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How Much Difference Does The Choice Of Wood Make?


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#37 Dana Johnson

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Posted 30 August 2006 - 09:37 AM

Johan,
Thanks for the more complete picture on the effects of varying chamber parameters. I found a similar effect to the sound hole moving, with a rectangular chamber with a moveable plunger for one end wall, allowing varying chamber length / volume. Your remarks on trying to approach the human voice are also a great example of the nature of the process. It is as though we were given an unprogrammed synthesizer and had to develop a recipie from bits of wood and leather and metal that when properly mixed produced a voice sound, and not a bell sound or any of the other possibilities the synthesizer could produce. I find it fun and interesting that similar results can be had through quite different construction. I have measured reed stiffnesses on a number of instruments, and found that good instruments can be made using different stiffness ranges, but other pan dimensions need to change to match the reeds. Learning to match reeds to the box is a challenge, but a worthwhile one, offering substantial improvements in volume and response in some cases.

For other readers, a good example of how resonance can create a valley in sound output can be found in some concert halls. If a singer stands in certain locations where there is a room resonance at the right frequency, they find they cannot sing that note at all. Mouth opens and nothing but air comes out. needless to say, a lot of remedial work gets done in those halls to change the room resonances.

for Tom, When I speculate on mechanisms for acoustic features, I usually start with trying to imagine what is moving, where is the energy, how is it connected to the surroundings, are there more than one source? and given the limited range of my understanding of musical acoustics and instrument construction (string and free reed ) and taking as the starting point, a question arising from some anomalous result I found through work experiments, I then try to guess as many possible modes of action as I can, and then think them through or test them to eliminate the false directions. My starting point is not theory though, but is the experimental result. For instance, because I knew that Big leaf Maple was lighter but still nearly as hard as Sugar maple, and made an excellent tone wood for violin family instruments, I expected it would give me perhaps a clearer ( less damped ) tone. I worried about this a little, since the cost of good Big Leaf maple was much higher than the more readily available quartersawn Sugar Maple. I was completely unprepared for the magnitude of the differences. I don't know really know what caused the difference. It existed in both right and left reed pans , which as I mentioned were machined with close tolerances to the same dimensions as the Sugar maple, and had all stabilized together at the same room humidity. since the reeds used were also the same, I was left with the difference being in the wood itself. You know my guesses at the reasons, but I wouldn't have given this much thought if the difference wasn't so large. In comparison, my other instruments with Sugar maple reed pans and action pans all sound nearly identical, and are often difficult to tell apart. Other variables that might be present don't seem to be affecting them to an audible extent.
Dana

#38 Johann

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Posted 30 August 2006 - 09:46 AM

You have me confused. Do you think wood material is important to musical tone in concertinas or not? Perhaps my memory fails me, but as I recall, didnít you once make accordion reed cavities from balsa wood and found no noticeable effect?

Yes is important, but for accordions it is often thought is a major influence.Or some builders here say it don't count at all, because the use of ply wood for cases is easier in accordion production. But even this builder do a lot on the reed block design and use of wood for the reed block.

I've played many accordions in which some have plywood and others aluminum soundboards (as we call the pallet/pad pan item that the reedblocks are secured to) - including Wurlitzer and Hohner PA's and Paolo Soprani and Castagnari BA's. Some of these are models are "twins" where their production had changed from wood to metal - I was hard pressed to discern much of any sound/reponse difference. It seems to me that the method to which the reedbanks are secured to the soundboard has a greater sound/response difference than what material the soundboard was made of.

I also note that most reedblocks I've seen are made of softwood bodies and hardwood shoes (or bases - where the exit holes are). Rarely is the top end of the banks or body made of hardwood. I've also seen accordions with plastic reedbanks. One single moulding of plastic per bank. These accordions DID sound somewhat different though very much within the range of "normal" accordions, and the difference could have been due to other factors.

-- Rich --


Richard, exactly what i would write about accordion sound board, and reed blocks little change in sound but noticeable.

I always did think it is the sound board that could make a big difference, but acutely it is the body, the 4 sides of the case and the reed block, that contributes notable.


My preference on the treble side is at the moment to build the sound board as thin as possible or even without, as i did on one box (pallets operate direct on the reed blocks, reed blocks are sealed and screwed to the case frame and removable).

And then my main interest is the bass section of helicon boxes. And for the bass side the difference is for me even more noticeable.

#39 John Wild

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Posted 30 August 2006 - 06:25 PM

Hi John Wild,

cant imagin that the reeds did not sound at all. -- hoorible -- differnt -- less volume -- i woul blive.


I know nothing little the technical side of things. I was merely quoting a relevant article for information. Hamish Bayne has been an instrument maker and player for many years, so I would assume he knew what he was talking about.

Best wishes

John Wild

#40 ttonon

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Posted 30 August 2006 - 07:59 PM

[


Some organ pipes are made of wood. The wood material does not directly affect the sound. The material that a flute is made of does not directly influence the sound of the flute. The material that a clarinet is made from does not directly influence the sound of the clarinet. The material that comprises the bell of a brass instrument does not directly influence the sound of the instrument


As I think more on this, except for possibly organ pipes and brass bells, these examples may not apply to concertinas. The woodwind instruments with circular cross section are very rigid to the pressure pulses inside the instrument, and thus their bodies cannot flex much in operation. There are no asymmetric bending modes on the instrument. Wooden organ pipes, though, are often rectangular in cross section, with walls that might be susceptible to flexure, but perhaps the wall thickness is far beyond that which guarantees rigidity. Iím not sure about brass bells.

What I have been talking about is the resistance of the reed pan to motion at different frequencies via the transfer of momentum to it from the reed / shoe assembly.


Dana, your comment here is well taken, and I overlooked the reed tongue vibration itself, visualizing only the air vibration. Thanks for the suggestion. With this in mind, there may indeed be sufficient energy to cause large enough amplitudes of wood vibration in concertinas to affect musical tone, especially because of the generally flat nature of the pans and boards, and that concertinas belong in their own class, somewhere between body-resonance instruments and air column resonance instruments.

