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#1 ttonon

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Posted 17 September 2003 - 04:06 PM

In discussions here, Helmholtz resonators, quarter wave tubes, and half wave tubes have been mentioned as possible models that might simplify free reed resonant chamber construction. Practical considerations – primarily space and dimensional requirements – limit the applicability of each of these models, and it appears that no single model can be applied to all reeds spanning the useful pitch range of bass, baritone, and tenor instruments.

Presumably, the goal of resonant design is to produce forceful (quick starting), possibly amplified, and pleasant sounding timbre. Much of these effects are, however, subjective, and although the goal itself can be a contentious issue, we assume here that the desired affect will be achieved by tuning resonance to the fundamental and/or lower partials (overtones). With quarter wave tubes, tuning to a given frequency will also result in tuning to odd multiples of that frequency, and with half wave tubes, all multiples will be tuned for. With the simple Helmholtz resonator, only the design pitch will be affected (more on this below).

As a slight digression, I believe the ideal sound spectrum of an isolated free reed is composed of overtones that are perfect harmonics (whole number ratios to the fundamental), simply because there is no excited overtone of the vibrating cantilever. (If such an overtone were excited, noise would result.) In reality, there is thus very little “stretching” that occurs with other (real) sound sources. Any stretching that does occur will be due to nonlinearities in resonant air columns mounted about the reed.

Thus, in using these models, the maker must first decide what overtone to design for, and this decision will often be linked to space requirements within the instrument. For instance, the fundamental of a low note may require an unduly large geometry, but the geometry that resonates with the first overtone would be considerably smaller. Thus, for certain reeds, one model designed for the fundamental may be practical, and for other reeds, a different model designed for the first overtone may be more appropriate. The hope is that such a patchwork application of models and designs can provide chambers that span the entire range of a given instrument. When model calculations result in a promising design, a prototype should be built, and hopefully, minor tweaking can achieve a final result.

For the desired effects, it’s not sufficient to provide a reed with only a properly tuned resonator. The resonator (including tubes) must also be large enough. The air associated with the resonator must have sufficient mass so that the energy of its vibration can influence the overall sound. For instance, a quarter wave tube is, in principle, a fine resonator, though its diameter must be sufficiently large so that it can influence the overall sound level.

Helmholtz resonators:
For the simple resonator, in which all significant dimensions are much less than the wavelength of concern, the resonant frequency is given by
f = (c/2/pi)*sqrt(A/V/(t + k*d)),
where c is the speed of sound, pi = 3.14, A the area of the aperture (pad hole), t the thickness of the reed plate (that is pierced by the aperture), d the diameter of the aperture, k a number in the approximate range 0.8 to 1.2, with the higher values chosen if the pad remains within a distance d of the hole upon opening (pads that remain close to the hole will decrease the resonator pitch.), and V the volume of the cavity = L*w*h, where w is cavity width, and h is cavity height. As I mentioned in a previous post, the term k*d is an “end correction” due to the mass of air vibrating in the vicinity of the opening.

From a practical point of view, L and w will often be related to the reed plate, assuming that one side of the cavity will be comprised of the reed plate itself. The quantities d and t can be somewhat independently chosen, or varied, and thus, the above expression will serve to calculate h, for given f.

It’s expected that this model will apply to some range of reed pitches, and in applying this model, the designer must always check the basic assumption associated with the Simple Helmholtz Resonator; i.e., that x/lamda << 1, where x is every characteristic length comprising the resonator.

At the lower frequency end of this range, designing for the fundamental may result in theoretical dimensions (values for x) that are too large to be accommodated inside the instrument. One then moves the design frequency to twice the fundamental (first overtone), which will result in a ½ scale resonator, as compared to the first design. If these dimensions are also too large, one must then go to the second overtone, and so on. Important here is that, always, x/lamba must be << 1 for the above equation to be valid. One can of course stretch this criterion, realizing simply that resonance can still be achieved, though the above expression for resonant frequency becomes less accurate. Furthermore, there is a question on how desirable it would be to amplify an overtone of the musical tone. Would this tend to shift its presence out of its proper octave, as perceived by the listener?
If it turns out that moving to higher design frequencies results in a violation of x/lambda <<1, without a solution to be found, then the simple resonator model becomes inapplicable, and more complicated calculations are required, should one still desire a Helmholtz geometry design.

