Valve Material

[ttonon]

Hi Rich,

 

Thanks for the opportunity to discuss these interesting issues.

 

RM:

I think of "airflow dynamic" as being the path the air takes and the things in that path which make the airflow change (constrictions due to the smaller pan slots, valve location and properties, path surface friction, pad operation...) and "pressure dynamics" as being the amount of air in that path (caused by bellows movement/time).

 

TT:

Let me try to interpret what your thoughts are from a scientific point of view, involving fluid dynamics and acoustics. It first becomes evident that you’re attempting to explain the dynamics of an acoustic phenomena, which is inherently “unsteady” in nature, from a purely steady state point of view. By “unsteady,” we mean that time derivatives in the governing differential equations are significant and cannot be neglected. “Steady state” analyses set all time derivative terms to zero, and in many other phenomena, this gives good results. The steady state view, however, cannot be expected to provide understanding of the acoustic phenomena.

 

Even with steady state phenomena, it’s often unfruitful, or even incorrect, to regard “airflow dynamic” and “pressure dynamics” separately. In truth, they are part of the same phenomena. The steady state governing equations are often adequately described by Conservation of Mass (Continuity) and Conservation of Momentum, which, in effect, becomes the Law of Conservation of Mechanical Energy. In cases where the fluid can be considered incompressible, as in the case here, this latter equation is known by the name of Bernoulli. Thus, potential energy (pressure) and kinetic energy (velocity) are converted back and forth, and at any moment, their sum is constant.

 

Rich, in my attempt to understand your approach, I tried to conceive of a situation where (steady) airstream direction might give us interesting effects, and the best I could come up with at the moment was the one you quote below. But, as I say, this effect is negligible in the case at hand, because the dynamic pressure (total energy) of the airstream through the cavity is very much equal to the (static) pressure. In other free reed situations, such as the harmonica, during upward note bending, using the technique called “overblowing” (the mechanism of which is much different than the mechanism behind overblowing in wind instruments) the direction of airflow is important, I believe, because of the formation of jets.

 

TT (previous)When the reed is mounted over a cavity, the airstream approaching the reed (in the case of opening bellows) and the airstream leaving the reed (in the case of closing bellows) is directed roughly normal to the airstream direction through the reed slot. With the reed operating without the cavity, these airstream directions are different, being much more in the direction of airflow through the slot.

 

RM:

What is "normal"?

TT:

"Perpendicular," and I thank Jim for making this more clear.

 

RM:

I don't think that the direction of the flow by itself is cause for the altered pitch, but the reduction of the flow (caused by restrictions of/in the airflow path.

 

TT:

Could you please explain what restrictions you refer to? I also see a "restriction," and this causes increased oscillatory velocity amplitude, but I think the physics here is much different than the steady state "restriction" you refer to. For completeness, we might want to introduce viscosity (friction) into our discussion and this complicates the problem, and again, this doesn't appear to explain why the old and new valves behave differently. I will note though, in principle, as explained by the solution of the Spring/Mass/Damper system in harmonic motion, friction will lower the natural frequency of the system. With the reed, there are “aerodynamical” effects, and here, friction can play a role (eddies, etc.). But again, the issue is to compare the reed pitch with simply a change of leather, and it’s unlikely that this change would significantly alter the (small) effects of friction.

 

RM:

There has been a lot of investigation and debate about this issue. Personally I think that there is no significant Helmholtzian propensities in concertina construction. The frequency, physical chamber sizes, and math just don't coincide. The discrepancy is HUGE.

 

TT:

I would appreciate very much if you could direct me to at least some of these investigations, associating reed cavities with resonators. I haven’t been able to find any. With the issue at hand, you must realize that we're talking about extremely small changes in reed behavior. One cent of pitch variation corresponds to about 0.0005 parts, or 0.05 % variation in fundamental frequency. Think of it! What a marvelous apparatus we have to hear with? And instruments to measure with! I think it’s entirely reasonable to allow for the possibility of a resonator-coupled interaction with the reed. Many experimenters and theoreticians have been fooled by the subtleties of musical instruments. When you say that the “descrepancy is huge,” I think you’re referring to the comparison of cavity resonant frequency to the pitch of the reed. In some cases, it’s not so huge, and when one considers overtones in the musical tone, the overlap can be significant. But again to the main point, a resonator tuned far away from the pitch of the reed can at least minutely affect the pitch of the reed.

