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Bellows pressure and musical pitch


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The pendulum has swung back an I'm resuming my theoretical interest in how free reeds work and it would help me to decide on a physical model if I knew how the musical pitch varies with bellows pressure, if at all. 

I ask this question mainly to the makers, but also to other enthusiasts who do their own tuning and tinkering in a serious way.  But please report what you are sure of.  If you're not sure, that's perhaps evidence that pitch variations are very small. 

Ideally, it would be nice to have quantitative data, such as cents pitch change with so much change in pressure, inches or cm in water column.  But even naked ear observations can be helpful, if they can be stated with confidence. 

It would also help in the ideal case if you could supply the magnitude of the bellows pressure along with the pitch information.  What minimum and maximum values for bellows pressure do you subject your reeds to?  What range of bellows pressure do you expect in all playing situations? 

I've read that at the lowest pressures, pitch may first decrease with increasing pressure, then might increase with pressure at the highest pressure levels.  Has anyone observed this?

 

In the near future, I hope to do my own experiments on this topic, and afterwards, I'll present the results.

I think that the pressure/pitch behavior is most fundamental to the free reed, and so reliable characterization in practice would be most appreciated. 

Best regards,
Tom
www.bluesbox.biz

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It varies and it varies enough that this effect is used for pitch bending by overblowing reeds on pull (yes, scale of effect depends on air direction relative to chamber) - lowest reeds (F2-F3) can be easily bend by -25 cents this way. With those lowest notes this effect is also heavily influenced by chamber length. In short chambers (reedplate length) this is so pronounced it is actually very difficult to play at stable pitch at all, while with 250% length chambers pitch is stable in the whole normal bellows pressure range, but still can be bent -5 cents when overblown. You can also affect this effect by changing padhole aperture, with smal holes being more bendable and large holes more stable. So your model must take all those parameters into account. Same effect is used by harmonica players, though they also modify chamber size and aperture on the fly.

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I have similar experience to Lukasz, though the longest reed I make is G2.  I have also found reeds around C6 and above can actually go sharp at the higher practical pressures.  Here, I haven’t seen more than +5 cents.  Lower notes are more affected, and quite audibly so, enough to be made part of technique.  Here, I do find that press works too  like draw, but you have to mean it.   
When tuning, I find it important to keep pressure constant since it easily affects reeds in the 3-5 cent range at normal playing pressure
The big thing Lukasz mentions is the effect of chamber length as its proportion to reed length varies at different pitches, and the pad hole size in conjunction.  On a C/G Anglo, I use 4 different hole sizes. ( 5 on a G/D ) because not only can a too small pad hole flatten the note, but it also causes a tone change where higher harmonics are reduced.  Wheatstone Linotas I’ve seen have relatively small pad holes and the tone change from exertion while playing is something I’ve heard Noel Hill use for effect.  
there seems to be a best size for different pitches, though it probably interacts with chamber length, so may not be transferable from one chamber layout to a different one.  I originally used one size for everything, but found by progressively reducing the diameter, I reached a point where smaller would actually make the note sound clearer, but still be large enough to prevent the tone change  at high pressures.   I used that break point to size all the holes.  The Wheatstone Duet I used to own had equivalent pad hole scaling (and chamber length scaling ).

   I do not understand how chambers and tone holes work, but a low reed un an undersized chamber may not operate at all.  My tuning block has a series of separate chambers sized for pitch ranges.  I switch chambers when a reed starts to be balky or not speak well at a particular chamber.  The effect of the chambers / pad holes is large, and trying to tune a reed in an environment where it is clearly getting damped compared to a reed that goes well with the chamber can easily mean 10 cents off what it should be.    I use little rubber sheets to cover the tuning ports not in use, and can have a balky reed sound good again by partially opening an unused port.  Since I tune at a constant pressure, I am guessing that opening the free port, changes something in the acoustics.  The chambers all share a common plenum and all have the larger pad holes emptying into it.

one thing I wonder about is the way air moves into or out of pad holes.  Air going into a hole looks like water going down a large drain, coming in from the sides as much as above, while air leaving a hole is more jet like.

the proximity of the pad to the hole may cause different effects on the press vs the draw because of the relative obstruction of airflow.

one last thing, poorly centered reeds are much more vulnerable to flattening audibly as pressure rises, as is a weak (thin ) reed for the given pitch.