For these latter calculations, one might consult “The Physics of Musical Instruments,” Fletcher and Rossing, Springer, pgs. 227 – 232. The calculations suggested in the reference allow resonator dimensions to be comparable to the wavelength in the “long” direction, but still require the transverse dimensions of the resonator to be much less than the wavelength. With these more complicated calculations involving wavelength effects, there then arises the possibility of overtones emanating from the Helmholtz geometry, which, in truth, is no longer functioning as the classical resonator.

I proceeded with the above approach and have come up with some interesting results, which are presented in table form here. But before presenting those results, I briefly describe the quarter wave and half wave models, which can perhaps be useful for the very highest concertina pitches.


Quarter wave and half wave tubes:
A tube the length one-quarter wavelength, with one end open and the other end closed, is a compact resonator. In theory, when the tip of the reed is placed near either the open end of the tube or inside the tube, near the closed end, the fundamental and odd number overtones will be in resonance with the air in the tube. With the reed plate hole placed at the open end of the tube, we have a candidate for a resonant cavity. In calculating dimensions, one should allow for an “end correction,” similar to that mentioned in reference to Helmholtz geometries. Thus
L + t + kd = lambda/4,
where L is the cavity length, t the concertina reed mounting plate, d the diameter of the air hole, and k is a number from between about 0.4 and 0.8, depending how close the lever pad remains to the hole.
A tube of length one-half wavelength, with both ends open can also perhaps serve as a useful model. Perhaps the most practical way to incorporate half wave tubes would be to make the cavity length equal to one whole wavelength and mount the reed along one side, with the free tip of the reed approximately centered from the two open ends. With this arrangement, there must be two air holes and two key pads that simultaneously close and open these holes. Additional lever pads may unduly complicate instrument design, but I present this concept here more or less for completeness. Thus,
2*(L + t + kd) = lambda
For both quarter wave and half wave tubes, the model is applicable for length to tube diameters much larger than unity.

Sample calculations and results
Sample calculations are presented in the table provided. The reed plate widths and lengths and pitches are taken from actual reeds. I don’t have English-style concertina reeds before me, so I’m for the moment restricted to the measurements given, which are for accordion reeds.


speed of sound 1100 fps = 13200 ips
width 0.687 in

Note -freq -rp ln -wvlth -x -w / 4 -w / 2 ---d-- ---t-- ---L-- ---h-- ------Solution

A2 220.00 2.12 60.00 6.00 15.00 30.00 0.30 0.38 2.12 6.56
A2 880.00 2.12 15.00 1.50 3.75 7.50 0.30 0.38 2.12 0.41 -----Hlmhtz, 2nd overtone


A4 440.00 1.60 30.00 3.00 7.50 15.00 0.30 0.38 1.60 2.17
A4 880.00 1.60 15.00 1.50 3.75 7.50 0.30 0.38 1.60 0.54 -----Hlmhtz, 1st overtone

E5 659.00 1.50 20.03 2.00 5.01 10.02 0.25 0.38 2.00 0.58 -----Hlmhtz, fundamental

A5 880.00 1.31 15.00 1.50 3.75 7.50 0.50 0.25 1.50 1.45
A5 880.00 1.31 15.00 1.50 3.75 7.50 0.30 0.25 1.50 0.71
A5 880.00 1.31 15.00 1.50 3.75 7.50 0.50 0.38 1.50 1.24
A5 880.00 1.31 15.00 1.50 3.75 7.50 0.30 0.38 1.50 0.58 -----Hlmhtz, fundamental

F6 1397.00 1.12 9.45 0.94 2.36 4.72 0.30 0.38 1.12 0.31 -----Hlmhtz, fundamental

D7 2349.00 0.88 5.62 0.56 1.40 2.81 0.30 0.38 0.88 0.14 -----Hlmhtz, fundamental
D7 2349.00 0.88 5.62 ----- 1.40 2.81 0.25 0.25 0.95 ----- -----quarter wave tube

A7 3520.00 0.81 3.75 0.38 0.94 1.88 0.30 0.38 0.81 0.07 -----Hlmhtz, fundamental
A7 3520.00 0.81 3.75 ---- 0.94 1.88 0.25 0.25 0.49 ----- -----quarter wave tube
A7 3520.00 0.81 3.75 ---- 0.94 1.88 0.25 0.25 2.85 ----- -----2 half wave tubes



The table doesn't come out too well, but I think the columns are lined up reasonably well. If you can look carefully, the top column headings lists the musical note, its frequency, the reed plate length, the wavelength, the maximum size for Helmholtz geometry dimensions, x, for the simple Helmholtz model to apply, the quarter wavelength, half wavelength, aperture diameter, aperture (or concertina reed mounting plate) thickness, cavity length, cavity height, and the kind of solution arrived at.