The other point that came to me upon further reflection is that the density of the wood can possibly directly affect the amplitude of the natural modes of wood vibration. In my comments regarding bending modes in my earlier post, I focused only on natural frequencies, and overlooked how the amplitude of these vibrations might be influenced by wood density itself. More massive woods might vibrate less than lighter woods. Thus, I can see that there may be a plausible physical mechanism (or pieces of it) identified that might explain the observations of you and others. Of course, we are still speculating, but I can at least see a pathway for it. Thus, wood density, a factor that I already noted as a reasonable explanation in an earlier post, might work to vary the amplitude of vibration of various natural modes, and itís reasonable to expect that some woods would vibrate with different amplitudes than others. It may be that the actual modes have different frequencies, but due the complexity of these, the specific modes may not be that important. In other words, any set of modes, with sufficient amplitude, might contribute to an identifiable timbre (within some limits governed by typical concertina construction practice).

Thus, the energy of vibration of the reed tongue, the generally flat geometry, and the influence of wood density could all provide the parts for a plausible mechanism that would allow sufficient amplitude of wood vibration.
There may be simple enough ways to theoretically evaluate and carry this conjecture further. I think the best experiment, though, would be to measure the amplitude of vibration of various wooden parts, and this would give many clues on how one can regard this conjecture.

Chris, do you know the relative densities of Sycamore and Tasmanian Blackwood? If you have some pieces, maybe you can cut two identical pieces of each and accurately weigh them. The obvious question here is, can wood density be a single parameter in predicting how the material will affect tone? I doubt things could be that simple, and perhaps thereís enough evidence already around to answer this question. I present another suggestion at the end of this post.

Dana, you have mentioned that you regard damping within the wood as an important mechanism for altering tone. Do you have an idea how the effect of damping might compare with some other consequence to vibrational modes in wooden members, such as, for example, movement of the reed shoe (plate) itself? In this regards, itís interesting to note that the hardwoods exhibit less damping than the resonance woods, in general by about a factor of two. Iíll have to think more on why the lighter Bigleaf Maple produced for you a louder, raucous tone. Do you have any idea why the lighter material sound went in that direction, than in say, to a softer, more mellower tone?

Iíd like to offer here a recent observation that came out of my thinking on this topic. With regard to resonance woods, a well know acoustician who did much work on musical instruments, Schelleng, proposed (The Violin as a Circuit, JASA, 1968, Vol. 35, 326-338), in the making of violins and similar instruments, a parameter, rho/c, where rho is the material density and c the sound speed, as being of prime importance when changing materials of construction in a way that would keep acoustic performance the same. I offer this here only to communicate what I have read and have not tried to evaluate this approach. The idea is (taken from Fletcher and Rossing, 1998, The Physics of Musical Instruments), suppose we wish to replace a plate with density rho-1, sound speed c-1, Youngís Modulus E-1, and thickness h-1 with another plate made from different material with parameters rho-2, E-2, c-2and h-2 in such a way as to leave vibrational performance unaltered. In order that both plates have the same stiffness and inertia, there follows, for the material properties, rho-1/c-1 = rho-2/c-2, and for the thickness, E-1*h-1^3 = E-2*h-2^3. Itís interesting to note that Norway spruce, a choice resonance wood, has both rho/c and Q value (a measure of internal damping, the less damping, the higher the Q) near the top of the list of most all woods. A conclusion here perhaps is that woods with higher rho/c would perform better, at least when acting as they do within string type instruments. For concertinas, there may be different conclusions, particularly if something like reed shoe (plate) movement itself is important. In any event, this result is interesting to me, because, if one were concerned only with natural mode >frequencies<, one need only make the ratio E/rho (neglecting the effect of Poissonís Ratio) the same, as I posted earlier. I think what Schellingís proposal does is to bring in the added effect rho has on the amplitude of vibrations. I could be wrong on this, but it seems like a reasonable observation.


Best regards,
Tom

#41 Johann

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Posted 31 August 2006 - 11:55 AM

Hi Tom,

Iíd like to offer here a recent observation that came out of my thinking on this topic. [...] In any event, this result is interesting to me, because, if one were concerned only with natural mode >frequencies<, one need only make the ratio E/rho (neglecting the effect of Poissonís Ratio) the same, as I posted earlier. I think what Schellingís proposal does is to bring in the added effect rho has on the amplitude of vibrations. I could be wrong on this, but it seems like a reasonable observation.


I state:
"the reed can produce much more as the natural overtone series dependent on the environments."
"Plus there is also always some noise within the sound of the reed resulting from the air stream."

So it is better to see all not only from a few point of the fundamental and the natural overtones of a reed as we usual do.
To see the reed as an distinct noise generator is the absolute opposite to the line above, but if we do this, this can help to understand sound formating better.


Tom you came this time quite close to my thinking, remember that if one adds noise as sound source, the wood serves as formating filter and transformer of the source.
In my test with noise as sound source the wood bass section of my helicon instruments always had some sort of damping and the resulting envelope of the spectrum curve never had a peak reaching over the amplitude line generated by the loudspeaker without the bass box added.
There are some similarity's between a loud speaker system and the bass chamber system of a helicon box.
I used the same test system on some bass section of accordions as i used for testing bass reflector boxes.


Also remember that amplification on passive loudspeaker systems is possible if horns are in use.
It is now some decades back when i experimented with speaker systems and bass horns. Still i also preferred to use passive filters. passive filters are better controllable in respect of phase shifting.

Because the wooden parts of instruments cant be made as stiff ans it is possible for load speakers we always deal with some kind of vibration on the wooden parts.
You also my reed about loudspeaker how the change the sound if the are made up by cases with walls that vibrate.

back to the instruments.




