination of leather valves, and the ability to maintain vibration during a change in airflow direction, there are, I believe, additional advantages to such designs, including a sound spectrum different from that of conventional reeds. This spectrum is also somewhat more amenable to alteration, by alteration of the tongue/slot features, and may add varying degrees of tone color, depending on vibration amplitude. I refer you all to the patent for more text and visual detail. I must say that I've had time to build only a couple prototypes, which worked reasonably well, though have not yet satisfied myself as to how true these claims are, but I think the design is notable because of its simplicity. Best regards, Tom http://www.bluesbox.biz

Hi Frank, I'm sure you know that stainless steel comes in many grades. If you don't mind sharing, what grade did you choose, and for what reasons? Thanks. Best regards, Tom www.bluesbox.biz

Actually, you can do it yourself, with an electroless nickel process. You can find information and materials on the web. Best regards, Tom www.bluesbox.biz

Granted, there are complex issues associated with the size of a musical instrument; however, one advantage I can see that develops as the size of the symphonium decreases is the ability of embouchure to affect the musical tone. I can also speculate that perhaps the effect of embouchure may have been regarded as a detraction in Wheatstone's time (an attitude I detect even in Goran's quote, above: "..safe and sound production.."). Regardless, am I right about this? When you play a symphonium, is it small enough for the musical tone to be affected by embouchure? Best regards, Tom http://www.bluesbox.biz

I believe the symphonium is the beginning of a good idea, which has been developed through the years, with the accordina one of the latest developments. Sound files made with this latter instrument can be found at: http://www.boite-accordeon.com/index5.html and a pictorial history of western mouth blown free reed instruments (including the symphonium) can be gotten from the following page: http://www.boite-accordeon.com/index3.html I suggest listening to all seven sound files, because of the variety of wonderful music displayed. The instrument allows some bending of notes and fluttering sounds. The musicianship in these files is superb. There are, of course, other modern developments in western mouth blown keyed free reed instruments, but I believe this is the latest, with remarkable results. In fact, in at least one of these files (# 5) there's also a clavietta. Other pictures of various instruments such as these can be found at http://www.akkordeonmaurer.de/documents/d/...ibrandoneon.htm Best regards, Tom

Greetings, Check out: http://www.dailynews.com/Stories/0,1413,20...1829850,00.html Best regards, Tom

Dave, I believe the hardening and tempering temperatures you state are correct numerically, though they should be expressed in degrees F, not degrees C. Another comment is that the apparent color of thin films is not descriptive of the material itself and more likely due to the interference of light waves bouncing off the front and rear surfaces of the films. This is true for any film with thickness on the order of the wavelength of the impinging radiation. This color is not well related to the color of the bulk material (large amounts of it). Although I haven't read much about the films on heated metal, I believe these concepts mean that the blue color represents a certain combination of tempering time and temperature; i.e., those conditions that grow a film of the thickness range that presents a blue color. Other tempering conditions will produce film thicknesses suitable for yellow, and so on. Many people in the thin film industry accurately judge the thickness of deposited film by their color, and I believe the correlation between thickness and color is independent of the film material, provided that the material is reasonably transmissive. Another point is that the thickness/color relationship is periodic, since the perceived color depends upon interference; thus, films with thicknesses of even multiples of the wavelength in question will produce the same color. A thickness limit is reached where the film material becomes too absorbent, attenuating the light in its second pass through the material, after rebounding from the back interface. At some point, the film material's bulk properties take over. Best regards, Tom

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Hi Goran, There are two issues here: 1) Whether resonant cavities have been built into concertinas, and 2) Whether there is theoretical basis for their successful operation, with reasonably sized components. It seems that you have delved extensively into (1), concluding that resonant cavities have never been incorporated into the entire pitch range of an instrument. I have not investigated this topic, so for now, I can let your statements stand. Concerning (2), the table I present at the beginning of this thread seems to provide theoretical bases for a resonant approach to cavity design. Do you agree? Do the predicted dimensions in the table appear to you practical? I realize that, after I first posted this table, you took it as proof of your position that resonant cavities are not provided in existing instruments. I believe your conclusion was influenced by my 9/8 post, which indicates some pessimism on the possibilities for resonant cavity design. As Gene has pointed out, my calculations in the 9/8 post contained an error, and I don't believe the table of this thread contains that error. This table, then, appears to me to support a resonant cavity approach. In any event, I'm curious about any comment you might have on the table in this thread. Best regards, Tom www.bluesbox.biz