It may be instructive to first look at the calculations for note A5. Here the diameter and aperture thickness were modified in order to obtain a reasonable cavity height, which came out to 0.58 inch. Notice the large affect of hole diameter. Is the final hole diameter (3/8 inch) reasonable? Would this allow sufficient sound to escape? Of course, with resonance, much more sound would come out of a 3/8 inch hole than a 1/2 inch hole. Moving upward, note E5 also appears suitable to the Helmholtz model, for the fundamental, though note A4 requires a first overtone target and note A2 requires a second overtone target. Proceeding downward, note F6 appears suitable to the Helmholtz model, for the fundamental, though higher pitches produce conflicts with this model. For note D7, the cavity length is becoming significant in comparison to the wavelength (larger than x). Note however, that this doesn’t mean there won’t be resonance, but only that the calculation becomes less accurate, and perhaps more experimenting would be required. A quarter wave model is also applied to note D7, producing a reasonable value for cavity length. Note however that the cavity width (0.69) is significant with respect to the cavity length, tending to reduce the accuracy of one-dimensional flow inside the tube. Situations like this can be improved by putting a partition down the center of the cavity, thereby halving the effective width of the tube. With note A7, neither the Helmholtz or quarter wave models apply. The reed plate length is larger than x, and the quarter wave cavity length is shorter than the reed plate length. Of course, alternate reed mountings could correct this issue, and a double half wave tube also appears workable, though with additional cautionary notes with regard to one-dimensional flow.

From the above calculation, I think one can see that reasonably sized geometries can be designed for resonant cavities in concertinas, using different models for the entire pitch range of the instrument. This is a much more optimistic outlook from my previous posts. Furthermore, the simple Helmholtz model can apparently be applied over most of the pitch range of the instrument - provided of course that higher overtone targets produce aesthetically pleasing results. In light of this, I'm curious whether other builders have tried to incorporate these concepts, and if not, why not, for the results seem workable. If we look at the primary result of the above table; namely, the values for h, the height of the cavity, some of these height are perhaps larger than what you find in existing instruments, though, I'd guess they could be accommodated because of the rewards offered by tuned cavities. In building the table, I required that all reasonable values for h be a maximum of about 0.6 inch. How does this sit with actual concertina builders? Richard?

In conclusion, there appears to be at least theoretical grounds for successfully incorporating resonant cavities into concertinas. Of course, the builder would have to build models and verify these results, and it's expected that these theoretical results can only be starting points for these experiments. My hopes are, however, that these results are not far off, and also that resonant cavities can be as rewarding as I'm assuming.

Best regards,
Tom
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Edited by ttonon, 19 September 2003 - 10:39 AM.


#2 ttonon

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Posted 17 September 2003 - 04:10 PM

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Edited by ttonon, 17 September 2003 - 08:42 PM.


#3 goran rahm

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Posted 18 September 2003 - 05:00 AM

Tom,
Thanks again for your indefatigable energy to substantiate this!! Many years ago I made the same calculations and tried to applicate it on some concertinas without any positive results supporting the hypothesis of a resonance based chamber design and as I have said the spectrograms did not give any hints to support it either....
Like I said however ....further and better lab studies are welcome but in my eyes we lack so far support for the presence of *significant resonance effects* having been tried out in the concertinas. Accidental effects of the kind may occur but so what...they would likely just cause unwished irregularities.

#4 GBlake

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Posted 18 September 2003 - 09:53 PM

Tom: Regarding your presentation on the Helmholtz resonance formula, you indicated that k is in the range of 0.8 to 1.2 "with the higher values chosen if the pad remains within a distance d of the hole upon opening (pads that remain close to the hole will increase resonator pitch)." Couple of things:

- do you have a reference for the k values? The Fletcher and Rossing text, perhaps? I've only been able to find k for the condition of a free and clear exit of air from the opening.

