ttonon

Hi Harpomatic, I guess we have different interpretations on what is meant by very conclusive proof. To me, it would mean a well performed experiment reproducing whatever is claimed. We are at the end of a long, interesting thread, and for simplicity, let me just state that I do accept as fact that both single reed and double reed bends are possible, depending on how the harmonica is blown. The issue I have concerns only the most common draw bend, made on reeds that have a lower pitched reed in the same chamber. When I took the covers off the harmonica, exposing the reed plates, and ddid such a draw bend, I was able to put my finger over and completely block the higher pitched reed slot, thus making it impossible for that reed to participate in the bend. Experimenting in this way, I could discern no difference in musical tone whether or not the lower pitched reed slot was covered. My own experimenting here thus makes this issue puzzling to me. In his above post, Pat Missin may offer a clue to my dilemna when he states: "As the bend deepens, the lower pitched reed starts to vibrate as an opening reed, at a higher frequency than its normal pitch." Thus, in my experimenting, I may not have achieved a deep enough bend for the lower pitched reed to respond. If this is the case, then, perhaps enough mean air flow is necessary to pass through the slot in order to bend (open) the tongue of this reed far enough away from its rest position, for the necesssary vibration. Speculating further, such a high mean flow (or Reynolds Number) may be necessary to produce enough vortex activity to initiate vibration. Such vortex induced vibrations are very common in Nature. Regards, Tom

Hi harpomatic. Thanks for your comment. Can you supply me with this proof? Thanks Best regards, Tom www.bluesbox.biz

Hi Chris, interesting that the material is phosphor bronze. Is this the traditional material going back a hundred years or so? Regards, Tom

Hi Don, I have found similar behavior. I’m not sure I saw it in the thread, but I sometimes use guitar string to make springs, and there are other musical instruments that use different materials for their wires (dulcimer, zither, and others). You might give it a try if you haven’t so far. In the worst case, I found it necessary to take out most the springiness in steel spring wire, though it should work for any heat treated spring metal. To do this, I made an annealing apparatus that would very evenly heat the wire along its length for a specific time and heating current. On a plywood mounting board, I screwed in an anchor to which one end of the wire is attached about 3/4 inch above the board. I screwed in another anchor at a convenient distance away, depending on what length wire I wanted to anneal. I used an anchor here with a round cross section, then doubled back the wire to an ending anchor at its beginning location, providing two lengths of wire. If you want more lengths, simply move in a zig-zag way across the board. The two end anchors had electrical connectors, to which I attached the outlet of a Variac (also called autotransformer), which you plug into your AC wall outlet, and the AC outlet voltage of the Variac goes from zero to 100 % of outlet voltage (some makes provide 140%), depending on the position of the dial on the top of the instrument. These devices are usually fixed with 10 amp fuses (for 115VAC input). For me, I wanted to take out most the springiness, and with a little practice, I selected a convenient Variac dial setting and counted out the right amount of seconds. (For a more sophisticated apparatus, you could add an ammeter and a timing plug to accurately control these parameters.) The wire got to a dull red, better visible when room lights were switched off, and it took about 4 – 5 seconds. My guess for you, a similar red color for perhaps only one second. For a given cross section (gauge) the same current will produce the same anneal temperature (neglecting heat losses), and the anneal time will depend only on the anneal temperature. At the end, it’s best to bring down the wire temperature gradually, to prevent hardening, although this would apply only to high annealing temperatures and certain heat treating alloys. Hi Discord, It seems to me you require a technical feature of “workability,” but the fact that makers have been using full-hard tempered brass that lasts for a hundred years certainly points to its advisability. If you’re serious about pursuing the use of brass for your springs, it may be helpful to understand some of the basics. I agree that the method for making hard brass is by mechanical deformation, and for springs, the degree of hardness is one important property, most commonly described as zero hard (annealed), half hard, and full hard. From your description, you are probably in need of full hard brass. But also important for springs is the alloy composition of the brass, which is part of the full designation of the spring material. Concerning material properties on a more basic level, the yield modulus is the property of interest for springs. A spring needs to withstand high stresses and not bend, and this is what this property measures. Although Young’s modulus describes the spring constant of the intrinsic material, it doesn’t change much with different degrees of hardness for a given alloy, but the yield modulus – as you’d expect – does undergo significant change. I suggest you go to matweb.com, a premier site for property values of all kinds of materials. A page there that describes “spring brass” is: http://matweb.com/search/QuickText.aspx?SearchText=spring%20brass. On these pages, springiness is described as “spring” or “extra spring,” probably correlating with the more common terms, half hard and full hard. Clicking on the names of these alloys brings you to a page that describes their uses (at the top), and property values. If one of the uses is for springs, it will say so, and from that info, you can see that the corresponding yield modulus needs to be a little above 100,000 psi for extra spring quality. Minimum useful values appear to be below 80,000 psi. I find that there are still several companies in the US that make what they call spring brass, and a web search works well. You can correspond with these companies on what they really mean by “spring brass” and if they make it in the diameters you will need. They may recommend procedures for buying what you need (through the company, or distributors). My guess is that small hand held spools with different diameter wire shouldn’t be too expensive, if you can find them, without large minimum orders. Once you know exactly what you need, you can also go to Ebay, Amazon, banggood, and other web outlets. Good luck, and I’d be curious to know what you find. Regards, Tom

This is a very interesting thread giving the preferences that makers/repairers have in choosing materials to make concertina springs. But apart from price and availability, I didn’t see many technical reasons given for these preferences. Perhaps the technical reasons are pretty well understood by this community and not worth mentioning? But I would be very interested in these. Would someone please care to elaborate? Best regards, Tom

Hi Dana. Thanks for your replies. The frequency of the various modes of vibration of an idealized bar are not related, in principle, to each other in any simple way, as they are, for instance, with an idealized string. They occur mathematically as a solution to transcendental equations, without any other special meaning, except, only in an approximate way (see below). But each mode does exhibit regular, periodic vibrations, when excited by a forcing function that matches the mode’s vibration frequency. The periodic motion that results in each case can be represented mathematically by a Fourier series with its own fundamental and harmonic overtones, and in this sense we can call the mode’s response “regular.” The fact that a given mode, when compared to a different mode, has a different frequency of vibration that is not related in any simple way to that of the other mode, doesn’t have anything to do with the fact that we call each mode’s own vibration “regular.” I don’t know of any term that would describe the group of frequencies that characterize the series of modes in an idealized bar, except to say that their frequencies are the result of a mathematical solution. Yes, the frequency of each mode goes as (beta,i)^2, where beta,i is the ith term in an infinite series of solutions to a transcendental equation - in particular, one involving the functions cosh and cos. And for i greater than 2 (first overtone), beta,i is practically equal to (i – ½). Thus, the frequency goes as (I - 1/2)^2, or i^2 when i is greater than about 4, which is then approximately parabolic. I find it interesting that in your instruments the second harmonic (octave) is suppressed and your third harmonic (fifth) is strong. Moreover, the even harmonics are in general suppressed, compared to the odd harmonics. In my own experience with free reeds, I find that I like more a musical tone that emphasizes the odd harmonics, which is characteristic of (one end) closed tubes, and which the clarinet approximates. Similarly, of the Asian free reeds, I like most the sound of the bawu, which again approximates a closed tube. If I push to find a reason for this, perhaps it’s because the even harmonics are just octave tones - octaves of the fundamental, or octaves of lower odd harmonic tones. They thus add little to the musical tone, and it’s the odd harmonics that add color (other harmonies in the scale). Unfortunately, I never heard your instruments, but my guess they have more of what I would call a “hollow” sound to the tone, and my speculation leads me to believe that I would like it. Incidentally, you don’t need very many harmonics to produce a beautiful musical tone. Some of the tones of the clarinet and of the trumpet contain only a few, or a couple, overtones. Do you think your instruments have a characteristic sound that differs from most other traditionally made instruments? I think it best here to keep a distinction between the physics of what’s going on and the mathematics that (for whatever reason) accurately represents the physics. It’s true that the wave form of the pressure pulses in the vicinity of the reed are difficult to intuitively understand. The important thing however is that these pulses are periodic events. With that physical fact, it then becomes straight forward to represent these pulses mathematically as a Fourier series. There is of course an uncanny relationship between physical events that happen in the so called real world and basic, purely ideological mathematical concepts. But the net result is that the Fourier description adequately represents these physical events. Then, when we also discover that our brains are also using such a description in making sense out of physical sound waves, the mystery grows further. I believe heterodyne frequencies are a mathematical phenomenon. When a signal contains two or more frequencies that are relatively close together, these extra frequencies occur within the mathematics, showing up in the Fourier series. But this is a much bigger topic, and maybe it would be worthwhile to first look at some experimental results of (physical) pressure wave forms produced by the free reed, and from these, try to explain their shapes with reference to the instantaneous position of the vibrating tongue. Perhaps in another thread. Best regards, Tom