Even if your explanation comes a bit closer to the results of or experiments, you also have to think about the grain structure of most ton woods. Wood from the tropical zones is homogeneous wood from zones grown closer to the pols the wood is with year rings.

One conclusion form my side could be that tropical woods would have less transforming effects. Frequencies are not altered if the run through the wooden board, if the gain is relative equal as preferred for string instruments the year rings are very constant on old wood grown in past century's.

An other thing to think about is that on reed instruments softer wood often is preferred for certain parts of the instruments.
For instance, we have one producer of instrument who uses tropical soft wood for the entire reed block except the sole.
And everyone can here the difference in sound to a reed block made by spruce with an soft top bar.

One accordion builder uses walnut as top for the reed blocks and spruce for the chambers and again the are different.

So homogeneous tropical wood like balsa is very effective in damping, without much transforming effect.
Result softer but less volume compared to spruce or other ton woods.
mahagony is often used to - could it be that this would result in less damping but no transformation as with ton woods?

So if wood cames into use that has year rings, could it be that the the grain plays a rule we don't understand up to now?

On the other hand if homogeneous wood or ply wood is used (again homogeneous in some way) could it be that the result is easier controllable but not outstanding?

#42 ttonon

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Posted 31 August 2006 - 10:00 PM

Iíve had a little more time to think on this topic and it occurred to me that, if the chief source of energy that imparts wood oscillation is the vibrating mass of the reed tongue, this fact would greatly simplify the picture. Big Idea: Itís a well-known fact that when you excite any acoustic system, no matter how many natural modes of vibration it contains, by forced vibrations at a single frequency, only that natural mode having the driving frequency will be excited. Refinement: With damping in the system, the response spreads from this single frequency to both smaller and larger frequencies, but this spread is small for lightly damped systems (such as vibrating wood). Caveat: We are assuming the systems are linear, which I think is valid, since I see no source for significant nonlinearity, which is a rather esoteric subject, not often encountered in acoustics.

Letís review first how the reed produces sound. An air stream excites the reed tongue to vibration in sinusoidal fashion, being chopped in the process. This chopping introduces rapidly changing pressure pulses in the air, resulting in a musical tone, complete with fundamental (reed tongue frequency) and higher harmonics (because of the physiological response of our ear/brains to the pressure pulses).

The first conclusion is that any wood oscillation produced as a result of energy transfer directly from the vibrating reed tongue to the wood will impart wood vibration at (essentially) only the excitation frequency of the vibrating reed tongue.

Some people might claim that overtones present in air vibration will also cause significant wood oscillation, at the frequency of respective overtones. I think this is highly unlikely, simply because I donít see that much force/energy available. I havenít proven my judgment here by any method - calculation or experiment. Itís just my gut feeling. On the other hand, I think itís reasonable to at least assume that the energy of vibration of the reed tongue, however, is capable of causing sufficient oscillation in wood. One can reasonably estimate, for instance, the power associated with the vibrating tongue, and compare it to that associated with the acoustic waves in the air (even including the fundamental). Itís my guess that the former is vastly larger than the latter. Maybe some day Iíll have enough time to do this calculation. Also, some people might claim that the reed tongue motion is not sinusoidal, but rather contains overtones. This may be true for high blowing pressures, and even then, the motion in the higher modes is orders of magnitude less than that of the fundamental. Itís certainly not true for low to moderate blowing pressures.

Assuming my hunches are correct, I conclude that all the discussion in this thread alluding to the complex arrangement of various natural modes of wooden members is irrelevant WITH REGARD TO FINDING A MECHANISM TO EXPLAIN THE OBSERVATION that wood material affects timbre. In other words, there seems to me not enough energy available to excite the many natural modes of the wooden parts. Only one mode will be excited, at the frequency of the vibrating reed tongue, because that is the only reasonably available source of excitation.

So then, what explanation can there be for the complex alteration in timbre observed, which implies an alteration of the overtones in the musical tone? From this point, the only mechanism I can think of to explain the observation is the effect that wood oscillation has on the reed shoe (plate), and the consequent effect this motion has on the chopping of the air stream. To see this, one should imagine the tongue passing through the window (slot), but with the window also moving. With this combined motion, the relative motion between the reed tongue and the window is altered. Both the tongue and the window move with sinusoidal velocity, but most likely with different phase. The sum of two sinusoids with different phase is also a sinusoid of varying amplitude Ė maximum when the phase is zero and minimum when the phase is 180 degrees. But here, I see difficulties, when I compare the relative amplitudes involved. I canít see that the window vibrates with much amplitude compared to the tongue, even when excited by the tongue. And so, this mechanism (effect of wood motion on the chopping of the air stream) starts to loose my interest. But letís continue anyway, assuming that for some reason, the reed shoe (plate) vibration is appreciable. In this case, the relative velocity between the tongue and the shoe is still sinusoidal, as it is without wood motion, but with different amplitude, depending on the relative phase. Relative velocity between tongue and shoe translates to tone volume. From this analysis, then, the only result of this mechanism would be to possibly alter the volume of the musical tone, and the alteration would be different for different reeds, according to where they lie with respect to nodes and antinodes of wood vibration. So this mechanism seems not able to explain a change in timbre, just volume.

At this point, I fail to see a mechanism for the reported results, and also feel that the mechanisms proposed in this thread are also not plausible explanations. Yes, I could be wrong, and would welcome anyone to find the error. I regard the conclusion that I make about the single-frequency excitation of wooden parts a firm conclusion, and it would be nice if anyone could substantiate, rather than simply assert, any claim that overtones in the musical tone can impart wood oscillations at natural frequencies that are the same as their respective exciting overtones. A suggestion here would be to calculate the pressure force on realistic wooden areas due to the pressure oscillations defining these overtones and estimate a resulting amplitude of wood oscillation. I havenít time for it at present.