 

RM:

Not necessarily. I can install new valves which will raise or lower the pitch.

 

TT:

At the risk of sounding redundant, if the new leather raises the pitch, I'd predict that the new leather bends farther away from the slot.

 

RM:

Following that argument would mean that any increase in air velocity would lower the pitch of the reed. And to only a VERY small degree does it. Consider the pitch difference between playing very softly and very loudly which is many times the air velocity (flow) difference yet the pitch is altered very little (which is one of the great things about free-reed instruments!). Now consider the same setup but with a more restrictive (secured in place or "tougher" new) valve. The valve's restrictions will make a much larger pitch difference than the pressure difference will.

 

TT:

 

Rich, you're pointing out the fact that the steady state (more properly now called "mean flow") plays secondary role in the oscillatory (unsteady) motion, and unwittingly I believe, illustrating the point I make at the outset of this reply, that unsteady behavior cannot be understood properly by addressing only steady state formulations. In the area of mathematical physics called "small perturbation theory," we take a steady flow situation and "perturb" it by mathematically introducing a small oscillation, then solving for the oscillatory motion. The steady state motion, also called "mean motion" is many times inconsequential, and often serves as merely a means to conveniently nondimensionalize the oscillatory results. In my previous post, I refer to the “velocity of the vibrating air,” and I apologize for not being clearer by stating instead, “amplitude of the oscillatory air motion.” So as a result, you’ve confused oscillatory motion with “mean” motion. On the other hand, you are correct in noting that the mean motion has little effect on pitch. In mathematical physics, this effect is called “second order,” and it occurs because of nonlinear aspects to the reed motion, which are of higher order when oscillatory amplitudes are sufficiently small (acoustic regime). I should point out, however, that, in some problems, and using certain methods of asymptotic expansions, one can capture nonlinear behavior in the "first order" (acoustic) results, the complete solution of which can be obtained only by recourse to second order formulations. It would thus not be correct to say that these nonlinear effects are always negligible at vanishingly small oscillatory amplitudes.

 

In any musical instrument, if one changes the geometry in such a way that the oscillitory velocity amplitude is increased near a velocity antinode, as in the case here, inertial loading will be increased and the pitch of the vibration mode governing that motion will decrease. This fact is used to tune cymbals, bells, and woodwinds. For instance, certain modes of vibration are altered in woodwinds by either adding or taking away material inside the bore, at a place where the air vibration is large. Adding material decreases the cross section, causing increased velocity amplitude and lowered pitch. Taking away material increases cross section, decreasing velocity amplitude, raising pitch. An even better example concerns the design of finger pads in wind instruments. Much theoretical work has been done on this topic, and I can give you references if you like. The reasons why pitch is lowered when the finger pad is brought closer to the tone hole are well understood, and are precisely the reasons I have explained here.

 

Finally, and perhaps most relevant to the experimenters among us, I have just done this simple experiment (tonight) in my home shop on the free reed. I can assure you that, if you set a reed vibrating with a steady flow of air and take a small screwdriver and gently move the leather valve closer to the slot, the pitch will drop, and if you move the valve further from the slot, the pitch will increase - by just the amount you have indicated. I welcome you to try it and would be interested to know if you can reproduce my results.

 

Best regards,

Tom

www.bluesbox.biz

Edited November 19, 2004 by ttonon

[Theo]

Finally, and perhaps most relevant to the experimenters among us, I have just done this simple experiment (tonight) in my home shop on the free reed. I can assure you that, if you set a reed vibrating with a steady flow of air and take a small screwdriver and gently move the leather valve closer to the slot, the pitch will drop, and if you move the valve further from the slot, the pitch will increase - by just the amount you have indicated. I welcome you to try it and would be interested to know if you can reproduce my results.

 

And I think any person with practical experience of tuning freereed instruments of any kind will be familiar with this effect.

 

As to the change of pitch which may result from using more bellows pressure - try listening to Alistair Anderson playing for dancing. One of the characteristics of his playing is to lay great stress on certain notes. The stress is applied by a sharp increase in pressure on the bellows. The result is a louder note and a slight but clearly audible drop in pitch.

 

Theo

[Alan Day]

I am writing to say Tom how interesting I found your artical on valves, I must say that it is something I have never considered to be a major factor in concertina design.Just to me a way of stopping air escaping when playing in the opposite direction and the accuracy of valve design has now been made clearer to me ,thank you.