Hi John, I understand you to mean that the 3rd and 5th overtones you refer to are the overtones in the musical tone, and not the frequencies of the higher modes of vibration that are possible with the free reed, which normally vibrates as a bar in its first vibrational mode. Thus, there is no inharmonicity in the sound spectrum, or adjustment to be made in order to “match correctly” to the fundamental, during the sustained musical tone. There is, however, an inharmonicity in the start transient of the tone, in which the steady periodic first mode is developing, and such a transient can occur for several dozen to tens of dozens of cycles (up to hundreds of milliseconds), until only the sustained, periodic musical tone remains. During this sustained tone, the tongue vibrates virtually in sinusoidal fashion, and contributions to this musical tone from higher mode tongue vibration is extremely small, most often probably below detection by human hearing. Such non-harmonic contributions have been measured by experimenters, and I can provide references, but the conclusion is that such contributions to the sustained musical tone occur only at relatively high blowing pressures. I also add that such contributions can also occur when the natural reed vibration is not properly supported by the reed cavity, resulting in screeches from these higher modes that resemble the screech caused by beginning clarinet players, and the physical mechanism is basically the same. Thus the overtones in the musical tone must be for practical purposes harmonic (integer multiples of frequency), without which, periodic motion would not be possible, resulting in noise (as detected by human hearing). I don’t understand why you say it’s possible to “match correctly” the musical tone spectrum, by means of adjusting the reed profile. Is this “reed profile” the same thing as builders refer to in describing a change in tongue cross section along the long axis of the tongue? If so, where did you learn of this procedure? Do you know of any builders that practice this procedure of matching correctly the musical tone spectrum? What would constitute a “correct match”? I also don’t understand what you mean by a “figure 8 pattern” in the vibration of the tongue. Is this while looking edge on towards the tip of the vibrating reed? Might it be a twisting oscillation? As other here have mentioned, the tolerances between the tongue and slot are very small, approaching less than 0.001 inch, and although I’m skeptical, I do think it’s possible. But it’s the phrase “if not filed flat” that intrigues me, and can you please elaborate? Audacity is a free sound file software, and it offers a Fast Fourier Transform to calculate sound spectrum. The version I have doesn’t allow you to see a real time display of the transform as the musical tone is generated, but there are other FFT software that does. But I don’t see a pressing need for real time, at least if you want to make adjustments to the tongue profile, which cannot be done as the musical tone speaks. Hi Dana, I don’t understand what you mean by “multiple harmonic modes.” You explain later on that the higher modes of a vibrating bar do not have frequencies that are in harmonic ratio, so was this just a typo? But another interpretation is that you think it possible to tune the higher modes of a reed tongue (no longer a “bar”) to harmonic ratios by profiling. Well, it may be possible, but barely, if we consider practicality. However, a determined maker might possibly succeed in doing so for one or two higher modes, and learning the skills to make it easier. Then, we’d have to ask why do it? There might be a fortuitous case that the self-excitation mechanism might possibly excite a higher harmonic mode along with the fundamental, in which case some higher harmonic (say near the 5th) of the musical tone would be emphasized. For the bar, these higher modes tend not to be excited, probably because they are non-harmonic. But I can see that a higher mode with harmonic relationship to the first might be excited. But finally, would it be worth all the work, when all you can do is emphasize at most just a few higher harmonics in the musical tone? Okay, I see that you are using the term “natural harmonics” to describe what are really “higher modes” of vibration. “Harmonics” probably goes back to Greek times and was related to the harmonious tones they found in musical sounds, using lengths of string that have whole number ratios in their lengths. The term then got combined into other, related mathematical concepts (such as in the harmonic functions, sine and cosine), so there are multiple meanings in common speech. But in science there is no doubt. A harmonic series in mathematics I believe is defined as a series having integer multiples of each other, and this rule is followed strictly when talking about sound spectrums. I’m curious, how did you excite these higher modes? As you verified, the mathematical solution for the vibrational modes of a bar (strip of metal with significant thickness) can be found in standard vibration texts, such as the old, still excellent, classic one by Phillip Morse, “Vibration and Sound” (or the later version, written by Morse and Ingard). In the idealized bar, the frequency of the second transverse mode is 6.27 x f1, where f1 is the frequency of the first transverse mode. The third mode vibrates at 17.55 x f1, and the fourth at 34.4 x f1, which as you say, are rapidly increasing in nonlinear fashion. Incidentally these ratios are proportional to the inverse square of the bar’s length, unlike with the idealized string, where the allowed frequencies depend on the inverse first power. If you still have your data, you can check this, though there could be differences since you were probably not working with idealized bars. Let’s recall that the tuning fork also vibrates more or less as a vibrating bar. When you strike a tuning fork, you first get a high frequency ping, a pronounced start transient (attack) which rapidly dies out to the sinusoidal fundamental cantilever-type vibration (as described above). This is basically what the free reed does, only the attack is not nearly as sharp, or as energetic, since it’s caused by much gentler aerodynamic forces When I measure the harmonic frequencies calculated by Audacity, I most often find integer ratios within very small percent errors. As I mentioned above, this result, together with the result of distortion due to a contribution from the second beam mode at high blowing pressures have been well documented in the literature. Agreed, with restrictions due to attack, high blowing pressure, and mismatched cavities. This is part of the “self-excitation” mechanism, which is periodic, and any periodic function describing that motion can be represented mathematically by an infinite series of sinusoidal functions (Fourier’s Theorem). Physically, the tongue’s motion is caused by an airflow (forcing function), and in feedback, the airflow is caused by the motion of the tongue. The asymmetric nature of these aerodynamic forces that you point out allow for a net transfer of energy from the steady airstream to the vibrating tongue. The sinusoidal response, which is the major response that interests us, is a result of the fact that, in periodic motion and at sufficiently low amplitudes, the governing equations are linear. With much natural phenomena and with small amplitudes of response (usually up to 10 % of their mean values), the effects are closely linear, but as amplitudes become large (around 20% mean value), linearized solutions lose accuracy. The study of acoustics illustrates the close relationship between physics and mathematics. How large are your fifth overtones (which would be 6th harmonic) compared to the fundamental? Please make the units clear in your results (amplitude as a length ratio, or in decibels). I’ve sometimes noticed that free reeds vibrate with a second harmonic (first overtone, or second partial) that is larger than the fundamental. I’ve never seen one with a larger 6th harmonic. Might your result be typical with traditionally made concertina reeds? I think it would be extremely difficult to appreciably alter the sound spectrum in a predictable way by modification of the tongue profile. Is “stiffness” the same thing meant by “spring constant”? Hi Chris, I don’t think the actual vibration is as you imagine. There cannot be different parts of the tongue that vibrate in “separate rhythms” during the sustained musical tone. Such behavior would preclude an overall periodic motion, and thus, air would not be chopped with a decided frequency, which in turn would result in noise. However, during a start transit, the different modes caused by these different parts could be excited, and in the special case when the frequency of a higher mode is harmonic to the fundamental, I could believe it perhaps possible that the higher mode could be somewhat excited during normal operation, as I explained above. But more generally, some spring/mass/dissipation systems do have more than one degree of freedom, as does the tongue you describe, and each degree of freedom will result in its own modes of vibration; however - when we consider sustained vibrations (periodic motion) - each of these modes needs to be continually excited by an appropriate periodic forcing function of the right frequency. Take a metal plate as an example, or a bell, or very commonly, a violin string. These each have many modes of vibration, most all of different frequencies, yet you can excite any mode in a sustained manner by applying a periodic force at the antinode of the mode’s vibration. The violin is distinguished in this group in that it’s made (along with its bow) to produced sustained vibrations, as is the free reed. A bell is made for its start transient; when hit by its clapper, most all modes are excited, but none are sustained. The piano is also primarily an attack instrument. Even though it seems to produce sustained tones, its musical tone is really a prolonged start transient. With a bell, there are so many modes with non-integer ratios in frequency that its sound is between noise and music. These higher modes, however, die out faster than the lower modes and we’re left with a low musical hum that goes on for a relatively long time in a big bell (a few tons). The higher frequencies in the higher modes produce larger particle velocities and higher cycle rates on which dissipative forces act and are thus shorter lived. For similar reasons, we only hear the low pitched rumbling of distant thunderstorms, fireworks, or bombs by the time the sound reaches our ears.

Rlgph, I congratulate you on your success so far, with a novel way to construct a free reed. I think you’ve demonstrated that it's possible to make an “asymmetric” free reed into a symmetric free reed, with the ability to voice upon either air flow direction. I think most of us here realize that, although this is a good start, there’s need for improvement, if this design is to be widely utilized. Before getting into too much detail, can you explain more about how you fed air to these reeds? Was the concertina disassembled and was the apparatus fixed at one end, as pictured, or did the sounds come from an assembled instrument, with you holding the bellows with both hands? Was the microphone mounted securely so that its position relative to the reed did not change during voicing? Where was that position? In the Audacity traces of the Bi-reed, could you identify which set of traces correspond to push and pull of the bellows? You indicate that the second, fourth, sixth and eighth traces with the larger amplitude are compressions, but could you be clearer about that? For the Uni-reed, was the voicing done with positive (push) or negative (pull) pressure in the bellows? For the Uni-reed, Audacity gives the frequency of the fundamental partial as 292.0 Hz, and that trace indicates that the bellows pressure was not very constant during voicing. I point out that Adaucity can give small variations in fundamental frequency, depending upon the choice of the number of sample points. The more points, the more accuracy, if the trace is strictly periodic. And if I may suggest, that in further experiments, you use some kind of mechanized air flow apparatus. For the Bi–reed, the odd number traces seem to be louder, despite the visual indication of lower amplitude. However, I notice that traces 2, 4, and 8 contain an audible click, which I assume is noise, and trace 6, which doesn’t have this click, does not show such a large “transient” amplitude. What about that click? I don’t know if this is really a transient, because the air delivery may not be constant, but if it is a transient, at about 500 msec, it’s quite long as far as musical instruments go. Here, I think Chris’s question is pertinent. It might be helpful if you performed a “bellows shake,” trying to determine the minimum time required to establish the musical tone. With the odd number traces, I also notice a slight drop in pitch towards the end. From Audacity, I get for the third trace, a pitch of 296.1 Hz for the steady part and 293.4 Hz for the end part, a drop of almost 3 Hz. Small but noticeable, and it’s puzzling how that could occur. Usually the pitch of a free reed will drop as bellows pressure is increased, and there is shown no increase in volume. Do you have any idea what would cause this drop in pitch? To me, the most interesting aspect of this experiment is the hollow, feathery sound that accompanies the odd numbered traces, and this may provide a hint at how to improve the musical tone of the free reed. For years, I’ve wondered how to improve the sound of the western (asymmetric) free reed (WFR). To me, the Asian (symmetric) free reeds have much more interesting sound, simply because they incorporate a resonating air column for their voicing, and the WFR does not. For instance, you can find the sound of the Bawu on the internet, and because of its mounting in a tube, it has the hollow tone of the clarinet. But it’s not just the tone itself. I think it would be an improvement to the tone of the WFR if each reed can be made to have its own signature sound, such that it could stand out better among other musical sounds, and in particular, among its own musical tones (as in playing chords). Looking at it from theory, the chief characteristics of the sound spectrum of the WFR are the lack of a distinctive start transient and the presence of a very large number of harmonics (partials whose frequencies exhibit very nearly exact whole number ratios). I believe modification of either one of these features would improve the musical tone of WFR instruments. The WFR produces sustained (steady) oscillations in the musical tone. Other musical instruments that also produce sustained tones, such as the beating reed instruments, the bowed string instruments, and the Asian free reed instruments, do not generally have such large numbers of overtones. I think their tones have more distinguishing character than those of the WFR, which have such a large number of partials with coincident frequencies that perhaps our hearing is overwhelmed by them. The individual notes of musical instruments incorporating strong start transients, such as stringed, and other, instruments that are hammered or plucked, can easily maintain their own identity among other, similar tones. In fact, the Hammond B3 electronic organ, I think, became such a jazz favorite largely because of its distinctive start transient. The instruments that produce their entire tones by a transient, such as the piano, guitar, xylophone, etc., contain inharmonicity in their partials, because of nonlinearities in their sound sources. Some of these even contain relatively large numbers of partials, but these partials can be discerned among themselves, perhaps because the partials do not exactly coincide in frequency. So again, maybe our hearing system doesn’t get confused. Getting back to the tone in traces 1, 3, 5, and 7, perhaps improvements to the tone of the WFR can be made by introducing a small amount of noise into the tone, such as what I detect here, which would cause inharmonicity - perhaps a good thing. Concerning the other chief feature of the WFR sound spectrum, perhaps a strong start transient can be introduced by a mechanized finger that plucks the tongue the instant the key is pressed. Of course, complex construction is a bad thing, so any attempted improvement must be very simple. Regards, Tom www.bluesbox.biz

This reminds me of the joke about Joe, an accordion player who met a friend for lunch in a restaurant, and in the middle of lunch expressed concern whether his accordion would be safe inside his car left on the street, even though he locked the doors. His friend said that locked doors didn't matter much because in the city, robbers just smash the windows. So after worrying through the rest of lunch, Joe makes back to his car, to find its back window smashed wide open. But then, when he opens the door, he finds not just his accordion, but two accordions. So getting back to Walnut Middle School, I wonder. Regards, Tom