Best regards,
Tom

#43 Johann

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Posted 01 September 2006 - 12:55 AM

Some people might claim that overtones present in air vibration will also cause significant wood oscillation, at the frequency of respective overtones. I think this is highly unlikely, simply because I donít see that much force/energy available. I havenít proven my judgment here by any method - calculation or experiment. Itís just my gut feeling.



*FEM - ein Rechnerverfahren zur Optimierung von Tonzungenprofilen
*Instrumentenbau-Zeitschrift 44 (1990) 9, S. 34, 36, 38 (3 Seiten)

read this this was point out to after i had presented may tests about higher mode frquenzys

#44 ttonon

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Posted 01 September 2006 - 08:12 AM

*FEM - ein Rechnerverfahren zur Optimierung von Tonzungenprofilen
*Instrumentenbau-Zeitschrift 44 (1990) 9, S. 34, 36, 38 (3 Seiten)

read this this was point out to after i had presented may tests about higher mode frquenzys


Hi Johann,

This appears to be an article on a computer procedure for the optimization of reed tongue profiles, and I don't see it's relevance to the quote of mine that you referenced. Is the issue you wish to address on overtones in reed tongue vibration? Does it deal with accordion reeds or organ reeds? Can you summarize this reference, please? Thanks.

Best regards,
Tom

#45 Johann

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Posted 01 September 2006 - 02:44 PM

*FEM - ein Rechnerverfahren zur Optimierung von Tonzungenprofilen
*Instrumentenbau-Zeitschrift 44 (1990) 9, S. 34, 36, 38 (3 Seiten)

read this this was point out to after i had presented may tests about higher mode frquenzys


Hi Johann,

This appears to be an article on a computer procedure for the optimization of reed tongue profiles, and I don't see it's relevance to the quote of mine that you referenced. Is the issue you wish to address on overtones in reed tongue vibration? Does it deal with accordion reeds or organ reeds? Can you summarize this reference, please? Thanks.

Best regards,
Tom



Yes is about calculating program for reed tongues.

The content deals with the natural higher mode frequency's es well.
Especially the 3rd mode are also calculated and taken into account for finding the optimum of reed profile.

I cant give a summery of this three pages at the moment, i had this pages on paper but i borrowed them to a friend who is also interested, i will be with him is a few weeks again.

But here is what Gunter Ziegenhals did reply as i forwarded my conclusions about higher mode vibrations of a reed tongue.
This was just a few week ago so i am still waiting for a other reply on the subject from his side. It is a very short reply but it defiantly states that the know it all before me.
You may contact him yourself and her what he knows. I keep on on the subject but it is to early to say more as i already did.

------
Sehr geehrter Herr Pascher,

[...]
Mit der Profilierung von Tonzungen hat sich das IfM in den 1980er Jahren befasst. Sie finden auf unserer Internetseite dazu VerŲffentlichungshinweise. Suchen Sie nach dem Autor MŁller, U. Der Einfluss der hŲheren Zungenmoden auf den abgestrahlten Schall ist sehr gering, da die Tonzunge ja nicht selbst abstrahlt. Bedenklich wird es, wenn eine falsche Profilierung zu Torsionsmoden fŁhrt. Das hŲrt man deutlich selbst wenn es nicht zum AstoŖen fŁhrt.

Mit freundlichen GrŁŖen

Gunter Ziegenhals
post@ifm-zwota.de
----

#46 Dana Johnson

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Posted 03 September 2006 - 09:02 AM

Letís review first how the reed produces sound. An air stream excites the reed tongue to vibration in sinusoidal fashion, being chopped in the process. This chopping introduces rapidly changing pressure pulses in the air, resulting in a musical tone, complete with fundamental (reed tongue frequency) and higher harmonics (because of the physiological response of our ear/brains to the pressure pulses).

Note that the chopping produces a more or less double frequency pulse, but since the pulses are not the same, both only repeat at the fundamental frequency, but together also produce at least the second harmonic.

Also, some people might claim that the reed tongue motion is not sinusoidal, but rather contains overtones. This may be true for high blowing pressures, and even then, the motion in the higher modes is orders of magnitude less than that of the fundamental. Itís certainly not true for low to moderate blowing pressures.

Due to the nature of the air flow forces on the reed, the down swing and up swing have diffferent shapes, producing a modified sinusoid, Depending on many facors in plate / shoe design, and prehaps other parts of the system, the resulting wave form is composed of the sum of many harmoncs, some of them quite strong. In some cases they are stronger than the fundamental. Also , the natural vibrating frequencies of a reed not driven by air flow, are totally non musical, rising in frequency in at least a third order curve. ( I've plotted this out for many reeds, both "ideal" (flat ) and not.
It would be useful to refer to Arthur Benade's work (Fundamentals of Musical Acoustics) for his treatment of the paradox that none of the natural reed frequencies are present in a blown free reed reed except the fundamental, and how the completely musically alligned series of overtones that are very and quite measurably present ( my wave analyzer picks them out quite well ) are produced from the non sinusoidal wave form. My experience is that the only time you hear natural harmonics are when a reed won't start easily and you get a nasty whine instead.
Regarding computer optimising the reed profile with respect to different harmonics, are these the natural ( non musical harmonics )? I'd think a writing a program for optimizing the Musical heterodyne produced harmonics would take a good understanding of the whole reed / chamber system, but possibly some factors cancel, or really don't have as much effect as I might expect.
Also it is my experience that only the higher notes on concertinas and accordions resemble sinusoids, and even they are a little too triangular in shape.
Dana

#47 Johann

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Posted 03 September 2006 - 01:20 PM

Due to the nature of the air flow forces on the reed, the down swing and up swing have diffferent shapes, producing a modified sinusoid, Depending on many facors in plate / shoe design, and prehaps other parts of the system, the resulting wave form is composed of the sum of many harmoncs, some of them quite strong. In some cases they are stronger than the fundamental.

true

Also, the natural vibrating frequencies of a reed not driven by air flow, are totally non musical, rising in frequency in at least a third order curve. ( I've plotted this out for many reeds, both "ideal" (flat ) and not.

can the plots be seen?
How did you activate the motion of the reed?