We discussed in another topic how concertina reeds could be effected by temperature drop or increase in humidity, could a damp valve alter (slightly) the pitch of the reed by say reduced airflow ?

Al

[Richard Morse]

Rich, in my attempt to understand your approach, I tried to conceive of a situation where (steady) airstream direction might give us interesting effects, and the best I could come up with at the moment was the one you quote below.

I don't to to what/which/where you refer.

 

I don't think that the direction of the flow by itself is cause for the altered pitch, but the reduction of the flow (caused by restrictions of/in the airflow path).

Could you please explain what restrictions you refer to?

As I'd mentioned earlier: "constrictions due to the smaller pan slots, valve location and properties, path surface friction, pad operation". I should clarify that by path surface friction I was referring to the properties of the chambers.

 

the issue is to compare the reed pitch with simply a change of leather, and it’s unlikely that this change would significantly alter the (small) effects of friction.

You lost me talking about friction.... Are you calling a the change of valve to be a different "friction'? And if by "effects" you mean "pitch of the reed"? If so, then it seems like this is exactly what you have demonstrated and so stated in your previous post's last paragraph:

 

I have just done this simple experiment (tonight) in my home shop on the free reed. I can assure you that, if you set a reed vibrating with a steady flow of air and take a small screwdriver and gently move the leather valve closer to the slot, the pitch will drop, and if you move the valve further from the slot, the pitch will increase

You just demonstrated that you were effectively changing the valve. A more laborious way to do it would be to actually CHANGE the valve (for a new one, and old one, the same one - it DOESN'T MATTER). In changing the valve to another one you will not be adhering it EXACTLY where the other one was. It will be covering the vent more or less, and the valve may be more or less pliable. The pitch of the reed before and after revalving will be different - which is what I've been saying all along.

 

There has been a lot of investigation and debate about this issue. Personally I think that there is no significant Helmholtzian propensities in concertina construction. The frequency, physical chamber sizes, and math just don't coincide. The discrepancy is HUGE.

I would appreciate very much if you could direct me to at least some of these investigations, associating reed cavities with resonators.

On this forum alone have been such under the Big reed performance, Chamber design, and Resonant cavity design models topics.

 

James Cottingham has done an amazing amount of investigative free reed work and has published much of his findings. I've also been in contact with other people who have performed such investigations though they haven't publicized their work. I could invite them to correspond with you (we should take this off-line...).

 

Unfortunately there seems to be very little else published on free-reed dynamics. Probably the most helpful book in English is the Fundamentals of Musical Acoustics by Arthur Benade.

 

I think it’s entirely reasonable to allow for the possibility of a resonator-coupled interaction with the reed. Many experimenters and theoreticians have been fooled by the subtleties of musical instruments. When you say that the “discrepancy is huge,” I think you’re referring to the comparison of cavity resonant frequency to the pitch of the reed. In some cases, it’s not so huge

Examples, please (which are relevant to concertinas)?

 

and when one considers overtones in the musical tone, the overlap can be significant. But again to the main point, a resonator tuned far away from the pitch of the reed can at least minutely affect the pitch of the reed.

Yes, the overlap can be statistically significant - but aurally nonexistent. I'm hard pressed to find ANY resonator-pitch affect in concertinas. Could you please provide examples? The only resonator effects I've observed in concertinas have affected reed responsiveness, not pitch.

 

certain modes of vibration are altered in woodwinds by either adding or taking away material inside the bore <snip>. An even better example concerns the design of finger pads in wind instruments. Much theoretical work has been done on this topic <snip>. The reasons why pitch is lowered when the finger pad is brought closer to the tone hole are well understood, and are precisely the reasons I have explained here.

Unfortunately, I don't have the background to follow much of your explanations. It does sound like you are talking about air columnar vibrational characteristics and resonance curves which are not relevant at all to concertina-type free-reed instruments.

[Chris Ghent]

(we should take this off-line...).

Please don't...

 

Chris

[ttonon]

Hi Rich,

I think we’re rapidly reaching diminishing returns in our discussion, and I find myself without the time and energy to continue in the minutest detail, though I offer the following.

Unfortunately, I don't have the background to follow much of your explanations.