- wouldn't the use of a higher k produce a lower resonance frequency, not higher? That is, wouldn't the chamber sound flatter if the pad stays close to the opening? Having played a few instruments, that's the effect I've seen, er, heard..Help me out here...the term k*d is in the denominator. If k*d increases, as it would if you picked a higher k, then f would have to decrease, not increase.

I am building a harmonium with resonance chambers for all reeds...but not necessarily Helmholtz chambers across the board...I'm intrigued by your quarter and half-wave tubes.....

On the use of an overtone octave to size the resonator chamber, your question ""would this tend to shift its presence out of its proper octave, as perceived by the listener?" I'd say "no" because I found Rayleigh's description of the effect of consonant tone so convincing, along with descriptions of several experiments.....and from my experience playing various instruments and singing in small and large groups....the ear hears the lower tone (an octave multiple away) as strengthened and the timbre is rounded when the octave is sounded....my return question is whether this perception of the ear can be measured, not just heard?

Earlier today, I offered a response to some of your recent comments but that post seems to be lost in Hurricane Isabel.....will re-post if it's truly vanished.

Note that CBH harmonicas (the concert chromatic) use tiny resonance chambers all the way up to C7 or C8....chambers are molded in Delrin, 1/1000" tolerance.

Gene

#5 goran rahm

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Posted 19 September 2003 - 02:12 AM

Gene,
Of course you can design "resonance chambers" according to the theoretical descriptions mentioned here but when you get into dimensions and frequences usually regarded as being beyond the human audible range you will get into certain diffculties to objectivize and evaluate the results..!
Even if your subjective impression is 'positive' you will remain on quagmire I'm afraid....but Good luck...with a harmonium however you may have access to dimensions large enough to actually contain long enough chambers and the idea itself surely is very tempting. To guid you with experimenting I suggest you use some of the free software available doing Fourier diagrams for you. But....
Concerning "resonance chambers" in Wheatstone's concertina I suggest you dispose of this as a myth unless something substantial pops up....(but I doubt that....)
Goran

#6 GBlake

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Posted 19 September 2003 - 08:15 AM

Richard Morse: Regarding air travel path, thanks for the insight. Bazin, a noted experimenter with reeds from the mid-1800s (lived in Canton, MA, built the first portable harmonium in the U.S. based on an early French accordion) was perhaps the first to note that reeds sounded better when the wind exited at the heel or rivet end.....Wheatstone concertinas have the pad opening at the rivet end of the reed. I have seen accordion reeds mounted with air exiting the tongue end and the reed end.

Tom: I read your 9/8 post regarding chambers and tube resonators. The dimensions you derived are way too small, I believe. Help me understand. You mention "At 1,000 hz, the wavelength is 1.1". A paragraph above you mention "Middle "C" (262 hz) has a quarter wavelength of about one inch." Middle C has a wavelength of about 4 feet, not 4 inches. Wavelength = speed of sound (34,300 cm/sec at 68 degrees F) divided by frequency. 34,300/262 = 130.9 cm = 51.5 inches. At 1,000 hz, wavelength is 34.2 cm or 13.4 inches, not 1.1 inches. You're one order of magnitude too low in your dimensions? I assume you are referring to the wavelength of the frequency for which you're trying to achieve resonance.

#7 ttonon

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Posted 19 September 2003 - 10:55 AM

- do you have a reference for the k values?  The Fletcher and Rossing text, perhaps? I've only been able to find k for the condition of a free and clear exit of air from the opening.

- wouldn't the use of a higher k produce a lower resonance frequency, not higher?  That is, wouldn't the chamber sound flatter if the pad stays close to the opening?  Having played a few instruments, that's the effect I've seen, er, heard..Help me out here...the term k*d is in the denominator.  If k*d increases, as it would if you picked a higher k, then f would have to decrease, not increase.

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

You are also correct in stating that higher k values will lower the resonant frequency. This was a blunder on my part, and I have edited the correction in my post. Thank you for spotting it.

Best regards,
Tom

#8 ttonon

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Posted 19 September 2003 - 11:06 AM

Tom: I read your 9/8 post regarding chambers and tube resonators. The dimensions you derived are way too small, I believe.  Help me understand.  You mention "At 1,000 hz, the wavelength is 1.1". A paragraph above you mention "Middle "C" (262 hz) has a quarter wavelength of about one inch."  Middle C has a wavelength of about 4 feet, not 4 inches.  Wavelength = speed of sound (34,300 cm/sec at 68 degrees F) divided by frequency.  34,300/262 = 130.9 cm = 51.5 inches.  At 1,000 hz, wavelength is 34.2 cm or 13.4 inches, not 1.1 inches.  You're one order of magnitude too low in your dimensions?  I assume you are referring to the wavelength of the frequency for which you're trying to achieve resonance.