It would be useful to refer to Arthur Benade's work (Fundamentals of Musical Acoustics)

is some of the relevant writing on the net?

for his treatment of the paradox that none of the natural reed frequencies are present in a blown free reed reed except the fundamental, and how the completely musically alligned series of overtones that are very and quite measurably present ( my wave analyzer picks them out quite well ) are produced from the non sinusoidal wave form.

Yes i think i and Tom know way and how the natural sera's of overtone get into existence.

My experience is that the only time you hear natural harmonics are when a reed won't start easily and you get a nasty whine instead.

This is one situation we realize that there are other overtones produced by a reed.

Depending on the resonance conditions for the reed some of the possible natural overtones (modes) my be generated by the reed as strong as the fundamental.
Usually the resonance conditions are not in away that higher mode are produced as strong to be heard as individual natural harmonic, the are in most cases about more as 10 times smaller as the harmonic overtones present in the acoustic sound, so the can only be noticed as part of the sound color (timbre ). The are so little in amplitude that the usual get lost in the spectrogram. The only can be heard as individual pitch if we already know for what we are looking.
(notic also what Mr. Gunter Ziegenhals did write to me: " [...] falsche Profilierung [...] Das hŲrt man deutlich selbst wenn es nicht zum AstoŖen fŁhrt...." Translation to English: wrong profile [...] this also is heard clearly even the reed is not tughshing the sides of the frame.)
To get this natural non harmonic modes strong enough so the can be easily identified within the spectrogram one has to adjust the resonance of the reed chamber so the the fundamental is damped by at the same time the higher mode is not , that also meas that higher mode as fundamental must be quite different and must not meet a harmonic of the fundamental ( this means wrong profile) , so this depends on the reed profile whether it is possible to enforce a higher mode in relation to the fundamental with resonance or not. So by accident it will in most cases NOT be that one will have higher modes present with very strong amplitude to be easily identified on a spectrogram.
But, after knowing this now i am convinced that profile and resonance condition change the timbre of the musical sound.
Resonance (damping) is not only present by the camber.

Also be aware that in some books this is not taken in account because is of less theoretical importance to understand the fundamental operation of a reed.
And usually spectrograms do not show the presence of higher modes.
The physics of the vibration of the beam modes in other fields of technique are better documented and mathematical models are in use.
It is absolutely no new territory of physics.

Regarding computer optimising the reed profile with respect to different harmonics, are these the natural ( non musical harmonics )?

Yes

I'd think a writing a program for optimizing the Musical heterodyne produced harmonics would take a good understanding of the whole reed / chamber system, but possibly some factors cancel, or really don't have as much effect as I might expect.

is not as complex as one thinks, still it needs a program to do the job.

#48 Dana Johnson

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Posted 03 September 2006 - 04:49 PM

Johann, I have only been able to dig up one old graph ( this stuff is about 15 years old, and has been through a number of moves and discarding of material thought to be of no further value Essentially, as soon as I realized the natural harmonics were not musically (to a measureable degree, and I have a quite sensitive wave analyzer) present I dropped the subject. In any case this was for a very low "reed" Fundamental (f) of 21Hz. 6 inches X 1 inch X.018 inches in size. the ratios to the Fundamental were: 2.1xf, 6.3xf, 17.6xf, 34.6xf, 57.2xf, 86.1xf, 120.4xf, 430xf. I believe as you say that this is simply the beam mode vibrations and as you say, long understood in physics ( fortunately for our modern infrastructure!). I Began this experiment not expecting anything substantilly different, and was simply concerned with how these harmonics might influence tone color as you mention. What took me totally by surprise as a neophyte was the dissapearance of these resonances in the Air driven mode. The initial set up involved a 6 inch loudspeaker in a box set up fairly close to the reed which was clamped in a sturdy vise. the loudspeaker was hooked up to an amplifier and a tone generator and frequency counter. the reed motion was detected with a small magnetic pickup a short distance from the reed tip, but far enough from it to strongly be attracted to it.. i measured the output of hte pickup on an oscilloscope. I did other experiments on other actual concertina and low accordion reeds, but no longer have the information at hand. I do have a trace of a comparison between a plucked reed (drawn back a short distance and released vs/ the same reed air driven. I believe the difference in the harmonic content is shown here, but is of little use as data.Attached File  Low_G__wheatstone_reed.pdf   18.84KB   205 downloads
The reed is a long scale Low G# wheatstone reed (second G# below middle C) the upper trace is the reed air driven over a box connected to a blower, and the lower trace is the reed plucked by lifting the tip a short distance and releasing it with a fingernail. Not very scientific, but shows the high frequency harmonic content of the plucked reed and the strong main peaks of the air diriven reed. Note the strong hump on the side of the waveform that is common to both. All my traces of many different accordion and concertina reeds showed variously shaped waveforms. the lower the pitch, the more prounounced the double hump, gradually eliminating it toward the high reeds where the waveform was a slightly triangular sinusoid. the waveforms in general leaned more toward sawtooth than sinusoid, that is the initial rise was steeper than the falling side of the wave.

If you contact me with E-mail, i can send you the few pages of Benade that relate, the book is Oxford university press, and is meant as a starting text for his class in musical acoustics at Case Western Reserve University in Clevleland Ohio. Sadly he is no longer with us and was a great writer and teacher. (physics )
the relavant quote is "We learned (in section 5.5) that a non sinusoidal but repetitive motion is made up of a set of harmonically related components whose amplituesare such as to make them add up to give the observed overall motion."