Hi Gene, What is a Vocalion Reed Organ? Is it different from standard reed organs? Could you explain a little more detail about these "specially designed reed cells"? In what way are they special? Also, in another post, you described an interest in harmoniums. Have you experimented with resonant chambers in such instruments? Can you describe how the reeds are mounted? Are they laid flat down against a "reed plate" or are they mounted in upright "reed blocks," as in many accordions? Best regards, Tom www.bluesbox.biz

Gene, I'm also optimistic that reinforcing higher harmonics through resonance will not greatly upset the sound of the instrument. The brain has interesting capabilities. Is the phenomenon you describe related to the recognized ability of the brain to supply the "missing fundamental"? By this, I mean if one plays a tone comprising twice, thrice, four times, five times, etc. of a base frequency, the brain identifies the base frequency with the pitch of the tone. I don't know how much this feature of the brain will be at play if, for instance, only the first overtone is (greatly) amplified. I do believe though, that regardless of what we can theorize, experimentation will provide the primary determination of the answers to these questions. Best regards, Tom www.bluesbox.biz

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Very good Gene. After I did the more careful analysis that I posted with the table in this thread, I wondered why I was so pessimistic about the use of resonators in my 9/8 post. Thinking on this and knowing my own tendencies for gross errors involving details, I suspected I failed to convert from feet to inches. But I haven't had time to go back over that post and verify this. Then you come along and spot the error. Thanks again for pointing out my errors. So then, assuming I made no similar blunders with the post in this thread, it appears that resonant cavities in concertinas can be realizable, along with relatively simple design models to choose from. The table in this thread was generated with a spread sheet, and I hope, is error free, but I welcome you or others to verify that. Best regards, Tom www.bluesbox.biz

Values for k can be found in the Fletcher and Rossing text. In the literature, I've seen values only for two conditions: 1) where the hole is mounted in an infinite wall, and 2) where the hole is identified with the end of a tube. The values for (1) will be larger because this condition tends to move a larger air mass. The high end of my suggested range for k (1.2) is really a guess of my own, reasoning that the presence of the pad will also tend to move more air, and I assumed that this effect can at most be equal to that of a single end correction. The original calculations for these corrections (see Rayleigh, The Theory of Sound, Parts I and II, I believe) depend upon frequency, and thus, the simplified values you find in the literature are in themselves approximations. But the numbers here are not too important because these calculations cannot be expected to very accurately represent the real situation and are only looked upon as guides for initial experimentation. You are also correct in stating that higher k values will lower the resonant frequency. This was a blunder on my part, and I have edited the correction in my post. Thank you for spotting it. Best regards, Tom

Hi Gene, The only resonant chambers, that I'm aware of, that are discussed in Wheatstone's patents relating to free reeds involve large pipes, which would be more convenient for reed organs and other, relatively large, console type instruments. Associating resonant chambers with reed mounting cavities in small, hand held instruments, however, is another issue. If you can confirm that Wheatstone has discussed the latter in patents, I would much appreciate it if you would supply the reference. Best regards, Tom www.bluesbox.biz

Goran, you may be confusing a simple concept here. The reed tongue vibrates in resonance. The sound that emanates is merely a result of this motion, and as you point out, is due to pressure pulses occuring during the motion. In more detail, the reed tongue vibrates in resonance to the forcing function causing its motion. The forcing function is the pressure force vs. time trace that acts on the tongue. The resulting motion is a form of self excited vibration, because the position of the tongue determines the time at which the forcing function acts. Consequent to this, the forcing function maintains the same phase relationship to the displacement of the tongue. In many other systems, this phase can vary, becoming zero at resonance. In all systems, the part of the forcing function in phase with the displacement is what powers the dissipation in the system, whether or not resonance is occuring. When the forcing function is in phase with the displacement, all the energy of the forcing function goes into dissipation, and this serves as a definition of resonance, because then, there is no imaginary component to the impedance. With the free reed then, since the forcing function is always in phase with the motion of the reed tongue, the motion is always resonant, and the energy from the forcing function is dissipated by sound production, friction, and heat. Best regards, Tom www.bluesbox.biz