The energy released on a pressurised vessel is called the burst energy. Basically the pressure differential between compressed air in an enclosed vessel to atmosphere, and between a partial vacuum and atmosphere is far greater when measured a little away from the point of release. If you blow through a drinking straw the jet airflow projects far further than any detectable air flow at the same distance if you suck at the straw at. the same rate. Not a factoid, but a matter of physics. Dave Hi Dave, I'd like to comment on the physics of the issue you raised, and not on the differences in musical response that you experience with push and pull of the bellows. I find the above paragraph you wrote confusing. Let me explain the physics the way I see it, in the hope we can arrive at a common picture. Let's first simplify by eliminating the reed and replacing it with a round hole, and let's consider only steady flow (no changes in time). With positive pressure in the (push) bellows, air flows from inside the bellows through the hole to the outside. Just downstream of the hole entrance plane, a jet forms, extending many jet diameters downward. The static pressure inside the jet is equal to the static pressure outside the jet - the atmospheric pressure outside the bellows. (This is not the dynamic pressure of the jet, which is equal to the static pressure plus an additional term proportional to the jet velocity squared.) There's an entrance region upstream of the hole, where the air velocity increases in moving toward and through the hole, reaching a maximum at the point where the jet forms (where the sides of the jet become straight and parallel). That is the point where the static pressure in the jet equals the static pressure outside the jet. At the entrance, air velocities are very small a short distance upstream from the hole, at roughly at a distance equal to a couple hole diameters. With negative pressure in the (pull) bellows, the picture is a mirror image of the positive pressure case. When we replace the hole with a reed, the flow field is much more complicated, because of the modulation in air flow caused by the vibrating reed tongue and superimposed on the steady airflow. Notice also that the reed is in the wall of the vessel, not at a distance downstream from the wall, but in the location where any momentary jet may attempt to form. If you agree with the above description, can you explain the physical point you'd like to make by relating it to this steady flow picture? If so, I think I can better understand what you mean. Regards, Tom www.bluesbox.biz

Chris, I think the concept of formants can in principle be applied to free reed instruments, but a remaining question for me is how many players/listeners can actually identify them. In theory, there are many similarities between the human voice and free reed musical instruments. Both have as sound source vibrating reeds that are uncoupled to the downstream resonating geometries, and these geometries act as passive filters. I’m probably repeating some of the things I said in an earlier post, but with other kinds of sound producing reeds, such as beating reeds, there’s a strong coupling to a resonating air column. Indeed, the Asian free reeds (so-called symmetric reeds) are also strongly coupled to a resonating air column. The length of this air column must necessarily be of a size comparable to a wavelength, or greater, and this air column is a major player in the resulting sound spectrum. In the case of the voice (and mammal vocalizations in general), the glottis sends out a train of clicks, which contains many partials. Some of these partials are selectively amplified by the vocal/nasal tract, and the resonant geometries can be easily identified because they are sized large enough to affect the lower partials. Said another way, these geometries are large enough so that their fundamental resonances are not too many multiples of the fundamental frequency of the glottis click train. The free reed also sends out many partials, and I think we all agree that the relative magnitude of these partials is modified by the cavity and nearby structures, but it’s not as easy to identify the resonant modes here as it is in the case of the voice, simply because the concertina geometries are rather small compared to the relevant wavelengths. In a previous post, I tried to argue that a “boundary effect” could provide such a resonant/reverberant function, though it introduced three dimensional concepts. (In contrast, with the voice, even simple tubes can provide believable resonant modes.) Also, with the free reed, there may be certain features in the reed design itself that contribute significantly to these observed formants. Concerning the identification issue, if you can identify within the Fourier analysis certain dominant regions that remain constant for a range of notes, this would certainly support your claim that you can hear them. Of course, if you cannot, it doesn’t prove that you cannot hear them. But this is a subtle point in the meaning of formants. The formant (dominant) region maintains the same frequencies, regardless of the fundamental pitch of the glottis train. Thus, even though the speaker changes the pitch of his/her voice, it doesn’t change the basic frequency span of the formant characteristic. If we can extrapolate this fact to the case of concertinas, this indicates that a geometry that produces identifiable formants for one note should produce the same formants for a range of notes. At least for those notes that have a fundamental pitch that is lower than the frequencies identified with the formant. (Otherwise there would be no frequencies to enhance.) So whether it’s the details of reed construction or cavity construction that cause these formants, we arrive at the concept of “scaling,” in which only a couple/few different geometries may be required to produce a formant that persists throughout the musical range of the instrument. I seem to observe that formants tend to lose their dominance in the highest range of the voice/concertina. I think many, if not all, instruments struggle to maintain their identity in the highest notes of their musical range, and builders have always struggled to produce instruments that maintain their identity in those highest ranges. One major contribution to the fact that the highest registers often thin out is made by the fact that our frequency range of hearing is fixed, and there are less hearable overtones in those highest notes. Regards, Tom

Hi Dana, from my reading, the seminal reference for the Acoustic Theory of Speech Production is a book by that very name written by Gunnar Fant (below). I haven’t read this book, nor tried to find it, so I can’t say how much intuitive explanation Fant includes. But you can probably find it new or used on the Web. A newer book is one by Stevens (below), and again, I haven’t read it. Gunnar Fant, Acoustic Theory of Speech Production, Mouton: The Hague, 1960 (second printing, 1970). Kenneth Stevens, Acoustic Phonetics, MIT Press: Cambridge, Massachusetts, USA, 1998 But as I’m sure you know, many universities now put some of their basic course works on the web, and I’ve learned much from “taking” these courses, in a picking kind of way. A link that explains most of what I posted, with additional material can be found here: http://clas.mq.edu.au/speech/acoustics/frequency/vocal_tract_resonance.html . This link is a most elementary introduction, and to see, for instance how complex things can get, you may want to (only) look here: http://www.soundtransformations.co.uk/TheEffecOfTheHypopharyngealAndSupra.htm . Finally – and this may be of most interest to many people here – here’s a link to an interactive applet that enables you to pick out a desired vowel sound and hear how a tube model would respond: http://auditoryneuroscience.com/topics/two-formant-artificial-vowels . In addition to the audio, there are shown Fourier Transforms, and the user can change the glottis pitch. So let’s say the “Holy Grail” for concertina builders is to have a buyer select from a sound file of various recordings of concertinas having different formants, with the builder then able to deliver as requested. An applet like the one above may be part of that process. You can hear the vowel (formant) and you can see the associated Fast Fourier Transform. Now all we need is the skill and knowledge of the builder to make an instrument that provides the desired spectrum. Having the spectrum, I believe, is a further step than simply specifying a sound, because the spectrum hints at what aspect the builder needs to pay attention to. For instance, overtones are sometimes affected differently by different key parts of the instrument, a feature where theoretical suggestions might be welcomed. Thus, such a tool might be helpful in efforts to “pin down the source of this common tone.” In fact, I would go so far as to suggest that the above applet be used as a kind of central reference when people here want to explain what they are hearing in their concertina music. I find interesting your observation of an “instrument formant,” which I like, and you appear to be serious about it. This is definitely part of grabbing that Holy Grail. Your observations on the complications with pad holes are also interesting. Tell me, is there any notice of asymmetry with regard to bellows direction? I can visualize, during the draw and with reduced hole area, that the mean airflow will cause a jet of air into the cavity – something that doesn’t occur with the blow. It’s my feeling that jet flow can cause a disturbance in the self-excitation mechanism of tongue vibration. (A major reason for the existence of the cavity may be to distribute airflow.) It may be that the sudden change in tonality with pressure increase that you observe may occur when the jet is strong enough to reach the tongue tip and cause such a disturbance. If you have the energy, you might try to install a tiny baffle inside the cavity, say a piece of wood placed an angle to the cavity major axis, attached to the cavity top near the hole, in the corner, and ending with a small gap between it and the cavity floor further in. The idea is to get the airflow as uniform as possible before the reed sees it. I don't see a need for a tight placement with the cavity walls, and in fact, you probably should leave a little gap there. (You can also experiment with a hole or holes in this baffle.) Such a baffle might also benefit in the blow direction, because with the added resistance it might force airflow through the reed to be more like that of a reed in free space. Even more so with the blow direction, jet formation on the outside of the cavity, caused by a smaller hole, might produce significantly more (viscous friction) dissipation. Airflow power in a jet goes as the cube of jet velocity, and since jet velocity goes inversely as area (diameter squared) for the same total flow, the total power goes as the fifth inverse power of hole diameter. This is a very strong dependency. Such increased dissipation might also produce a change in timbre. In general with vibrations, added friction lowers the sharpness of their resonance peak (Q value) and widens the response into adjacent frequencies, perhaps lowering brightness. Up to now, I’ve been talking mainly about the mean flow through the cavity/hole, which can be steady in time. But there are acoustic effects riding on this mean flow. Thus, if a mean flow causes a jet, the oscillatory flow will be superimposed upon this jet flow, and one can draw, I believe, many of the same conclusions with oscillatory, unsteady flow as with mean flow, in this case. The “breathiness” of the tone, as you describe, indicates to me that turbulence as perhaps caused by a jet is the underlying culprit, causing an inefficient conversion of energy to the sound field. Because of these different mechanisms, the asymmetric behavior may not be as pronounced as I first imagined. But it’s difficult to try to cover all possibilities without seeing any drawings of the relevant geometry. Yet it still may be possible to discern even very slight differences, using these wonderful ears Nature has bestowed on us. I praise the advances in ear protection and associated laws that have prevented much hearing loss. I, however, did some damage to my ears before such methods became a no brainer. Finally, looking only at the acoustic effect of smaller holes, we can perhaps draw some insight from the behavior of possible cavity resonances, though this would admittedly apply only to the highest pitched reeds. It’s important to know just what kind of resonance is occurring; e.g. quarter-wave or Helmholtz. But speaking generally, a smaller hole should cause an increase in resonant frequency for quarter-wave resonance. This is because of the “end correction” used to replace the actual tube length with a length that includes the inertial effect of air vibration immediately outside the tube’s open end. For most practical situations, this end correction goes as the hole diameter. Thus, smaller diameter means less end correction, which means less effective length, which means increased frequency. For Helmholtz resonance, we have the well-known expression for resonant frequency: f = c/2/pi*(Le/A/V)^0.5, where c is speed of sound, pi = 3.14, Le is effective length of the constricted region, A is the area of the constricted region, and V is cavity volume. This expression is valid for any consistent set of units, and it also shows that decreasing hole diameter (A) will also increase resonant frequency. (The effect on Le goes as the diameter, whereas A goes as diameter squared.) In fact, it may be instructive for you to fool around with these calculations for resonant frequency (for quarter-wave, f = c/4/Le) and compare them with reed pitch. Such comparisons can greatly accelerate theoretical understanding. As I mentioned in another post, harmonica builders have lots of trouble with some kind of resonance in the highest reeds; it seems much more than do accordion builders. They seem to have a rule that, when the cavity resonant frequency is less than reed pitch frequency, there will be a tendency for offensive resonance between cavity and reed. And of course, they add their vocal/nasal passageway to the mix. But they measure the cavity resonance frequency by taking the comb out of the instrument and placing a very tight cover over the cavity. They then blow on the cavity, and it sounds like a whistle. With this method, I do believe they are measuring quarter-wave resonance. But one cannot rule out Helmholtz resonance with the assembled instrument, and the total geometry needs study in order to rule out this possibility. Concertinas have much larger cavities than harmonicas, so the possibilities for Helmholtz resonance are more numerous with concertinas, at least from the calculations I made. I guess the main reason I just explained these details about harmonicas is to impress upon you the importance of cavity resonance with free reeds, for the higher pitch reeds. Although not usually viewed as a resonance (perhaps more as a reverberation), the boundary effect I mentioned in a previous post may also come into this discussion, for reed pitches throughout the instrument's range. A smaller hole diameter may increase this effect by producing more wave confinement. Any acoustic oscillation about the hole region because of the boundary effect, can be affected in the same way Le is affected in quarter-wave and Helmholtz resonance. Additionally, smaller holes will in general reduce the radiated sound, causing the buildup of more oscillatory energy within the cavity. But another reason to mention about harmonicas is that perhaps you can use a similar method to measure a resonant frequency of the cavity. A major benefit of that measurement would allow us to separate quarter-tube resonance from Helmholtz resonance. You would probably have to build a test cavity, having the same precise dimensions as the real cavity, with blocked reed included inside the cavity. Blowing air across the pad hole brings with it certain issues (e.g. disturbing the external vibrating air mass) but some of these can be corrected for, and I think that the major benefit will be realized. Regards, Tom