This is unlike the natural harmoics which are visible with a stroboscope as multiple wave structures with different periods. In the air driven case the movement of the reed is kept from being sinusoidal by factors mentioned earlier, I think most importantly, the with vs. against the air stream aspect of the cycle. ( this is only a guess on my part) Simply retarding the upswing is enough to generate the nonsinusoidal but reptitive motion he speaks of. How much it is retarded and any other influences like wall drag in the tight clearance of a reed window or who knows what else determines the harmonic content. Of course other things like the tiny portion of the natural harmonics may add to it too.
Sorry, I have to make dinner now
Dana

#49 ttonon

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Posted 04 September 2006 - 12:27 PM

In studying the free reed phenomenon, we need to distinguish between the motion of the reed tongue itself and the motion of the air, which is integral to, but separate from, the motion of the tongue. Itís easy to confuse them. The driving force for all motion arises from the excess (static) air pressure on the side of the reed where the tongue is placed on the shoe (plate).

Letís look at the tongue. Like all elastic bodies, the tongue can vibrate freely (as if plucked), and/or it could vibrate in forced oscillation, as when it produces a musical tone, being forced by air pressure. Vibrating freely, the tongue possesses natural modes, and as Dana points out, these modes are not harmonic (contrary to the vibration of flexible strings), and thus, are non musical. (As an aside, ďharmonicĒ describes whole number ratios. In some vibrations, the overtones are precisely harmonic, and in others, they are clearly not harmonic.) With forced motion, the tongue will vibrate at the frequency of the exciting force. If the exciting force contains numerous frequencies, the tongue will vibrate at the same numerous frequencies, with varying amplitudes. This is basic Physics, and when we apply it to concertinas, the crux of the issue at hand becomes, What is the relative amplitudes of possible separate vibrations that make up the vibration of the reed tongue? I have an answer for this, but now, letís look at the air.

The air pressure force acting on the tongue is very complex, described by what Iíll call a step-function-like force. At the risk of belaboring this picture to some, I need to point out that, when the reed is inside the slot (vent), it experiences essentially the full static air pressure difference. When it exits the top side of the shoe (where the static pressure is positive), the pressure force acting on it rapidly drops to nil. When it comes back down, the pressure force rapidly increases again to the maximum, with the tongue again in the slot. There is a smaller change of pressure force as the tongue moves through the slot, as air leakage around it increases, causing more air velocity within the slot, and because of Bernoulli, the pressure force on it decreases. If the tongue exits the bottom of the slot (it may not), the pressure force again rapidly drops to nil. There are additional complications, such as the fact that, since the tongue sometimes moves upwind to the mean air stream and sometimes downstream, a dynamic pressure component is included. Also, when the tongue is near the opening in the slot, air velocity around it, because of Bernoulli, tends to change the pressure force in a slightly more gradual way. Some of these effects may be negligible compared to others, but in any event, one can see that the pressure force acting on the tongue is complex, not sinusoidal, and, if there are no non-harmonic parts to the tongue motion itself, this pressure force will be periodic (see note, below).

Itís a well known fact that a periodic forcing function with rapid changes in time can be represented by a harmonic series of terms, with each term a sinusoid. As the quote from Benade that Dana posted says, the total function is non sinusoidal, but itís made up of many sinusoids. This is basic, and itís true for both the reed tongue and the air vibration.

We can thus see right here that the musical tone we hear is a direct result of these pressure forces traveling as waves through air, and is complex, not sinusoidal, just like the originating source. This musical tone is made up of a series of harmonic terms, with large contributions from overtones. Many of us have seen these terms in spectral data of the emanating musical tone. Thereís no question that the air contains vibrations with many frequencies, no doubt varying in relative amplitude as we compare different kinds of reeds in size, material (brass vs steel), cavity geometry, etc.

A further conclusion is that the step-function-like pressure force will, in principle, produce tongue motion at many frequencies. Now we address the question at hand: What is the relative amplitude of these separate vibrations that make up tongue motion?

For the answer, we look to experiment. The only published experiment that Iím aware of that treats specifically this issue is, ďThe Motion of Air Driven Free Reeds,Ē By Cottingham, Lilly, and Reed, at the Physics Department at Coe College, Cedar Rapids, IA. I have this paper in pdf form and would be glad to send it to anyone interested. In their experiment, the authors measured the actual motion of the tongue from a free reed organ by a variable impedance method, and then analyzed the motion. They present data for this at two driving pressures. In general, the higher the driving pressure, the less is the tongue motion sinusoidal (single frequency), but even in the worse case, with the higher than normal driving pressure, the departure from a sinusoid is very small. Figure 4 in this reference is a beautiful plot of the results for this case, which plots the spectrum of the Amplitude of tongue vibration. In this plot, the Amplitude of the second harmonic tongue motion is about a tenth of that from the fundamental; the third harmonic is about half of the second, and all others are less than about 1/100 of the fundamental. The first overtone of the tongueís natural (free) modes can be seen on the plot at about 6.3 times the frequency of the fundamental, and itís amplitude is about 1/1,000 that of the fundamental. In other words, even though the tongue is excited at many frequencies by the complex pressure force, it remains relatively insensitive to all frequencies except the fundamental. Apparantly, itís stiffness is too much for the air pressure forces at these frequencies, most of which lie far away from the higher natural modes of vibration.

Itís important to note here that Power scales as the square of the Amplitude. Thus, the second harmonic, being of one tenth the Amplitude of the fundamental, contains 1/100 the power of the fundamental. Thus, about 99 % of all the energy of reed vibration is contained in the fundamental mode. Incidentally, the power contained in the second mode beam vibration is on the order of E-6 times that of the fundamental.

In the context of this thread, I thus maintain the conclusion I made in my previous post, that, if the reed tongue is capable of exciting wood members of a concertina to vibration, the resulting vibration will be essentially at the fundamental frequency, since relatively so little energy at other frequencies is available. One might argue that concertina reeds are different from harmonium reeds. Fine, if thereís not just speculation, but rather a real argument based on experimental evidence, or at least physical principles. Until something better comes along, the Cottingham paper, in my mind, takes precedence over speculation.