Very good Gene. After I did the more careful analysis that I posted with the table in this thread, I wondered why I was so pessimistic about the use of resonators in my 9/8 post. Thinking on this and knowing my own tendencies for gross errors involving details, I suspected I failed to convert from feet to inches. But I haven't had time to go back over that post and verify this. Then you come along and spot the error. Thanks again for pointing out my errors.

So then, assuming I made no similar blunders with the post in this thread, it appears that resonant cavities in concertinas can be realizable, along with relatively simple design models to choose from. The table in this thread was generated with a spread sheet, and I hope, is error free, but I welcome you or others to verify that.

Best regards,
Tom
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#9 ttonon

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Posted 19 September 2003 - 11:21 AM

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Edited by ttonon, 19 September 2003 - 12:53 PM.


#10 ttonon

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Posted 19 September 2003 - 12:52 PM

On the use of an overtone octave to size the resonator chamber, your question ""would this tend to shift its presence out of its proper octave, as perceived by the listener?"  I'd say "no" because I found Rayleigh's description of the effect of consonant tone so convincing, along with descriptions of several experiments.....and from my experience playing various instruments and singing in small and large groups....the ear hears the lower tone (an octave multiple away) as strengthened and the timbre is rounded when the octave is sounded....my return question is whether this perception of the ear can be measured, not just heard? 

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

Best regards,
Tom
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#11 GBlake

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Posted 19 September 2003 - 04:15 PM

Dear Tom:

Golly, hope you don't think I'm searching for errors in your stuff....I've been working on this issue for about two years, pretty much in solitude, and now that I've found someone else who's interested I don't want to dump on you...I just wanted to make sure I wasn't missing something in applying the science.

I ran over to Boston Public Library at lunch and got copies of the relevant pages you mentioned in the Fletcher reference along with some of the other pages...that stuff is really thick....and yeah, it actually says (way back on page 600-something) that blockage of the outlet hole will flatten the resonance of the chamber a bit....but only if the pad is less than 1 radius away, not 1 diam.....I don't know about the action on a concertina but harmonium action gives about 1/4" of lift, so there's possibly a slight effect.

I'm searching for data used to build the Vocalion Reed Organ (in Worcester, MA) which made the best use of different types of chambers for different timbre effects, specially designed reed cells if you will....not Helmholtz resonators.

Goran, I would be interested in your thoughts on why there are these differently sized chambers in Wheatstone concertinas and why, if their sizes correspond to Helmholtz' resonance formula (you agree?), that they wouldn't be resonance chambers.....Wheatstone, as in "one of the great minds of the 19th century"...he was wrong?

#12 GBlake

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Posted 22 September 2003 - 11:41 AM

Tom:

If you have access to Rayleigh's text, check out pages 444-445...Mayer's many experiments with consonant tones through several octaves of separation (up to 4) and the inevitable finding of multiple observers and experiments that even a much more intense higher octave sound only serves to reinforce the lower tone, not only making it louder by improving its quality. Using tuning forks sounded together, he even was able to get people to hear the lower toned fork after it had ceased to vibrate. While this effect is not possible in a reed chamber, it shows the ability to reinforce a reed's fundamental tone by augmenting the intensity of a higher sounding octave, a key in resonant chamber design.

#13 ttonon

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Posted 22 September 2003 - 12:29 PM

I'm searching for data used to build the Vocalion Reed Organ (in Worcester, MA) which made the best use of different types of chambers for different timbre effects, specially designed reed cells if you will....not Helmholtz resonators.

Hi Gene,

What is a Vocalion Reed Organ? Is it different from standard reed organs? Could you explain a little more detail about these "specially designed reed cells"? In what way are they special?

Also, in another post, you described an interest in harmoniums. Have you experimented with resonant chambers in such instruments? Can you describe how the reeds are mounted? Are they laid flat down against a "reed plate" or are they mounted in upright "reed blocks," as in many accordions?