Adrian, you really hit the nail on the head here. In fact, experts on harmonicas have told me that the problem of reed choking is a serious problem for the highest notes in the higher keyed (register) instruments, and my guess is that the addition of the vocal/nasal tract is a significant part of the problem. Some builders have to give up on certain designs for the higher keys, because it seems, there's no general solution for it. But some of the choking of the lowest pitched reeds in this category can be eliminated by certain tricks, which indicates to me that, in these instances, cavity resonances may act more or less independently from the vocal/nasal tract. Also, professional players talk about and share embouchure tricks, which I would guess would be very difficult for novices to master. To illustrate to accordion-minded individuals the power of the vocal/nasal tract, take out a typical accordion reed block and play it with your mouth, like a harmonica. In my experience, many of the reeds completely choke, or at least, cannot be made to voice properly. Some of those reeds, however, will play if I block my nose shut while playing. Such a simple change in the nasal tract, and voila! Regards, Tom

This thread reminds me of the problem in Acoustic Phonetics – a branch of Linquistics – in which acousticians study how the sounds of human language are made. The geometry of interest here is defined by the air passageway between vocal chords (larynx) and lips, including the nasal passages. As usual, the complex problem is first broken down to see how much can be learned from simple models, and these models are often explained in beginning textbooks on phonetics. The simplest approach is to replace the complicated air passageway between vocal chords and lips with simple tubes having different lengths and crossections and to eliminate the nasal passages, since with English, nasal sounds do not occur much during speech. There are two-tube, three-tube, and four-tube models. As I understand, the vowel sounds are fairly well produced using the two-tube and four-tube models. The three-tube model can fairly well produce at least some of the fricative (consonant) sounds. Here, assumptions are made that the larynx is not affected by the air passageway and that the air passageway is not affected by the input provided by the larynx, which varies in frequency and volume. These are good assumptions, because we don’t notice that our larynx struggles to operate during speech and that we can change the shape of the vocal tract without hindrance from how we operate the larynx. The larynx operates much like a double beating reed, as in oboes and other musical instruments. Air pressure supplied by the lungs separates the larynx’s fleshy folds, and once flow (air velocity) is established, the pressure in the air stream drops, via Bernoulli, bringing the folds back together, and the cycle repeats, in self-excited fashion. The larynx thus produces a train of rapidly occurring clicks, with frequency and intensity controlled by the speaker, and the sound of this train is modified by the tubes, which act as passive filters. Tube resonance thus plays a major role in creating the “formants” of speech. Formants are the portion of the resulting sound spectrum that are identified with recognizable speech sounds and are usually the result of resonances in the vocal tract. Such formants maintain their identity, regardless of the frequency and intensity of the sound input from the larynx, and thus male, female, and child sounds can be fairly well reproduced. It’s amazing to me how such a simple train of clicks can be so modified to produce the complicated sounds of speech. As a further simplification, the separate tubes within each model can be considered to operate independently from each other, in which case, it’s a simple matter to calculate the resonant frequencies, using simple expressions for quarter-wave, half-wave, full-wave, and Helmholtz resonances. Acousticians have gone far beyond the above-mentioned simplifications of the phonetics problem, even including the nasal passages, often by breaking all the passageways up into small segments, each about a half centimeter in length, and by building an associated analog electric circuit to calculate the response. In fact, people have also analytically studied the singing voice, including Tuvan throat singing, with decent results. With opera singing, there appears to be an additional formant that does not occur during normal singing. Hence the “opera sound.” There are similarities here with concertina reeds and cavities, although large differences can occur because of the disparity in passageway lengths. Another difference is the fact that the self-excitation mechanism of the vibrating tongue can be disturbed by certain resonances. An average male passageway from larynx to lips is about 17 cm, whereas in concertinas, the corresponding cavity length is typically only a fraction of that. But again, feature lengths by themselves don’t mean very much in acoustics, and so these lengths must be compared to the wavelengths of interest. Also, we are not only concerned with fundamental wavelength, but also with the wavelengths of harmonics. I already did some calculations that explored the possibilities for resonance all along the pitch range of concertinas, including harmonics (http://www.concertina.org/archive/pica/pica_2005_2/pdf/reed_cavity_design_resonance.pdf ), with the discovery that both quarter-wave and Helmholtz resonances are possible for typical cavity geometries throughout the Concertina pitch range. For Helmholtz resonance, typical cavity geometries might resonate with only higher harmonics of the lower pitched reeds, but resonance with the fundamental becomes increasingly possible as reed pitch increases. There’s also possible resonance with quarter-wave geometries, although these occurrences are more spotty than with Helmholtz resonance. But for the general reed/cavity problem, we are left to our intuition in trying to physically explain much of what experimenters have found. One tidbit of information here is that, when a sound wave collides with a rigid, non-absorbing wall, it bounces back, in mirror-like reflection, with the reflected wave adding to the impinging wave. Thus, the oscillatory maximum pressure amplitude near the wall is twice that of the impinging wave. By “near the wall” we mean some length compared to the wavelength, and in this case, the length is about an eighth of a wavelength (the extent of the “hump” of the sound wave). This phenomenon is exploited by so-called “boundary microphones.” Now let’s take the case of a reed oriented such that its tongue tip is mounted at the cavity end far from the pallet hole. On the blow, the vibrating tongue meters pulses of air into the cavity. One can infer from the boundary effect that these pulses cause an increase in oscillatory pressure amplitude above that which would occur if the cavity weren’t there. My intuition leads me to guess that the volume of the musical tone should be increased, and because of the additional "loading" of the reed, its frequency to perhaps decrease. To pass judgement on the spectral response, we need to calculate first the highest frequency that the boundary effect can support. I believe cavities are normally wider than they are deep, so the first limitation on the spectrum will be determined by cavity width. Consider a width of about one inch. Thus, 1 = 8*Lamb, where Lamb is the wavelength, giving a wavelength of about an eighth of an inch (3 mm), and a corresponding frequency of over 100,000 Hz. Such a large frequency indicates that all pitches and harmonics in free reed music will respond to enhancement because of the boundary effect of the cavity. For the draw reeds, the reasoning is the same, since a wall enhances rarefactions the same way it enhances compressions. Note also that this analysis incorporates two- and three-dimensional effects, which greatly complicate a mathematical approach, though of course, numerical methods to solve partial differential equations have become much more adaptable for such problems. However, I’m not aware of a good analytical solution to this problem. Concerning the effect of chamber depth, the above approach again yields frequencies far above the musical range. Thus all reeds throughout the pitch range should be affected similarly by the boundary caused by the floor of the chamber. As Chris has pointed out, this boundary, if too close to the vibrating tongue, might start to interfere with reed performance. Perhaps this is so because the boundary produces increased pressure amplitude - and a corresponding decrease in velocity amplitude – very near to the vibrating tongue’s self-excitation mechanism. If that’s true, perhaps the in-cavity reeds will first experience a disturbance made by a too-shallow cavity depth. Also, one can reason that mounting the reed so that the tongue tip is near the pallet hole causes a reduction in this boundary effect, since much of the sound energy passes directly out of the hole, before it can acoustically couple to the air in the cavity. I don’t think that this intuitive reasoning can explain all the observations that Dana, Chris, and others have made, but it at least tries to involve acoustic principles into the discussion. Incidentally, as I indicate above, I do agree with Dana when he wrote that the direction of airflow is not key to understanding these acoustic phenomenon. Regards, Tom

I'd recommend to anyone interested in the subject to read Benade's book, a classic. He stresses intuitive understanding of how things work, and since we're not dealing with Quantum Physics, our intuition on these topics can be valuable. Regards, Tom