Quotes from Danaís Sept 3, 9:02 AM post:

Due to the nature of the air flow forces on the reed, the down swing and up swing have diffferent shapes, producing a modified sinusoid, Depending on many facors in plate / shoe design, and prehaps other parts of the system, the resulting wave form is composed of the sum of many harmoncs, some of them quite strong. In some cases they are stronger than the fundamental.


I agree with this, if the ďmodified sinusoidĒ of the ďwave formĒ you mean is that of the oscillating air pressure in the musical tone. If you mean to describe the tongue motion in this way, I disagree and must ask for some substantiation, for it directly contradicts experimental evidence.

It would be useful to refer to Arthur Benade's work (Fundamentals of Musical Acoustics) for his treatment of the paradox that none of the natural reed frequencies are present in a blown free reed reed except the fundamental, and how the completely musically alligned series of overtones that are very and quite measurably present ( my wave analyzer picks them out quite well ) are produced from the non sinusoidal wave form.


Iíve read the Benade book you reference, and Iím not aware of any mention of free reeds, and a quick check now shows no mention in the index. In any event, here, and elsewhere, you seem to be mixing up the motion of the tongue itself with the wave form of the pressure oscillations. Without seeing a clear physical distinction between these, there will undoubtedly be confusion on this issue. For instance, unless Iím wrong, and please correct me if I am, I doubt that you have done an experiment that measured the actual tongue motion, and thus, I donít understand how youíd be able to see the overtones of the tongue motion on your wave analyzer. On the other hand, if what you saw on your wave analyzer described air vibration, we are in agreement.

My experience is that the only time you hear natural harmonics are when a reed won't start easily and you get a nasty whine instead.


Same here. Itís something like the squeak of a clarinet or sax reed.

I'd think a writing a program for optimizing the Musical heterodyne produced harmonics would take a good understanding of the whole reed / chamber system, but possibly some factors cancel, or really don't have as much effect as I might expect.


I donít understand the relevance to free reeds. Heterodyne frequencies are produced by some sort of nonlinearity in the vibrating system. What source of nonlinearity do you envision with the free reed? Non harmonic overtones can be produced by linear systems. I understand our ears are nonlinear and produce heterodyne frequencies, but thatís also beside the point.

Also it is my experience that only the higher notes on concertinas and accordions resemble sinusoids, and even they are a little too triangular in shape.


I totally agree if you are referring to the air pressure wave form we hear. Although the evidence shows that all concertina reed tongue motion is essentially sinusoid, I could believe that slight departures might increase as the pitch of the reed drops.

In the air driven case the movement of the reed is kept from being sinusoidal by factors mentioned earlier, I think most importantly, the with vs. against the air stream aspect of the cycle. ( this is only a guess on my part)


This is the statement that spurred on my post here. Itís helpful to see your qualification, and it indicates to me that you are open to suggestion on this issue, so I took the (considerable) time to do it. I hope it goes well in that direction and that you understand my reasons for it.

Simply retarding the upswing is enough to generate the nonsinusoidal but reptitive motion he (Benade) speaks of.


Dana, I understand that, to one who isn't aware of experimental evidence to the contrary, it's reasonable to suppose that such asymmetry can possibly introduce significant nonsinusoidal behavior in tongue motion. I explain this mechanism myself in this post. It's a supposition, however, and experimental evidence indicates that, although correct in theory, the magnitudes involved are quite small. Again, if you're interested in the Cottingham results, I'll email it to you.

Note: We know the tongue motion is essentially periodic, because it results in musical tone. Thus, any non harmonic (which also means non-periodic) contribution must be very small.


Best regards,
Tom

Edited by ttonon, 04 September 2006 - 02:02 PM.


#50 Johann

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Posted 04 September 2006 - 03:13 PM

A further conclusion is that the step-function-like pressure force will, in principle, produce tongue motion at many frequencies. Now we address the question at hand: What is the relative amplitude of these separate vibrations that make up tongue motion?

For the answer, we look to experiment. The only published experiment that Iím aware of that treats specifically this issue is, ďThe Motion of Air Driven Free Reeds,Ē By Cottingham, Lilly, and Reed, at the Physics Department at Coe College, Cedar Rapids, IA. I have this paper in pdf form and would be glad to send it to anyone interested. In their experiment, the authors measured the actual motion of the tongue from a free reed organ by a variable impedance method, and then analyzed the motion. They present data for this at two driving pressures. In general, the higher the driving pressure, the less is the tongue motion sinusoidal (single frequency), but even in the worse case, with the higher than normal driving pressure, the departure from a sinusoid is very small. Figure 4 in this reference is a beautiful plot of the results for this case, which plots the spectrum of the Amplitude of tongue vibration. In this plot, the Amplitude of the second harmonic tongue motion is about a tenth of that from the fundamental; the third harmonic is about half of the second, and all others are less than about 1/100 of the fundamental. The first overtone of the tongueís natural (free) modes can be seen on the plot at about 6.3 times the frequency of the fundamental, and itís amplitude is about 1/1,000 that of the fundamental. In other words, even though the tongue is excited at many frequencies by the complex pressure force, it remains relatively insensitive to all frequencies except the fundamental. Apparantly, itís stiffness is too much for the air pressure forces at these frequencies, most of which lie far away from the higher natural modes of vibration.

Itís important to note here that Power scales as the square of the Amplitude. Thus, the second harmonic, being of one tenth the Amplitude of the fundamental, contains 1/100 the power of the fundamental. Thus, about 99 % of all the energy of reed vibration is contained in the fundamental mode. Incidentally, the power contained in the second mode beam vibration is on the order of E-6 times that of the fundamental.


Tom way you want to prove that the non harmonic content of musical ton does not count?

So actually you agree that higher modes (non harmonics) are present.

Usually the are very small depending on the reed type and on the resonance condition.
Still, in many cases a lot different exists and this is easy to prove by test you can perform your self.
The tests made by Cottingham are not representative at all, the have to be repeated with different reeds,
and under different resonance conditions as i did.