Sorry not to have a lot of hard data, but given how interactive things seem, it would be easy to misattribute any particular effect.  You are going to have to build your own setup where you have more control than I do, where I try to find what gets the results I want without trying to figure out why.  
Best Wishes,

‘Dana

 

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I concur with what Łukasz and Dana have already said. The other thing is the effect of scaling - a shorter than usual bass reed (i.e. more heavily weighted at the tip and/or very thin near the clamp to pull it down to the required pitch) will bend more easily than a longer one. This was often done to squeeze in more buttons or a lower range without increasing the overall size of the box. Some vintage instruments are quite tricky to tune because you have to aim for the bendy bass reeds coming into tune with the rest of the instrument at the player's normal volume level (which varies with playing style). If you then play at a significantly lower pressure the bass reeds go sharper than the treble, and if you play at a higher pressure the bass reeds go flatter than the treble.

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Well IMHO 

 

Minimum bellows pressure would be a slow waltz played in the lounge whilst your wife reads the paper next to you, and maximum pressure would be a morris team.

 

When playing at morris team pressure DONT SPANK IT TOO HARD Y'hear? If you do that it can go flat, especially the low notes. Its important to file the reeds not too thick and not too thin, its sort of a matter of opinion what is too thick and too thin.

 

Practice and get a good understanding of the instruments dynamics. Then practice more, THEN MORE!!!! The mark of a true musician is to practice.... eeeeven more. A good musician can tell when a reed has the right level of pitch deflection, basically you have to be a player to make reeds I reckon.

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Greetings to all,

 

Thanks for the comments.  I was hoping for more reports of detail - even quantitative measurements observed during tuning.  Most of us have meters that can measure cents changes in musical notes, and perhaps some of the more curious have sometimes measured the bellows pressure during tuning.  I understand that the needs of the maker are far more practical.  But these other qualitative reports are also useful, and I'll glean from them as best I can. 

Many of you have mentioned the geometry of the cavity parameters, and that's also useful information.  But let me explain here the fact that my present theoretical model, based on a fluid mechanical approach, does not include a cavity.  This is only a first phase study, which basically takes the reed, mounts it in a wall that separates the static pressure on each side.  The air blows through the reed and passes essentially into an infinite region with uniform pressure.  Once I'm confident that the physical model for the basic tongue vibration works, I can then couple it to a resonator, or a cavity, using the appropriate physical principles.  

I'm under the impression (or hope) that not all cavity geometries affect very much the basic vibration of the reed tongue.  (Some cavities have profound effect, as Dana describes.)  This vibration is completely different than the acoustic sound field we hear coming from it as a source for that sound.  The pressure oscillations, of the order of the bellows pressure difference are orders of magnitude larger than those of the acoustic sound far field.  I think it's reasonable to suppose that some cavity geometries may not affect tongue vibration very much.  For instance, comments here suggest that only certain geometric feature can have an effect, but only in the most extreme cases.  Here, I'm interested in the less extreme cases, hoping that it describes the behavior of the isolated reed.

Some of the reporting here is convoluted with the authors' intuitive explanations of why these geometries can produce what they hear.  Some of these underlying explanations are pretty good, while others are erroneous, or at least misleading, missing some key physical mechanisms.  For instance, no one mentioned the effects of the volume of the cavity, in addition to its length and the port opening.  But the volume also plays a significant acoustic role, and together with the port, forms a Helmholtz resonator which can have significant influence on both tongue vibration and the sound field.  Again, I say "can have," because it's not always the case, at least on tongue vibration.  The cavity length itself has an important role at the very high frequencies, when it can form the sizes of quarter wave tubes.  There are some very practical effects such as what Dana mentions, with the formation of jet-like behavior during draw, and these are very difficult to theoretically model.  

But I cannot get into a detailed discussion on cavity effects here, other than point readers to an article I wrote for the International Concertina Association, in their Proceedings (PICA) Dec 2, 2009, titled, "Reed Cavity Design and Resonance": https://concertina.org/2009/12/05/reed-cavity-design-and-resonance/?doing_wp_cron=1630012537.5247180461883544921875

Comments on the postings here: 

Lukasz, much of what you say agrees with my own experience, though for midrange and high range reeds, I'd not think you could bring down the pitch 5 cents from increased bellows pressure.  I must explore this more.  Can you please give me an idea of a quantitative measure of the pressure needed to "overblow" a reed?  What pressure magnitudes do you regard as "normal" playing pressures?