I echo the same sentiment and add that we learn by understanding what we don’t know. I observe this thread to contain a combination of empiricisms and speculative theorizing. Speaking truthfully, I have more respect for the empiricisms collected by people who have performed experiments. On the theorizing, I see a lack of acoustic principles, even the simplest principles that I believe everyone here can understand. Let’s face it, sound is an acoustic phenomenon, and it’s obvious that any adequate theoretical understanding of how musical instruments work must involve acoustic principles. For example, take resonance. In general, this can be a very complicated subject, requiring some very involved mathematics. However, there are also simple models that can sometimes shed much light on a given instance of resonance. In particular, we have the resonance of simple tubes (cylinders of constant cross section) and so-called Helmholtz resonance, produced with acoustic excitation of an air volume closed everywhere except for a relatively small opening (say, the area of the opening is much smaller than the area of the entire enclosure). Thinking only in terms of “length of the air passage,” or “dead air space” etc., as has occurred here, suggests that the thinker is taking a steady flow perspective that eliminates any acoustic principle. Such an approach will fail to theoretically describe the acoustic phenomenon. It would be much more productive to think in terms of lengths in comparison to the wavelength of oscillation, in terms of the inertia of a vibrating air mass, or in terms of the springiness supplied by the compressibility of air. Importantly, the air is oscillating, as the source of sound. There may be a mean or average velocity due to flowing air, but impressed upon this mean motion are oscillating (vibrating) air particles, and this oscillation is fundamental to acoustics, an inherently unsteady phenomenon. Thus, when the length of a tube, closed at one end and open at the other, is equal to a quarter wavelength, there will be resonance. This can be seen graphically by drawing a quarter of a sine wave alongside the tube, starting at zero at the tube’s closed end, and its maximum at the open end. This is the graph of the air velocity amplitude of oscillation, since there are zero oscillations at a wall and maximum oscillations at the opening (the boundary conditions of the problem). The graph of pressure amplitude is the mirror image, maximum at the wall, minimum at the opening, and this fact illustrates the law of Conservation of Energy (the sum of potential energy and kinetic energy is constant). If the tube were open at both ends, it would resonate with an acoustic wave having a wavelength twice the length of the tube (half-wave tube). Here the sine wave can be drawn with a maximum at both ends, and such a graph would represent the oscillatory velocity amplitude, since it must be maximum at the openings. Pressure amplitudes again will have zero points at each end. One can thus reason through the situation with full wave tubes and larger. In all these examples, the essential parameter is the length of the tube divided by the wavelength of oscillation and it ranges from somewhat near unity (0.25) to larger. With the Helmholtz resonator, in order to apply the simple model, all resonator dimensions must be much larger than the wavelength (again, wavelength being an essential parameter), in which case, there is a simple expression to calculate the resonant frequency, utilizing cavity volume, hole area (diameter) and wall thickness. The vibrating air mass in and around the hole interacts with the springiness of the air within the cavity, analogous to the vibration of a spring/mass system. In proceeding with such an approach, more complicated mechanisms can be incorporated, such as friction, and radiation of sound. As an example, and to fill in a gap I’ve noticed in this thread, we can look at the case when a reed tongue tip is mounted near the closed end of the cavity and the length of the cavity is a quarter of the wavelength, defined by the pitch of the reed. In this case, the reed will probably choke, and the only way to explain this behavior is to resort to acoustics. When the tongue is working, air pulses, produced by the siren effect, emanate from the reed. Thus, the vibrating tongue is a flow control device, which requires that it be able to move air in an oscillatory fashion. But if the resonance of the tube demands that there be zero velocity amplitude at the closed end and the vibrating tongue requires that air oscillation be large there, there arises a conflict, and many times, the self-excitation mechanism of tongue vibration may be disturbed enough to prevent the reed from speaking, or at least speak with a weak sound. This choking phenomenon now and then happens with accordions, with the highest pitched reeds, since the wavelengths involved only there become commensurate with the cavity length, and I’d assume, also with concertinas. From knowledgeable sources, I understand that it happens quite a bit with harmonicas. There are a couple simple solutions that makers have learned. One is to simply turn the reed 180 degrees, so that the tongue tip is near the pad hole, which eliminates the conflict that produces choking, and possibly in addition, stuff the cavity so that it’s cross section is very small near the tongue rivet and gets larger towards the pad hole. This triangular shape changes the resonant frequency of the tube (non-constant cross section). Another solution is to not change the reed orientation, but to drill a small hole near the closed end. The leaking air there will reduce the otherwise maximum pressure amplitude and dissipate the energy of tube vibration. Thus, applying acoustic principles can be productive, although I admit that the experimenters are often ahead of the theoreticians. (I tend to think that the solutions I mentioned above to cure reed choking were probably discovered by makers, without theoretical consulation. But maybe not.) Sometimes, theory can help reduce the dog work associated with a trial and error method of discovery. Perhaps this has been less the case with free reeds than it has been with other instruments, most notably, violins. I hope I haven’t bored too many people with this post, and I hope I don’t put a damper on those willing to guess and conjecture. It’s only a suggestion for what concepts to juggle in one’s head. Then of course, we have the human trait which says that the more we know, the more we want to know. In any event, I do find such discussions interesting, for many reasons. Regards, Tom www.bluesbox.biz

Hi Ron, your “1.(alternative)” post contains no less than a colossal error! The air in the top and bottom reservoirs, having static pressures P1 and P2, respectively, is at rest. This is the meaning of a “reservoir,” and as I made clear in my first post: “…let the pressure of the motionless air in the reservoir above the reed be P1 and the pressure of the motionless air in the reservoir below the reed be P2.” In other words, we consider the air in the bellows to be at rest. Do you really think the air inside the bellows is moving? If so, with what velocity? In any event, your V1 is zero, and the conclusions you made are incorrect. I hope it helps if I elaborate on a few concepts necessary to understand the physics of how a free reed operates. These concepts are readily applied by a fluid dynamicist, and they must provide a theoretical basis for understanding our little friend. Steady, quasi-steady, and unsteady flow: Picture an edge view of a vertical plate, where the reservoir on the left is at pressure P1 and the reservoir on the right is at P2, with P1 > P2, and there is a hole (orifice) drilled through this plate. There will be airflow from left to right through this hole. First consider the pressure difference (P1 – P2) constant in time. At any point there is airflow, there will be no change in its pressure and velocity. The only changes are spatial (convective), as air molecules move from left to right through the hole. This is called steady flow. Now suppose P2 stays constant, but P1 changes, and consider an air molecule just as it enters the left-side of the hole. Suppose in the time that it takes P1 to drop only 1% of its value, the molecule zips through the hole and reaches a distance more than ten hole diameters downstream. As far as this molecule goes, it experiences essentially the same situation as a corresponding molecule in the above case of steady flow. Thus, if the stay time of a fluid particle in the region of interest is much much smaller than the time it takes for the pressure to change, we call the flow quasi-steady. Many times, we conduct quasi-steady analyses when the stay time is only much smaller than the times needed for changes, and still get good results, say, within about 10%. Now suppose that P1 changes 50% in the time it takes for the molecule to reach only to the middle of the hole. This molecule is thus influence by a range of appreciable pressure differences during its flow, and thus, it will experience changes in velocity in time as it flows. Such accelerations are time derivatives, and these cannot be neglected, as they are in quasi-steady flow. This is unsteady flow, and it can result in flow regimes that are entirely different than those experienced in steady, or quasi-steady, flow. Let’s again consider P1 > P2, with constant values, as in steady flow, or with changing values having a characteristic time (period) that is much larger than the stay time, as in quasi-steady flow. Airflow will be from left to right through the hole. The air molecules on the left will be essentially motionless, except those very near the hole. Imagine yourself exiting a very crowded room through a small door. You move very slowly, until you are very near the door, and once within the doorway, your motion greatly increases. Similarly, when the approach of the air molecules gets to a distance approximately one or two hole diameters away from the hole, they experience significant convective acceleration (not temporal acceleration), increasing their velocity up to a maximum as they are ejected from the hole. Air emanating from the hole forms a jet. This is because the airflow separates from the downstream edge of the hole. Separation occurs because it would require (theoretically, with “potential flow,” which is frictionless flow) an infinite velocity and zero absolute pressure for the flow to turn around the sharp corner. But since air has viscosity and it sticks to surfaces, the actual air velocity goes to zero at the hole/wall surfaces. The air cannot have enough momentum to round the turn, so it separates, forming a jet, shooting into P2. The sides of this jet are called a “free surface.” The jet persists for many jet diameters into the right reservoir, and the static pressure within the jet must equal the pressure immediately outside the jet, or P2. Thus, the exit pressure the airflow sees is P2. The reason for this is as follows. Assume the jet pressure to be less than P2, as soon as the jet forms. The jet diameter would then contract as it moved to the right, into a region of greater pressure, which compresses the free surface boundary. This contraction would cause an increase of jet velocity, because in satisfying Conservation of Mass (the Continuity Equation), the same airflow passing through a region of smaller cross section must speed up (as did the air molecules to the left of the plate). With an increase of velocity, the pressure in the jet must decrease, from Bernoulli. Since the jet pressure was already assumed to be less than P2, it’s thus not possible for the jet to adjust to P2. Yet P2 is the boundary condition of the problem; the flow must end up with this static pressure. Thus, the jet pressure just to the right of the hole cannot be less than P2. You can apply the same reasoning when assuming that the jet pressure just to the right of the hole is greater than P2, causing the jet diameter free surface to increase outward, causing smaller velocities and higher jet pressures, and you arrive at a similar contradiction. Thus, the jet “sees’ the static pressure P2 upon exiting the hole, and the exact spot where the pressure is P2, the jet velocity is maximum, since the pressure difference driving the orifice flow is the maximum, (P1 – P2). Incidentally, this reasoning applies only to subsonic flow. With supersonic flow, different mechanisms play out in adjusting the jet pressure to P2, and in particular, normal and oblique shock waves form in order to first bring the flow subsonic. With steady flow, or more generally, with quasi-steady flow, there must be a jet, and in fact, if we know that jets form in a particular flow situation, we can assume steady or quasi-steady flow. For oscillating flow going through zero, it’s true that, in the moments near zero velocity, the stay time greatly increases. But if the oscillation amplitude is large enough, the fraction of the oscillation period in which there is quasi-steady flow becomes close to unity, resulting in fairly accurate results. With unsteady flow, the flow regime looks much different. There are probably no jets, or there are only momentary jets, with momentary flow separation, eddies and vortices. In this case, with P1 increasing, imagine an air molecule first in the center of the hole, and by the time P1 doubles, the molecule just exits the hole on the right. The rapidly increasing P1 causes time acceleration of this molecule, causing it and its neighbors to push with increasing pressure on the air just downstream, which resists, because of its inertia. This crowding of the air causes increasing pressures that would move any free surface radially away from the hole axis. Thus, a steady free surface is not likely to form. The airflow thus hugs against the right side of the vertical wall, and the discharge flow near the hole looks something like a mirror image of the approaching radial flow on the left of the hole, except with flow arrows reversed in direction. The frictionless, steady, incompressible Bernoulli equation is written for two points 1 and 2 within the same streamline of flow: P1 + ½*rho*V1^2 = P2 + ½*rho*V2^2 where the “p’s” are static pressure and the “v’s” are corresponding flow velocities. Ron, you are correct in stating that this equation is the statement of conservation of potential and kinetic energy for the mechanical system all the flow assumptions require. But you seem to forget that it must be applied to flow in the same streamline. When you write this equation relating the jet velocity only to P2 and not to P1, you violate this condition, because you do not acknowledge that the airflow originates where the total pressure is P1. Writing this equation for a streamline that exits the vibrating reed, with the presence of a steady free surface (jet): P1 + 0 = P2 + ½*rho*Vj^2 because, as I proved, the static pressure in the jet must equal P2. Writing Bernoulli for a streamline that originates where the pressure is P1 and that impinges on the top surface of the tongue, where the flow stagnates (reversibly diffuses to zero velocity): P1 + 0 = p1 + 0 or, p1 = P1 The pressure on the top surface where the flow is stagnated is equal to P1. This fact illustrates the case for a frictionless system, where pressure measures potential energy and velocity measures kinetic energy. The system is conserved. Potential energy (P1) is used up to generate flow (kinetic energy), and when you reversibly recover that kinetic energy back into potential energy, you wind up with the same potential energy you started with (P1). Your statement that p1 > P1 thus violates the law of Conservation of Energy. Now writing it for the same streamline as above, but at an intermediate (i) position upstream of the tongue, where the velocity has reached v1: P1 + 0 = pi + ½*rho*v1^2 Thus, pi is the minimum static pressure in the streamline, where there’s a combination of potential and kinetic energy. I don’t know how to state this more clearly, without repetition. Best regards, Tom