Best regards,
Tom
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#14 goran rahm

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Posted 23 September 2003 - 02:51 AM

Gene:"Goran, I would be interested in your thoughts on why there are these differently sized chambers in Wheatstone concertinas and why, if their sizes correspond to Helmholtz' resonance formula (you agree?), that they wouldn't be resonance chambers.....Wheatstone, as in "one of the great minds of the 19th century"...he was wrong? "

Goran:
I said elsewhere but again:
a) The Wheatstone 1844 patented concertina had reed chambers of (basically)equal size for all notes and of course these chambers do not at all correspond to any frequence progression
B) Some time early (according to Neil Wayne sometimes even in the 1830s) some partitions appeared on some of the top notes and this routine grew 'downwards' although it varies a lot with models and makers.
Seemingly in the 1880-90s it became common to add partitions for all chambers by makers and by repairers and players. The later two usually by adding cork parts as close to the reed ends as possible and without any regard of frequence relations...do check a greater sample of instruments...
c) The rational reason to use the partitions is what it looks like..to reduce the volume of the chambers to facilitate the onset and increase 'response'
Take the partitions away and check the effect ...and also the effect on tone!
d) Sizes of these 'reduced' reed chambers may by accident (like you may have found) correspond to certain frequence relations but NOT consequently ( do NOT waste your time trying to proove something else...you are just fooling yourself!..)
e) No one so far has come up with any original documents saying that the reed chambers were intended as "resonance chambers" ....at least not C Wheatstone himself so there is no reason to mean he was "wrong"....someone else has been 'wrong'.....
f) Sometimes it is referred to experiments by CW to 'proove' the hypothesis of "resonance chambers". Yes, such experiments have been documented and for instance the 1844 patent papers (page 9 fig 18 the "eight improvement") show application of resonance pipes for harmoniums and similar instruments.

Conclusion: the hearsay about reed chambers of the Wheatstone concertina being designed as "resonance chambers" is a myth founded on misinterpretations of the construction and coloured by some historic details

Goran

#15 ttonon

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Posted 23 September 2003 - 08:42 AM

Conclusion: the hearsay about reed chambers of the Wheatstone concertina being designed as "resonance chambers" is a myth founded on misinterpretations of the construction and coloured by some historic details

Hi Goran,

There are two issues here: 1) Whether resonant cavities have been built into concertinas, and 2) Whether there is theoretical basis for their successful operation, with reasonably sized components.

It seems that you have delved extensively into (1), concluding that resonant cavities have never been incorporated into the entire pitch range of an instrument. I have not investigated this topic, so for now, I can let your statements stand.

Concerning (2), the table I present at the beginning of this thread seems to provide theoretical bases for a resonant approach to cavity design. Do you agree? Do the predicted dimensions in the table appear to you practical?

I realize that, after I first posted this table, you took it as proof of your position that resonant cavities are not provided in existing instruments. I believe your conclusion was influenced by my 9/8 post, which indicates some pessimism on the possibilities for resonant cavity design. As Gene has pointed out, my calculations in the 9/8 post contained an error, and I don't believe the table of this thread contains that error. This table, then, appears to me to support a resonant cavity approach.

In any event, I'm curious about any comment you might have on the table in this thread.

Best regards,
Tom
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#16 ttonon

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Posted 23 September 2003 - 01:16 PM

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Edited by ttonon, 23 September 2003 - 01:18 PM.


#17 GBlake

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Posted 23 September 2003 - 02:28 PM

Dear Goran, thanks for the reply....I came in late on your line of thinking.

Tom, most American reed organs used narrow brass reeds where the reed tongue had an inverse U arch above the plate and then a bend back up right at the tip of the tongue, along with a twist.....the voicing changed the overtone structure of the vibrating reed (along with wasting a lot of air) and produced sounds similar to a string, flute or horn. Each reed sat in a cell that was designed to further augment the timbre. Recent research by Coe, through spectrograph analysis and a process of moving reeds into different reed cells in the same organ, may have shown that the timbre was mostly due to reed voicing, not the cell design. The Vocalion, on the other hand, did not opt for this dramatic reed voicing and instead used very wide reeds with common voicing, but situated in various shaped chambers to achieve the desired timbre. The Vocalion was based on ideas for reeds and resonant chambers developed through the research of Hermann Smith, a British fellow (see Helmholtz' Sensation of Tones).