I appreciate your forthcoming, and your situation, which became evident to me early on, is perhaps unfortunate, because physical and mathematical principles can indeed assist one in understanding how these little vibrators work. Your practical experience, however, is very valuable input to the general progress of free reed instruments, and I hope we together can make meaningful contributions.

On this forum alone have been such under the Big reed performance, Chamber design, and Resonant cavity design models topics.

 

James  Cottingham has done an amazing amount of investigative free reed work and has published much of his findings. I've also been in contact with other people who have performed such investigations though they haven't publicized their work. I could invite them to correspond with you (we should take this off-line...).

 

Unfortunately there seems to be very little else published on free-reed dynamics. Probably the most helpful book in English is the Fundamentals of Musical Acoustics by Arthur Benade.

I’m aware of the three threads you mention. I myself participated in them. I’ve read three of Cottingham’s publications regarding free reeds ("The motion of air-driven free reeds," "Theoretical and experimental investigation of the air-driven free reed," and "Variation of frequency with blowing pressure for an air-driven free reed"), and I’m not aware of others. None of these three, however, deal with the interaction between the free reed and a resonator. I’ve read Benade’s wonderful book, and recommend it to anyone who would like a deep, intuitive feel of how musical instruments work. The man is a physicist, and his intuitive approach is based on sound physical principles. Unfortunately, nowhere in the book is there a treatment of free reeds. Any other treatment of free reeds, that I'm aware of, does not treat a reed that is acoustically coupled to its cavity used as a resonator. One of Wheatstone' patents treats only huge resonators.

 

Benade’s book, however, contains relevant information to our discussion. In Section 13.7 of the 1990 Edition, titled, “A Loudness Experiment Comparing Two Saxophone Tones," Benade explains a method to produce a “louder and more penetrating tone” for saxophones. The discussion is relevant here because the method produces (by a change in mouthpiece) a new musical tone with enhanced overtones, which is precisely what my calculations in Resonant cavity design models predicts. In more detail, please look at Benade, page 245, Fig. 13.8., which shows that the fundamental of the new musical tone is 50% lower than in the original tone, and despite this drop in the fundamental sound pressure level, the enhanced overtones result in a musical tone that is roughly 1.33 times louder than the orginal tone, or, alternatively, the new tone in the altered sax is as loud as 2.6 saxophones playing with the original tone. It appears no one has quantified any effect reed cavities (can) have on the operation (sound) of free reeds. Until this is done, we can only speculate on the magnitude of such an effect; however, the calculations in Benade certainly at least give promise to the idea.

It does sound like you are talking about air columnar vibrational characteristics and resonance curves which are not relevant at all to concertina-type free-reed instruments.

I regret that you haven’t been able to understand my arguments. But that's okay; perhaps in another thread we can take this up further. In the meantime, for a more elaborate discussion on how modification of inertial terms (acceleration) is used to tune plates, check out Benade, Section 9.4, “Adjustment of Frequency Relations by Variations of Thickness,” and for the tuning of a clarinet, see Section 2.3, “Adjustments of Natural Frequencies by Means of Small Changes in Air Column Shape.” Benade’s approach is almost all intuitive, explaining physical concepts with a minimum of mathematics, and I highly recommend this book.

As to the change of pitch which may result from using more bellows pressure - try listening to Alistair Anderson playing for dancing. One of the characteristics of his playing is to lay great stress on certain notes. The stress is applied by a sharp increase in pressure on the bellows. The result is a louder note and a slight but clearly audible drop in pitch.

Hi Theo,

For a theoretical treatment of this effect, see the third Cottingham paper mentioned above. In the paper, this effect is attributed to “aerodynamic” effects, which is acoustician terminology that describes viscous friction, eddys, jets, and other departures from Potential (Irrotational, Inviscid) Flow. In the realm of Small Perturbation Solutions in Fluid Dynamics, at least some of these effects can probably be captured in the mean flow terms, if one who is clever enough to formulate and solve the governing differential equations. (It’s not likely anyone will ever do this.) In any event, the paper explains that, for blowing pressures often encountered in normal playing, the frequency of oscillation of the reed decreases in an approximately linear fashion with increasing blowing pressure, and as the blowing pressure is increased well above normal playing levels, the frequency levels off and eventually rises. Has anyone here noticed this latter effect? I should point out that these statements are not derived in the cited paper from first principles, but rather, experimental values of growth/damping coefficient (aerodynamic effects) are inserted into a theoretical framework, and the stated influence of pitch on blowing pressure is produced, giving some credence to the entire approach.