Hi Don, the start transient of a free reed, as used in concertinas and accordions can in general be considered to be several tens of milliseconds. In more detail, this transient involves at least two processes. One is to establish the wave form characteristic of the sound field, and the other is to establish the volume of the note. In my experience with accordion reeds, these two events can take considerably different time durations. In my observations looking at microphone traces with audio software (such as Audacity), it seems that the reed tongue vibration must first establish its fundamental mode of oscillation, and the sound field with the pitch and timbre we recognize becomes established from that oscillation. Establishment of the steady state volume of sound can take considerably longer. There is often a volume overshoot, which then settles down to the steady state value. Also, the tongue vibration, vibrating as a cantilever, during this start transient, probably contains overtones, and there is also a possibility that a torsional mode is excited. I do believe that the start transient is an inherently unsteady process. As with other tone generators, it’s likely that this transient contains the shedding of eddies and vortices, and because of the turbulent nature of these processes, it’s not too surprising that these other modes of tongue vibration are excited. Incidentally, the overtones of a vibrating cantilever are not harmonically related (they are not multiples of two). The following data that I obtained from accordion reeds may be useful, giving the note identification, the frequency, and the duration of the time necessary to establish the tone and timbre of the note, not the transient to establish a constant volume. The number in parentheses is for different reeds, but of the same pitch, when a tone chamber (cassoto) is used. A2, 110 Hz, 97 ms (50 ms); C3, 131, 147 (46); A3, 220, 45 (60); C4, 255, 86 (50); A4, 442, 40 (32); C5, 512, 17 (36), A5, 878, 41 (25); C6, 1035, 61 (21); A6, 1768, 86 (82) There is perhaps a trend here, where on average, the presence of a tone chamber causes a shorter start transient, concerning identity of the tone. The tone chamber also usually causes a larger initial sound amplitude, which then takes a while to die down to the steady state tone. For instance, for the C3 note, it takes an additional 168 ms for the volume to establish its steady state value. The tone chamber gives a more sudden sound, and it’s curious to me that concertinas do not contain such a chamber. I suppose it would make the instruments unacceptably large. For the purposes you mentioned, I think you can consider the start transient to be something like 50 - 60 ms for the above frequency range. Reeds with lower frequencies than those will involve longer duration start transients. In fact, during the 20th century, the free reed was discontinued for decades as a sound source in pipe organs because of its relatively long start transient. However, later in the century, people brought it back, mainly because they liked its timbre, which contrasted with the sound produced by the other pipes’ edge tone generators. But the start transient of the free reed is much more complicated than I can describe here. Cottingham did a study that some may be interested in (http://www.public.coe.edu/~jcotting/PMA035061.pdf ). In this study, done using free reeds from a Williams American reed organ, he found that the start transient of one reed lasted about 100 ms. He also found overtones of the cantilever transverse bending mode, the first torsional mode, and the first transverse bending mode that is perpendicular to the main bending mode (in the plane of the tongue!). He notes that the torsional mode of vibration is involved in the very start of tongue vibration and suggests that it might be able to exploit it - by tongue design - as a way to reduce the start transient. In a separate thread, a few of us discussed at length how a free reed starts vibration, though none of us considered the presence of more than one mode of vibration. Our little friend baffles us again. I should note that the typical reed tongue of a reed organ has a bend in it, near the tip, bringing the tip closer to the slot. This bend is absent in concertina and accordion reed tongues. Best regards, Tom www.bluesbox.biz

Hi Dana, you raise an interesting question, one that I’ve asked myself, so now we have an opportunity to think more on it. In my first post, I did a calculation that gave a tongue tip maximum velocity (139 ft/sec) that corresponds to an air pressure difference of about 4.3 inches water column, which would cause the same velocity in an air jet experiencing that pressure difference. I concluded that, since 4.3 in.W.C. can be a typical blowing pressure, these velocities are about the same order. Yet, this comparison may not be that relevant, if we are focused on understanding only tongue vibration. It’s probably more relevant towards understanding of the sound field, but staying with the tongue vibration, the presence of a jet is more important than the velocity of the jet. With its presence, we know that the pressure below the tongue is very close to P2, and that’s all we really care about. The jet forms because of flow separation at the bottom corner of the tongue, and the “entrance flow” into any hole is generally quite small, except only very near the hole. This is because the area feeding this flow is much larger than the area of the hole (imagine over a hole in a wall a hemispherical region with a radius reaching to where air motion – which is radially directed – first starts). But this implies that the jet velocity is greater than the tip velocity. Is it possible to form a jet if the tip is moving downward faster than the maximum air velocity in the jet? I think so, with flow separation occurring only at the top corner of the slot, and only with a lot of turbulence formed within the jet flow by the faster moving tip. But if we look only at the pressure acting on the top surface of the tongue, very near the tip, in quasi-steady flow, if the air flow separates from the tip (Vt < Vj) and causes a jet boundary, there will be airflow parallel to this small upper area and probably a stagnated flow away from this area. Thus, most the top area does not experience much air flow. (There is no jet flow above the tongue.) And we must also acknowledge that the tongue velocity varies nearly linearly along its length, from maximum at the tip to zero near the other end. With some repetition, with quasi-steady flow, I can visualize a generally downward air movement above that impinges on the tongue on its way into the jet, and most of this airflow will stagnate on the top surface, thus regaining the stagnation pressure it started with, P1. (I’m assuming here an idealized perfect tongue/slot fit.) Any air that moves parallel to the top surface will produce a slightly lower pressure than P1 on the top surface (from Bernoulli), but parallel flow. For unsteady flow, I can visualize a true suction, where air above the top surface is pulled by the downward moving tongue, which would cause a rarefaction pressure pulse to combine with the sound field. So again, we have to decide on the flow regime before we can come to a clearer understanding of the effect of air motion on tongue vibration. It’s my guess that, whatever the nature of the flow field, the pressure on the top surface of the tongue is at least approximately the stagnation pressure, P1, for the purpose of determining the pressure forces acting on the tongue and for the established periodic motion. We’d need to be more accurate if we wanted to understand the sound field. With that said, I will gladly supply the equation necessary to calculate the air jet velocity, and for other interested people, also the calculation for the maximum tip velocity. In this latter calculation, I will neglect the fact that, with increasing blowing pressure, the sinusoidal midpoint where this velocity is maximum shifts downward a bit into the slot. For the air jet velocity, from Bernoulli, P1 + 0 = P2 + ½*rho*V^2/gc where gc is a dimensional constant that depends upon the system of units used. In the Lbm/Lbf system English system, this constant is 32.2 Lbm/Lbf*ft/sec^2. Rho is the density of air, or 0.075 Lbm/ft^3. The pressure difference, (P1 – P2) is expressed normally as Lbf/ft^2, but to convert it to in.W.C., we need to incorporate the factors 144 in^2/ft^2 and 0.036 psi/in.W.C. Thus, V = sqrt(2*32.2*144*.036*delP/0.075) or V = 66.7*sqrt(delP), V is expressed in ft/sec, and delP is expressed in in.W.C. For the maximum tongue tip velocity, we reason that, with sinusoidal motion, the tip goes from zero velocity to its maximum in ¼*T, where T is the period of oscillation = 1/f, where f is the frequency of oscillation. For a sine wave, the (maximum) amplitude is equal to twice the average, and so, given the displacement amplitude, A, and noting that there are 12 inches in a foot, we get, Vt = 4*f*2*A/12 or Vt = 0.667*f*A Vt is expressed in ft/sec and A in inches. A is the height the tongue tip reaches above the slot. I also have some data on tongue vibration amplitudes and frequency, so I’ll present some of the results here. But now, I have to go out of town for a couple days and will resume this interesting thread when I get back. Best regards, Tom

Hi Dana, it’s always a pleasure to read your posts. I do think that the kick the tongue gets because of bellows pressure is applied at about the same place in its motion, when moving downward, and that location is when it first enters the slot, because then, the maximum pressure difference always delivers its maximum force, (P1 – P2)*A. There may be an exception to this if, just before entering the slot, jets form in the small spaces between tongue and reed plate. With these jets, the pressure on the bottom surface of the tongue will be P2 (as it is when the tongue first enters the slot), producing the same maximum force. I agree with Lucasz in suggesting that the sudden increase in vibration amplitude you observed during the start transient begins when the tongue is in the positions I mention in the above paragraph. In fact, I observed this very same thing – or at least, that’s what it appeared to be - when I was looking at the start transientt many years ago, while closely controlling the magnitude of blowing pressure. It’s amazing how much one can lose track of, until reminded. With all this discussion, my own conclusions on how the tongue starts vibrating, I think, are a bit clearer. I would suggest the following. The very first motion is a small vibration just above the slot, and this motion is inherently unsteady, enabled probably by periodic shredding of eddies and vortices off the bottom surface of the tongue. I don’t understand the details there, nor why the amplitude of this vibration increases until the tongue enters the slot. Nevertheless, when the tongue just enters the slot (or a little before, if jets are formed), the tongue experiences the maximum pressure difference, (P1 – P2). Before this entrance, inertial effects of the oscillatory air motion around the tip of the tongue keeps the pressure on the lower surface of the reed just a little under P1, not all the way down to P2. With this sudden increase in pressure force, the vibration rapidly builds up to a maximum, where the energy input balances aerodynamic losses and acoustic energy that radiates outward. Thus the tongue position at the top of the slot is most important, from the standpoint of energy addition. As the tongue travels further into the slot, the tip of the tongue moves away from the wall of the slot and eventually a jet forms below the tongue. With this jet, air flows over the top surface of the tongue, and the pressure on that top surface becomes (from Bernoulli) less than P1, reducing the net pressure force on the tongue. Tapered slots will enhance this latter process. Thus, the maximum pressure force is applied for only a short instance in the swing cycle, and it is always in the direction of the moving tongue, which means this energy input is balaced by energy losses and periodic motion is achieved. I do recall our very interesting discussion of the paper by Ricot, et al., and I also recommend others who are so interested in these topics to seek it out. If anyone has problems finding it, I can provide a link. One major experimental finding in that paper (and I believe what you also observed in your smoke experiments) is that jets are formed for most of the time that the tongue is near and inside the slot. Relating to the discussion here, this means that the quasi-steady assumption should be pretty good for vibrating tongues that operate below some maximum frequency. Best regards, Tom

“I hope this time my point of view is finally clear enough to be seriously considered (either as true or false) as a coherent "theory" based on actual physics ” Lukasz, The bank, Coanda, and venturi effects are not, in themselves, basic physics. In fact, they can all be explained, at least in part, by an appropriate application of the quasi-steady, incompressible Bernoulli equation, as long as the velocities and time derivatives are not too large, and this equation is basic enough, at least for me. This also goes for the operation of the free reed, which also operates by the same basic principles. It’s up to us to seek out what the basic principles are and understand how they are applied. It’s not a valid approach for you to point out a flow phenomenon as if it's a basic principle that reminds you of a vibrating free reed, then say “Oh look, see, this phenomenon is basic and it is what explains how the free reed works.” Would it be correct for you to say, alternatively for instance, “the Coanda effect is explained by what happens in the operation of the free reed?” No. Adequate explanations must be based on the same fundamental laws of Physics that are at the core of how all phenomenon work. Best regards, Tom