Re. your question, the reeds in a harmonium (not all, but the better ones) are mounted on a reed pan laid out in a pressurized stop chamber beneath the keys, similar to a Wheatstone concertina....not mounted in reed blocks as in the accordion. Below the reed pan is a little chamber for each reed, scaled to the size of the reed. A pad or valve lies against the aperture in the bottom of each chamber. When a key is pressed, the valve is opened and the air in the stop chamber rushes past the reed, through the chamber below the reed and out into the environment, or into a tone chamber and then into the environment. The tone chamber is about 1" deep, 6-8" tall and the width of the instrument, with escape holes....this acts like the accordion casotto.

Tom, re. the end correction for a Helmholz chamber where the outlet hole is simply a hole in the chamber wall, as for Wheatstone concertinas, it looks like the correction should be 2 x 0.82R (per Rayleigh, or about 0.8D as you mentioned). Helmholtz said the minimum value would be about 2 x 0.785R, close enough to 0.8D. The increase in effective length due to an opened key pad being only R away from the aperture is, per Fletcher, slight. Note that in the harmonium, the presence of valves or pads (for adjacent notes) immediately on either side of the chamber aperture would also increase the correction factor (in theory). Hard to see where it could increase by 25%+, to 1 or 1.2D. When I conduct my experiments (now making a test bellows), I'll post the findings.

I wondered why cork (see Goran's last post) would be present in the chambers of some Wheatstone concertinas, it's not known for its tone qualities....consider this.....one way to "tune" the chamber volume to a consonant octave tone of the vibrating reed would be to use a length correction factor that's obviously too high, say 1.0D. The V determined by the formula would then, in theory, be too small and the resonant frequency would be too high or sharp. By decreasing V, such as by shaving down a cork piece that's located inside the chamber, you could sharpen the chamber to produce perfect resonance. Given that numerous tunings were used in making Wheatstone concertinas, there would have been a need for a way to tune the chambers to the selected reed tuning. Cork.

#18 goran rahm

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Posted 24 September 2003 - 03:47 PM

QUOTE (goran rahm @ Sep 23 2003, 02:51 AM)
Conclusion: the hearsay about reed chambers of the Wheatstone concertina being designed as "resonance chambers" is a myth founded on misinterpretations of the construction and coloured by some historic details



Hi Goran,

There are two issues here: 1) Whether resonant cavities have been built into concertinas, and 2) Whether there is theoretical basis for their successful operation, with reasonably sized components.

It seems that you have delved extensively into (1), concluding that resonant cavities have never been incorporated into the entire pitch range of an instrument. I have not investigated this topic, so for now, I can let your statements stand.

Goran re now:As I have said, we lack reliable documentation supporting the hypothesis and since we also lack lab support for it I mean we better skip the speculation OR try to objectivize an assumed effect


Tom:Concerning (2), the table I present at the beginning of this thread seems to provide theoretical bases for a resonant approach to cavity design. Do you agree?
Do the predicted dimensions in the table appear to you practical?

Goran re now: I have not scrutinized every detail, I just checked you have basically made the same calculations I did and the problem remains that you arrive into 1) a physically 'truly' predicted resonance situation in some cases at least but there you happen to be beyond normal audible range and 2) the possible assumed reinforcement fo the *perceived* (not physical) fundamental not stays being another hypothesis *maybe* possible to evaluate by investigating a listener population but still hardly possible to objectivize and thus to be not being very meaningful to waste time on....



om:I realize that, after I first posted this table, you took it as proof of your position that resonant cavities are not provided in existing instruments. I believe your conclusion was influenced by my 9/8 post, which indicates some pessimism on the possibilities for resonant cavity design. As Gene has pointed out, my calculations in the 9/8 post contained an error, and I don't believe the table of this thread contains that error. This table, then, appears to me to support a resonant cavity approach.

Goran: Seems not to change much still I'm afraid....The factual measures of the concertina chambers do not present a regular and consequent progression anyway to correspond to a meaningful initial attempt by the maker to produce an instrument 'truly' based on the said acoustic intentions. Compare other instruments were this *have* been practised, the harmoniums spoken of for example. In fact the Wheatstone "eigth improvement" in the 1844 patent papers is a quite interesting example. Has absolutely nothing with his *concertina* to do however!
It would be absolutely absurd ( I would say stupid..) using a sixsided box for the purpose by the way...The sizes of the reed chambers in Wheatstones concertina are purely related to the accidental box sizes and reed sizes.

Goran




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