Dana, your comment that reeds around C6 and above can go sharp at the higher practical pressures is useful.  Again, can you give me any quantitative pressure info?  What would be "higher practical pressures?"

In fact, I'd be very curious to know the experience of people here with the absolute minimum pressure it takes to start most reeds.  I agree that quiescent standoff distance is most important, but let's say for optimum standoff and other geometry, what are those pressures, which probably varies with the extremes of reed pitch.  

Alex, I think you make a good point about weighted reed tongues.  Such issues and many others are exceedingly difficult to theoretically analyze.   

For those interested, I present here a graph of a plot I made from this Phase I theory, showing vibration frequency variations in cents vs bellows pressure.  These solutions are for the case when the tongue appears below the reed plate, and thus the lowest pressures are higher than the minimum starting pressures, when the tongue remains in the slot.  We can deal with the latter case later.  The reference frequency is the calculated frequency treating the tongue as a cantilever beam. This calculated frequency is a bit higher than the frequency that occurs in practice, because of the effects of air friction and inertia.  Thus in the second graph, we'd need to lower the natural frequency line a few cents.  The model does account for air friction, aerodynamic drag and air inertia.  

These results seem consistent with some of the reporting here.  The increase in frequency at the higher bellows pressure may also be realistic.

Again, thanks and more as of and when.

Best regards,
Tom
www.bluesbox.biz

Free Reed I Amplitude.png

Free Reed I Avg Position.png

Free Reed I Cents.png

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3 hours ago, ttonon said:

Many of you have mentioned the geometry of the cavity parameters, and that's also useful information.  But let me explain here the fact that my present theoretical model, based on a fluid mechanical approach, does not include a cavity.  This is only a first phase study, which basically takes the reed, mounts it in a wall that separates the static pressure on each side.  The air blows through the reed and passes essentially into an infinite region with uniform pressure.  Once I'm confident that the physical model for the basic tongue vibration works, I can then couple it to a resonator, or a cavity, using the appropriate physical principles.  

 

My current tuning bench doesn't have reed chambers like Dana's; the reed holder simply sits over a set of bellows. The reeds definitely don't perform as well in the open air as they do in the instrument, especially at the low end, below perhaps G3. Once you get down to G2 or so they won't even start in the open air - you have to pluck them, then they sound extremely quietly. If you somehow built a real instrument with no chambers I think it would perform very poorly. I'm planning to build a new tuning bench soon and intend to incorporate several chambers in a range of sizes.

 

4 hours ago, ttonon said:

In fact, I'd be very curious to know the experience of people here with the absolute minimum pressure it takes to start most reeds.  I agree that quiescent standoff distance is most important, but let's say for optimum standoff and other geometry, what are those pressures, which probably varies with the extremes of reed pitch.  

 

It depends on how well they are made and how you set them up. If I'm setting up an instrument for a gentle player, I'm typically aiming for them to start at less than 25 Pa (0.1 inches of water) on the tuning bench, though for technical reasons I find that isn't achievable at very high pitches and I have to settle for perhaps 50 Pa. Once in the instrument, the valves start to make a difference to the minimum pressure that is practically achievable because the reed you're currently trying to sound may not start until there is enough air leaking through the opposite reed to pull its valve closed. With good valves that close very easily, you can barely feel any force on the bellows before the reeds start to sound. If I'm setting up an instrument for a loud player, it's necessary to set the reeds higher or they will choke too easily, and that has the side effect of raising the minimum playing pressure - maybe to 100 Pa or more.

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Hi Alex, I presume that after the tuning bench, you measure the pitch while the reed plays in the instrument, note the difference between when on the tuning bench, put the reed back on the bench and change its pitch accordingly.  It's important to accurately use the same pressure during the bench measurement.  In my experience, the reed always sounds lower in pitch than when on the bench.  But perhaps some of the higher pitched reeds have the same pitch between bench and instrument.  Do you concur?

 

Thanks for the very valuable and interesting info on the minimum pressure for sounding.  I never would've guessed that you could go as low as 0.1 inch wc.  

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I’ve mentioned chamber length and not volume for two reasons: first, this pretty much the only variable available when working with hybrid concertinas and anyone working with physical reeds imidiately learns, that they either work poorly or don’t work at all without the chamber, thus volume. Secondly, length and volume are two separate degrees of freedom when working with most difficult reeds - lowest and highest. As Alex wrote above, below certain reed size (this varies with particular properties of reed construction) reeds don’t speak at all with chambers that are too short, (this includes setups without chambers) so you have to first increase the length to make reed speak properly and only then you work with volume to shape the tone. With highest reeds, combined volume of chamber and air canal can prevent reed from speaking at all but you obviously cannot make chambers shorter than tongue length, so you have to decrase depth instead. 