Rlgp, I apologize for the flippancy with witch I posted above. I’ll consider you a real physicist, because you have earned the title. I’ll also concede that ma is not considered to be strictly a force. The ma term is often loosely regarded, in laymen’s terms, as the “force of inertia,” and when you draw a free body diagram in dynamics, you show all the forces acting on a mass using arrows denoting the direction of the force, and you also draw an arrow at the center of mass, labelling it ma. This diagram thus shows a dynamically balanced condition. So I’ll compromise a bit here and call ma an “equivalent force.” More importantly, and I think you would agree, no description of the dynamics of a vibrating system can be complete without acknowledging this equivalent force of inertia. Thanks for your note about the progression of higher harmonics in the Fourier analysis of trapezoids and rectangles. Like you, I’m retired, and it’s been long enough now that I lost track of such details, but I actually do recall those facts. (So far, for me, it’s a terrible thing to grow old.) The criterion that determines whether or not a fluid flow is incompressible, in steady state, is that the square of the Mach number be much less than unity, M^2 << 1, or M less than about 0.3. When this is the case, all the terms arising from compressibility can be omitted, and one can still calculate with good accuracy. For air at ambient conditions, this translates to an air velocity less than about 325 ft/sec. From the Bernoulli equation, for air, a pressure difference of about 24 inches water column will produce such a flow velocity. Most accordion and concertina bellows pressures are less than about 10 inches water column. Thus, the airflow through a free reed can be considered incompressible. It’s odd that you would say that we cannot consider the higher pressure region to be incompressible, when you do proceed to consider the lower pressure region incompressible. The two regions are intimately connected, differing only (dynamically speaking) by a very small pressure difference. It’s incorrect to say that the pressure on the top of the tongue produced by downward flowing air is higher than the pressure the air started out with (P1). In fact, the dynamic pressure produced by an airstream that impinges on the top surface is its stagnation pressure, which is equal to P1, the static pressure of the air at rest. From Bernoulli, any air particles originating from quiescent air and experiencing velocity, have a pressure less than P1 by an amount precisely equal to the V^2 term. In other words, upon stagnation, the air stream restores the pressure it started out with (P1). This stagnation is thus essentially frictionless and reversible. Therefore, the pressure on the top surface of the tongue, with the quasi-steady assumption, is P1, and the ordering of pressures that you arrive at is erroneous. The Bernoulli equation you wrote, P2 = p2 + 1/2 rho*v^2 is incorrect. It purports to calculate an air velocity without acknowledging the pressure difference that causes it. The correct equation is P1 – P2 = 0.5*rho*v^2. And again, the ordering of pressure magnitudes that you write is incorrect. I’m not sure that a square wave is a “pretty good approximation” of the waveform Cottingham shows. The jagged edges in the actual pressure waveform may produce more higher harmonics than a square corner. Would you agree? Incidentally, in that article, Cottingham mentions my pitch bending invention, and in the references, mentions also a web-published article that I wrote for Concertina.org. (So I guess I tooted my own horn, as well.) “…but the frequency will be twice the frequency of the tongue oscillation.” I don’t know why you would insist on asserting this. I’ve done experiments in this regard, and I’ve read a fair amount on it. I’m quite sure you have very little experimental experience with free reeds, yet you have no reservations in asserting what you imagine. I think this communication would be more comfortable if we talked in person and got to know one another, and one another’s experience. The forum here is valuable, although it can be rigid. I can’t do much else than again suggest you do the experiment I suggested in my earlier post. I also suggest in a friendly way that you think more about the need for experimental evidence to support theoretical predictions. Best regards, Tom

Hi Lucasz, your observation that the tongue begins vibrating with an amplitude too small for it to enter the slot in the shoe is important. Years ago, I had noticed that, but I forgot about it when I wrote my previous post. If indeed this happens all the time during the start transient of the free reed, then the actual situation becomes very difficult to explain in detail, without further experimentation. It would be nice if someone made a slow motion video of the starting free reed in order to verify this speculation, complete with smoke entrained by the airflow, so that the air stream becomes visible. I say the actual situation becomes very difficult because I’m very sure that such “pre-vibration” is inherently unsteady. I can’t explain the details on how that works. It may have something to do with turbulence and the shedding of eddies and vortices under the tongue. It seems I have difficulty convincing you of the difference between unsteady flow and steady flow, and in your explanations, you don’t make distinctions. When anyone invokes the so-called “Bernoulli” explanation on how a free reed works, they implicitly adopt a quasi-steady assumption, because the Bernoulli equation referred to is the one for steady (and incompressible) flow. As I wrote before, with this assumption, the gap under the tongue during starting will cause a jet of air, and the pressure all along the bottom surface of the tongue is P2. This is true in part because the pressure inside a subsonic jet must equal the pressure immediately outside the jet. In this case, the jet velocity is the maximum velocity that can be obtained by the pressure difference (P1 – P2), and the pressure difference (P1 – P2) is the maximum for the system. Let me try another way. Bernoulli can be written: P1 + 0 = p + 0.5*rho*v^2 The zero is because P1 represents a quiescent reservoir. We can write this as P1 – p = 0.5*rho*v^2 I’m saying that p = P2, which is the lowest pressure in the system, and thus, (P1 – P2) is the maximum pressure difference that the air could experience – when unsteady effects are not important. Thus, when you adopt a quasi-steady approach and say that there must be a pressure force greater than (P1 – P2), you are equivalently saying that p is negative, which is impossible. I’m in favor of discarding the quasi-steady assumption for the very beginning of the start transient, and to accept that the flow field is inherently unsteady, and I am at a loss to explain the details of that flow field. The question I asked in my previous post was in the context of the quasi-steady assumption, and when I make that assumption, I cannot explain completely the start mechanism. And I’m sorry, I don’t understand your explanation. Perhaps this means that the quasi-steady assumption is inadequate to explain the start transient, simple because this assumption is wrong, and one needs to invoke some principles of unsteady flow in order to understand it. The “pre-vibration” you describe suggests to me that the quasi-steady assumption is inadequate. Most other musical instruments contain sound sources that involve unsteady effects, such as the flute, trumpet, and reed instruments, thus, why shouldn’t the free reed? However, for the air motion during periodic motion (speaking), as I mentioned, the quasi-steady assumption may be accurate for the lower frequency reeds. Indeed theoretical papers have been written that make this assumption. Best regards, Tom