Then all the the othehr differences that make up a SPECIAL reed instrument are very little too.
I if we want something special and or ears are sensitive we hear this little differences!


In all this we overlook the transient conditions of a reed, starting and stopping contributes much to
how we identify a sound with or human ear but this is more difficult to document because FFT is not mad for this.

it looks like we don't want the non harmonic partials, if this is actually the case
Then we would have to optimize the reed tong in a way that the reed is profiled in a way
that higher modes are dumped as much as possible.
The second juice is to tune the higher modes to fit as close as possible the harmonic content of the fundamental.

resonance should never damp the fundamental.

since higher mode are much higher in frequencies as the fundamental resonance (actually damping)
of the wood may well have an effect on the higher mode frequency's.

The non harmonic content of a reed is always a part of the sound we all know very well.
It is this metallic ringing sound we all know.
Reducing the higher mode result therefore in every case in a more pleasant sound.
Subjective description again but i think we do not have an alternative to it.
Sorry if i cant put it in a better explanation, i wish i would be a native speaker, but even in
German language it is not a question to describe it with many pages.

To all here building instruments, please use your ears and do more experimenting and trust what you hear.
Spectrum analyzes are not of much use to see the difference.
Every Instrument has it own personality, no matter how hard we tray to copy th original.
some my be close to the original still not exactly the same.

#51 Larry Stout

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Posted 04 September 2006 - 03:15 PM

Thanks for this detailed discussion-- from this one and another on reeds I gather the following:
1. The shape and thickness of the reed shoe, particularly the amount of camber to the slot make a big difference in getting a concertina rather than an accordeon sound from the reed. Since the shape of the reed shoe has significant effect on the air pressure curve that the motion of the reed tounge induces this fits with the sound spectrum of the instrument depending on the air behavior rather than particularly on the reed.
2. The shape, size, and end conditions in the reed chambers are important to concertina tone.
3. Traditional woods used for the reed pans matter, thoug I'm not sure why or how.
4. Wood used for the action box doesn't make a lot of difference, though fretwork may.
5. Metal ends give a much brighter sound. There is much more difference acoustically between metal and wood than there is between kinds of wood.

Have I got all this right?

A question-- I have the first edition of Fletcher and Rossing (the one that doesn't have a section of free reeds). Is the section that was added to the second edition sufficiently enlightening to make it worth the bother of getting it through interlibrary loan? Both universities in town have the first edition but not the second.

I learn a lot from reading here.

#52 Johann

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Posted 04 September 2006 - 03:27 PM

Johann, I have only been able to dig up one old graph ( this stuff is about 15 years old, and has been through a number of moves and discarding of material thought to be of no further value Essentially, as soon as I realized the natural harmonics were not musically (to a measureable degree, and I have a quite sensitive wave analyzer) present I dropped the subject. In any case this was for a very low "reed" Fundamental (f) of 21Hz. 6 inches X 1 inch X.018 inches in size. the ratios to the Fundamental were: 2.1xf, 6.3xf, 17.6xf, 34.6xf, 57.2xf, 86.1xf, 120.4xf, 430xf. I believe as you say that this is simply the beam mode vibrations and as you say, long understood in physics ( fortunately for our modern infrastructure!). I Began this experiment not expecting anything substantilly different, and was simply concerned with how these harmonics might influence tone color as you mention. What took me totally by surprise as a neophyte was the dissapearance of these resonances in the Air driven mode. The initial set up involved a 6 inch loudspeaker in a box set up fairly close to the reed which was clamped in a sturdy vise. the loudspeaker was hooked up to an amplifier and a tone generator and frequency counter. the reed motion was detected with a small magnetic pickup a short distance from the reed tip, but far enough from it to strongly be attracted to it.. i measured the output of hte pickup on an oscilloscope. I did other experiments on other actual concertina and low accordion reeds, but no longer have the information at hand. I do have a trace of a comparison between a plucked reed (drawn back a short distance and released vs/ the same reed air driven. I believe the difference in the harmonic content is shown here, but is of little use as data.Attached File  Low_G__wheatstone_reed.pdf   18.84KB   205 downloads



Thanks dana, yes this arrengmemt works, the relations of the frequences depend on the reed shape and profile.

#53 Dana Johnson

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Posted 04 September 2006 - 06:52 PM

Thanks dana, yes this arrengmemt works, the relations of the frequences depend on the reed shape and profile.

it was clear nearly from the beginning that profile would certainly effect the distribution of the natural resonances, ( reed shape as well, ie. tapered paralell sided or reverse taper (fish tail ). each portion of the reed's profile + taper effecting strongly harmonics that affected that region, and less so, harmonics that were large enough to cross between regions.
In thinking about how the reed's spring profile, (where it bends most, and the shape of the bend in general ) influences the aerodynamic forces on the reed, I think that the reed profile + taper have a lot of influence on this. As an example, a reed that has a relatively long and thin section near the tip will have a lot of curvature there, and the amount the pressure forces and venturi forces are able to affect the reed will vary by a larger degree during the cycle ( due to the angle the forces are able to act on the reed, and probably more) than would affect a reed that remainde straighter ( ie. focused the bending closer to the root ) during it's cycle.

On another note, I try not to visit the forum during the work day, and do find these discussions keep my mind busy during the repetition of fitting valves, springs, and reed tuning. ( don't get me wrong, I love what I am doing!) The summer has been too full of vacation time!
Dana

#54 ttonon

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Posted 06 September 2006 - 06:36 PM

A question-- I have the first edition of Fletcher and Rossing (the one that doesn't have a section of free reeds). Is the section that was added to the second edition sufficiently enlightening to make it worth the bother of getting it through interlibrary loan? Both universities in town have the first edition but not the second.

Hi Larry,

The section on free reeds is only about 3 pages, and I'm not sure of your interest, but if you'd like, I could copy the pages and send them to you. You can send me your address by email.

Best regards,
Tom




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