We discussed in another topic how concertina reeds could be effected by temperature drop or increase in humidity, could a damp valve alter (slightly) the pitch of the reed by say reduced airflow ?

Hi Alan,

This is an interesting conjecture, and to substantiate it, we’d have to know whether the elastic properties of the valve are affected enough by humidity. Perhaps humidity softens the leather, in which case, I’d guess the pitch of the reed would increase very slightly. We should realize here that a shift of only a couple cents in musical tone would, in most cases, go unnoticed during a session. Many other instruments experience inaccuracies in tone production, either because of (sometimes unavoidable) instrument construction, or because of player skill, even beyond a couple cents. As Theo points out, the human ear is capable of accurate measurement, if the conditions are right. For pure sinusoidal tones played at concert levels (60 – 90 dB) and under ideal listening conditions, the Just Noticeable Difference (JND) is a constant 1 hz up to about 1 KHz, and beyond 5 KHz, rises rapidly. (It’s no accident that the piano keyboard stops at 4186 Hz.) However, for many situations involving complex musical tones, with rapid and simultaneous notes being played, a couple cents inaccuracy is not serious offense. In fact, it’s an extremely rare free reed instrument that has all its notes tuned within 2 cents of exact. If it exists, it will soon change. Even better, many electronic tuners that are used for such tuning are themselves off by this much.

 

Best regards,

Tom

www.bluesbox.biz

[Richard Morse]

I’ve read three of Cottingham’s publications regarding free reeds... and I’m not aware of others. None of these three, however, deal with the interaction between the free reed and a resonator.

He seems to have quite a number of articles out there, mostly associated with the Acoustical Society of America from which it is nearly impossible to access their articles. I'm fortunate that a library near here has a ASA Journal "subscription", and hence bound copies of decades of their contributors work. I can't remember if he has published any work on resonators or not (at the time I was researching this I was focused on the reed tongue dynamics).

Unfortunately, nowhere in the book [ Fundamentals of Musical Acoustics by Arthur Benade] is there a treatment of free reeds.

Quite so, though I was able to find useful information under his pg. 128 section on "Mode Shapes of Rectangular Plate Having Free Edges" and pg. 148 "Excitation of a Pendulum" (Sinusoidally Driven Oscillations).

In Section 13.7 of the 1990 Edition, titled, “A Loudness Experiment Comparing Two Saxophone Tones," Benade explains a method to produce a “louder and more penetrating tone” for saxophones. The discussion is relevant here because the method produces (by a change in mouthpiece) a new musical tone with enhanced overtones

That discussion seems to be primarily about sound pressure level (and spectra) strength due to the mouthpiece change. Resonance due to the "column" (in a sax or the "chamber" in a concertina) appears not to be factor.

 

In a similar vein, there are ways of altering the reedplate vents to enable the reed tongue to achieve higher sound pressure levels.... Most of the work along this line fall into the area of bell-shape paths and seem to be more along the hyperbolic and exponential lines (loudspeaker type) than bessel type (musical horns like trumpets). There are also impedance and resonance issues there too.

 

Reedplate vent alteration seems to be similar to Benade's sax mouthpiece alteration as both involve a reed (free-reed and beating reed) tone generator and exit path to enhance the sound energy. I wish he would have described the alterations they did to the mouthpiece!

 

check out Benade... for the tuning of a clarinet, see Section 2.3, “Adjustments of Natural Frequencies by Means of Small Changes in Air Column Shape.”

Hmm, you mean 22.3... But my observations (or I should say: my surmisations of why...) are that concertina chambers are not "air columns" and don't act as such. Also that the note's chamber cannot be (practically) sized to enhance it's reed's natural frequency, though possibly some overtones, but by the time you get to anything approaching the correct size, the affect is so minuscule that its effect is overwhelmed by other considerations.

 

I look forward to understanding all this stuff! Checking out your website shows me how much effort you put into your investigations. Congratulations on now having those boxes to show for it! I've been working way at our project too, which someday will bear lovely fruit (err... boxes!).

[Ken_Coles]

You guys lost me a long time ago, but I note with interest the references to Arthur Benade. One of his popular books ("Horns, Strings, and Harmony") was a great boon to me as a kid, combining as it did my interests in music and science.