Greetings, thanks to all you posters for an interesting thread. I’d like to make a few comments that I hope can correct what I see as misconceptions. “It will continue to move downward until the air flow is effectively cut off as the reed end comes very close to the inside end of the lower frame. (Assuming that the frames are such that this cutoff occurs before the spring force gets too large.) When the air stops flowing, the partial vacuum is no longer maintained and the force due to air pressure is greatly reduced.” Incorrect. Rlgp, continuing with the quasi-steady assumption that has been assumed in this thread, let the pressure of the motionless air in the reservoir above the reed be P1 and the pressure of the motionless air in the reservoir below the reed be P2. When the tongue first enters the slot, the pressure force acting on the tongue becomes maximum, and is equal to (assuming a perfect seal), (P1 – P2)*A, where A is the flat area of the tongue. Confusion arises over this point I think when people imagine a “suction” or “vacuum” under the reed caused by the air velocity there, and that this suction is somehow greater than what's physically possible. We know from the steady state Bernoulli principle (p + 0.5*rho*V^2 = constant, where p is static pressure and V is fluid velocity) that the pressure under the reed is less than P1. P1 is the stagnation pressure (some fluid dynamicists call it total pressure) of the air in the top reservoir. The pressure under the tongue can never be lower than P2, the exhaust pressure the air ultimately experiences after leaving the upper reservoir. The above Bernoulli equation would yield an imaginary velocity if the airflow is claimed to experience a pressure less than P2. During the start of motion, the pressure the tongue experiences varies over its surfaces, but is bounded by the expression P2 <= p <= P1, where <= is read, “less than or equal to.” To see this, just picture the tongue frozen inside the slot where it stops, with the air still. You only have two reservoirs at different, uniform pressures, separated by a still reed tongue. “Note that there is an asymmetry in the operation. When the tongue is below its equilibrium position, the spring force is acting upward and that due to air pressure downward (with the latter decreasing as the air flow slows).” Incorrect. Rlgp, the “latter” increases as the air flow slows. Before it slows, the net pressure under the tongue is at some pressure Pi, intermediate between P1 and P2, and when the air flow stops, that pressure decreases to P2, causing higher pressure difference and more force on the tongue. Let me take this discussion one step further. If you maintain the quasi-steady assumption, you must consider the formation of jets in the airflow. The pressure in such a jet must equal the pressure in the ambient air immediately surrounding the jet (for subsonic flow). Thus, if a jet forms very soon after air starts flowing and continues into the lower reservoir, as the tongue moves into the slot, the total force on the tongue will be the maximum, (P1 – P2)*A once the jet forms. In truth, the air motion through and around the tongue is at least somewhere and sometime not quasi-steady, but unsteady. Unsteady flow is flow in which time derivatives are important. Changes in velocity, or acceleration, cause inertial effects of the air to become important – important in our formulations and in our imaginations. It is the frequency of the reed vibration that mainly determines the flow regime, whether unsteady or quasi-steady. Quasi-steady means simply that there is motion, but with all time derivatives negligible compared to the other terms in the governing equations. From an order of magnitude study, you can show that, for the smallest reeds (those with the highest pitch), the steady, periodic airflow field is mostly unsteady, and for the largest reeds (lowest pitches), the periodic flow field is appreciably quasi-steady. The dividing line is somewhere in the vicinity of 1,000 Hz. It thus seems to me that jet formation will be minimal for reeds with pitch much above 1,000 Hz. With unsteady flow, the description of the flow field becomes too difficult for our imaginations to guide us very well. It’s my guess that the start of vibration, before periodic flow is established, is entirely unsteady. “Note that if you want the air flow to be cut twice per cycle you need to adjust the thickness of the frames and the V-shaped cutout so that the reed end passes very close to the frames at both ends of the oscillation. In this case, though, the frequency would be twice what it would be if the cut is made only on the low pressure side.” Incorrect. Rlgp, the human ear/brain system is not so easily fooled. The period of oscillation of the vibrating tongue determines the pitch we perceive, because our hearing system perceives the fundamental frequency as the pitch. There is no way the two pulses of air that you imagine can be precisely the same. One simple reason for this is that they occur in different places that have different geometries. Mathematically speaking, a Fourier transform will produce the same fundamental frequency that we perceive in the pitch. You can verify this for yourself with audio software, constructing a wave form consisting of two pulses, starting with two identical shapes, then altering one of them in the most minute way. You may be surprised at how good our ears are. “In a conventional reed, as well as in this design, the maximum distance of the oscillation from the equilibrium position on the high pressure side is smaller than on the low pressure side because on the high pressure side both the pressure force and the restoring spring force act together to bring the motion to a stop, whereas on the low pressure side (after the air flow is cut off), only the spring force brings the motion to a stop.” Partially correct. Rlgp, you are correct in saying that the amplitude of tongue motion above is smaller than that below. They differ by about 30% for average blowing pressures, and the reason is that the persistent downward net pressure forces on the vibrating tongue shifts the equilibrium position of (biases) its motion, which is very close to sinusoidal. But nowhere does pressure force serve to stop the reed motion (vibration is not stopped). Spring force is the only force that stops it. While speaking in periodic motion, when the tongue reaches its highest point above the shoe, it is bathed in P1, and my guess is that it experiences only very small unbalanced pressure forces. “Fig.1 represents the typicall reed in it's starting position. The lift force is orders of magnitude higher than the force from pressure gradient.” Incorrect. Lukasz, the “suction” caused by the air velocity illustrated by your arrows cannot possibly cause a force on the tongue that is larger than (P1 – P2)*A. If you haven’t already read my explanation above in explaining the role of the Bernoulli equation, I suggest you do so. Assuming a quasi-steady flow field, the airflow would not hug the underside of the tongue as you draw it, and it’s likely that it would form a jet, with the pressure inside the jet equal to P2. In the unsteady case, however, things can be much different, and perhaps there is some kind of airflow, generally as you draw it (in which case, the flow field will be Potential, or Irrotational). The unsteady case is too difficult to discuss here, but even in that case, I see no mechanism for a “lift force” to be “orders of magnitude” higher than pressure forces. Can you provide good physical reasoning for your statement? There is another complication here, when the tongue has established its periodic motion, even with the quasi-steady assumption. In this case, when the reed is moving upward through the slot, its top surface collides with air, producing a dynamic pressure that is higher than P1 by the increment 0.5*rho*Vr^2, where Vr is approximately the maximum tip velocity of the reed. From my own measurements, an accordion tongue of pitch 696 Hz vibrates with amplitude of about 0.3 inches (forgive the English system of units). This means that the average velocity in one quarter cycle is 0.3/12*696*4 = 69.6 ft/sec, and the peak velocity will be twice that, or 139 ft/sec. The dynamic pressure produced when this tongue collides with air is 0.5*0.075*139^2/32.2/144 = 0.156 psi, or 0.156/0.036 = 4.3 inches water column above P1, which is roughly about the normal bellows pressure (P1 - P2). In other words, for a brief moment during the swing cycle, the tongue experiences on its top surface, only near its tip, a pressure force, while moving upward, approximately twice the bellows overpressure. Also, when the tongue is moving downward, when it first enters the slot, a similar event occurs on its lower surface. Both of these over-pressures are contrary to motion and will produce aerodynamic drag, and since they occur for both tongue directions, their effect on tongue motion may largely cancel. However, they should have a noticeable effect on the sound field, and for some reeds produce a feature of the tone we perceive. It’s also difficult to judge the force on the tongue that these over-pressures cause, since we don’t know the areas and the duration times involved. Since these over-pressures oppose tongue vibration, we do know, in spite of them, the tongue does indeed vibrate very well! “Fig.2 represents your design. You can see how the lift is created on both sides of the tongue, with values much smaller that on the "classic" assymetric reed.” Incorrect. Lukasz, keeping with the quasi-steady assumption, the pressure on the top of the tongue near the tip is approximately P1, simply because the airstream, in striking the tongue, stagnates there, approximately producing the airstream’s stagnation pressure over some undefined area near the tip, which is P1, and causing a downward force on the tongue. But over the vast majority of its upper surface, the tongue experiences pressure very near P1. In any event, I see no “lift force” pushing upward on the tongue in this instance during the start transient. “Fig.3 represents an additional lift force created when tongue passes through the shoe. It is again working towards the resting point and propels the resonant oscilation slightly.” Incorrect. Lukasz, I make the same comments here as I do in the above paragraph. You seem to think that, wherever there is a moving airstream on the tongue, it creates a “suction,” or “lift force.” This is not correct. The airflow effect on the tongue depends upon the angle that the flow makes with the tongue. When it’s perpendicular towards the tongue, the pressure on the tongue is the stagnation pressure of the flow. When it’s parallel to the tongue, the pressure on the tongue is equal to the pressure in the airstream. The steady state Bernoulli equation allows you to calculate the difference in pressure from the air velocity, or conversely, to calculate the velocity from the pressure difference causing the airflow. “This is the moment when gap suction aerodynamic effect occur, sucking air from above the corner, creating dynamic underpresure on the closer surface of the paper, moving the paper and closing the gap.” Incorrect. Lukasz, here, there is no “sucking air from above the corner,” since such an airflow would necessarily have to move counter to your breath as it loops around the paper’s edge. This would violate thermodynamic laws. I don’t understand the term, “dynamic underpressure,” but I fear it has something to do with a belief that moving air near flat surfaces causes “suction”. The only external forces that could act here are pressure forces, and we need to understand the magnitudes of the various pressures (and the areas they act on, along with their duration) in order to understand the effects of the forces they produce. “From a physicist's point of view, there are only two forces involved -- the force due to the pressure gradient and the internal spring force.” Incorrect. Rlgp, a real physicist would acknowledge a third force, the inertial force, due to acceleration of the masses involved. But I can understand why you would ignore this force, because you are reasoning from a quasi-steady assumption. Although the air flow, in some instances, can be considered quasi-steady, as with the lower pitched reeds, the tongue motion is indeed always unsteady, which means that its inertial forces are of the same magnitude as the forces you mentioned. In Newton’s second law, F = ma, the two forces you mentioned are contained in F, but you are neglecting the right side of the equation. “Let me re-emphasize: The pressure difference between the top of the tongue and the bottom of the tongue is dynamic, and apparently gets a lot larger than the static pressure difference between the inside and outside of the bellows.” Incorrect. Rlgp, you have given no physical line of reasoning that can justify your conviction that the pressure difference across the tongue is larger than the pressure difference between the top and bottom reservoirs, when the tongue is starting to vibrate. I have presented a calculation above that suggests there can be an approximate doubling of pressure difference on a small portion of the tongue when the tongue collides with air in both directions, as it moves with its maximum velocity, and during its established periodic motion. Other than the possibility that this collision can have a significant effect on the sound of the reed, it’s difficult to conclude much about its effect on tongue motion because we don’t really know the area and time duration over which these over-pressures act. In fluid dynamics, there is a term “dynamic pressure,” which is well defined as = p + 0.5*rho*v^2, where p is static pressure and v is flow velocity, but you have not invoked this definition. “And yes, dynamic pressure (lift force) on the low pressure side of the tongue is what drives the oscilation, which I was telling you from the very start of this whole debate.” Not clear. Lukasz, perhaps there’s a language problem. Your use of the term “dynamic pressure” is not conventional, as understood by fluid dynamicists. Dynamic pressure is not necessarily connected with a “lift force.” “As the end of the tongue approaches the frame below, the air flow is blocked, so that the downward force due to pressure (or whatever terminology you want to use) is greatly reduced.” Incorrect. Rlgp, this is a re-statement of the same error. When the airflow is blocked, the pressure force pushing down on the tongue increases to a maximum, as I explained above. “The spring force will bring the motion to a stop and send the tongue back toward equilibrium. It will pass through equilibrium and move into the region above.” Correct! Rlgp, how does that happen? This is one thing about the motion of a free reed that I do not understand: what mechanism causes the tongue to return to a point that is above its equilibrium position? We know it must, and it must return to higher and higher positions during the start transient, if it is to speak. But how does it do that, especially because, in travelling upward, it works against a maximum pressure difference? Anyone? “Remember, however, if the oscillation amplitudes are such that the air flow is cut at both the top and bottom of the swing, the frequency of the reed with two frames will be twice that of the one with a single frame.” Incorrect. This is a repeat of the same error I corrected above. “This is false, I suspect that the diagram is just that, a diagram, showing an idealised view and not a scale drawing of an actual reed in operation.” It’s both true and false. Theo, the very high pitched reed tongues do not travel below the reed plate, although the medium and lower pitched reed tongues do. “This parcel of air would be shorter that the other two and would presumably create a second much higher note. So you would have a note, a much higher note, and then the first note again every time the reed swings a full cycle.” Incorrect. Chris, with due respect, the pitch perceived will be a single note, equal to the frequency of vibration of the tongue, as I explained at the beginning. I’m amazed that this misconception has been so ingrained in people who busy themselves with the operation of the free reed. Our little friend holds many surprises for us. There is no such thing as a note produced during each “full cycle.” A musical tone is produced by regular, periodic vibrations. It’s not possible for the free reed to produce two different notes at the same time. All the pressure pulses that occur within one cycle are repeated periodically, and it’s the periodic occurrence of all pulses that produces the tone we perceive, once we have heard the tone for a sufficient number of cycles, and the sufficient number of cycles depends upon the cycle frequency. “And you are correct that with two cutoffs the frequency would be higher -- about twice as high in fact, as i said earlier.” Rlgp, as I said earlier, incorrect. “For example, i think that filing the inner edges of a conventional reed frame may lead to less abrupt cutoff and recovery of the air flow, and thus a more trapezoidal shape for the wave form. This shape puts relatively less energy into higher harmonics, resulting in a more mellow sound, something that would be desireable to many.” Rlgp, are you just guessing that any trapezoidal shape will put less energy into the higher harmonics than any rectangle, or have you studied Fourier transforms of both rectangles and trapezoids? But I think you are being distracted by such thinking. You may imagine the shape of a pressure pulse, but I can assure you that the pulses that actually occur will be far different. It’s one thing to assert what will happen, based upon imagination, and it’s another thing what Nature actually does, especially when your thinking does not invoke all of the physical mechanisms at work. “With this i expect that it's time (many would say long past time) for this thread to end. I've enjoyed it because of the mental stimulation it has brought -- something i've missed since retiring as a physics professor about 10 years ago.” Rlgp, may I ask, what grade level of Physics did you teach, and what level of formal education have you had in Physics? Thanks. Let me make some comments of a general nature. The free reed vibrates primarily as a simple harmonic oscillator. With high blowing pressures, the second mode of vibration can be slightly excited, and the jagged pulses of air forcing the motion do cause a small amount of overtones in the lowest mode cantilever vibration, but these are confined to about 10% of the motion. This system also demonstrates what we call self excited oscillation, whereby the oscillation itself determines when the forcing function acts during the cycle. In order for there to be sustained vibration that overcomes friction and produces audible sound energy, a force must be applied at any time when the tongue motion is in the same direction. Much like a child on a swing, with a parent pushing at the right moment and in the direction of swing motion, the condition P1 > P2 ensures that, for some of its downward motion, the tongue experiences a downward (forward) kick once per cycle. Mathematically, this means that the product of complex pressure and complex velocity has a non-zero real part, and this translates in physical terms to mean that work is being done by the pressure difference (P1 – P2), and that work fuels all the air and tongue motion, establishing a sound field we perceive as a musical tone. Such a simple view might satisfy some, though I acknowledge that accurate understanding of the details of this description can prove challenging. Best regards, Tom www.bluesbox.biz

Hi Lukasz. Every prototype I’ve made so far is a modification of an existing instrument, and each instrument has been different. Thus, I have had to make things fit and make things work, and the methods I’ve used vary, depending on the stock instrument. What works in one may not work in another. It’s thus difficult to say just what the space requirements are, and judging from my experience so far, I can probably modify a concertina enough to fit in the technology. I have some reservations, because all my prototypes thus far have been accordions, and concertinas are, in general, smaller. I thus cannot guarantee that it would be worth trying to adapt the technology to every note, but I’m sure at least some notes can be set up for pitch bending, and hopefully, the result would provide a prototype adequate for evaluation of the technology. The situation would change greatly if I were to design a new instrument, in which the pitch bending apparatus is part of the basic construction. The result would probably be an instrument slightly larger and slightly heavier than the average, stock instrument. There are variations in size and weight in existing instruments of a given type. Perhaps it would be possible to keep the new instrument within the maximum dimensions and weight of a given type, though a detailed study would be required to verify that. Best regards, Tom