 

Lowest reeds problem is also the gratest example why simplified, reductive models aren’t neither accurate nor useful. You can’t simply disregard chamber geometry, valve properties, padhole size, air channel length and action box geometry and still get something realistic. Each of those parameters not only shape the tone or set the pitch, but influence basic reed response. For example, you can stabilise the pitch of the reed and lower starting pressure by enclosing outer box, without having to increase chamber length. You also mention Helmholz resonator, but in my experience real reeds care very little about our simplistic math. I use non-cuboid chambers of quite unorthodox geometry for lowest reeds with great success, Alex tested L shaped chambers and some bass concertinas with layered reedpans rely on air canal volume (effectively another variant of L shaped chamber) to improve reed response.

 

Regarding lowest pressure, I concur with what Alex wrote - with proper, oversized chambers my lowest reeds start basically immediately after lifting the pad under natural fully closed bellows springiness. They are responsive to the point where it is difficult to not make any sound with the pad lifted, so you can safely assume, that starting pressure in your model should aproach zero with increasing tongue length. Also, as Alex mentioned above, you have to account for reeds choking - if you apply too much pressure to stationary tongue, then instead of oscilating the reed will behave as a simple pressure valve. 

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2 hours ago, ttonon said:

Hi Alex, I presume that after the tuning bench, you measure the pitch while the reed plays in the instrument, note the difference between when on the tuning bench, put the reed back on the bench and change its pitch accordingly.  It's important to accurately use the same pressure during the bench measurement.  In my experience, the reed always sounds lower in pitch than when on the bench.  But perhaps some of the higher pitched reeds have the same pitch between bench and instrument.  Do you concur?

 

Yes, that's right. Also a stiffer valve lowers the pitch in the instrument. I don't really understand why that is, but I've observed it many times. Sometimes very high reeds have no valves, and those can be fairly close to the same pitch in or out of the box.

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Posted (edited)
1 hour ago, Łukasz Martynowicz said:

As Alex wrote above, below certain reed size (this varies with particular properties of reed construction) reeds don’t speak at all with chambers that are too short, (this includes setups without chambers) so you have to first increase the length to make reed speak properly and only then you work with volume to shape the tone. With highest reeds, combined volume of chamber and air canal can prevent reed from speaking at all but you obviously cannot make chambers shorter than tongue length, so you have to decrase depth instead. 

Lukasz, thanks for your comments, which indicate a considerable amount of experience in trying to understand the idiosyncrasies of the free reed, which I believe is among the most complicated sources for musical tone.  I think I can explain the observation you mention in your above quote by means of the following table, which is in the PICA article I mentioned above.  (If you can't take the horse to water, bring the water to the horse 😋)

 

- - - - - - - - - - - - - -

Table 1: Cavity Geometry from Resonant Acoustic Model Calculations

 

 

 

 

 

-------- Helmholtz Calculation -------

 

--- Tube Calculations ---

Note

Partial

ν

λ

Vadj

W

L

d

t

H

S max

H fixed

L-QW

L-FW

 

 

 

 

 

 

 

 

 

 

 

 

 

 

G1

1

49

277

-0.26

1.00

3.00

0.40

0.25

166

41.5

0.8

68.69

138.12

G1

9

441

30.7

-0.26

1.10

3.00

0.32

0.38

1.11

4.61

0.8

7.12

15.09

G1

11

539

25.2

-0.26

1.20

3.50

0.40

0.38

0.84

3.77

0.8

5.67

12.27

G1

15

735

18.4

-0.26

1.20

3.50

0.40

0.38

0.48

2.77

0.8

4.00

8.92

 

 

 

 

 

 

 

 

 

 

 

 

 

 

G2

1

98

138

-0.19

1.00

2.50

0.40

0.25

49.9

20.8

0.75

34.10

68.94

G2

6

588

23.1

-0.19

1.10

2.50

0.32

0.31

0.85

3.46

0.75

5.26

11.28

G2

7

686

19.8

-0.19

1.20

2.70

0.32

0.30

0.56

2.97

0.75

4.45

9.64

 

 

 

 

 

 

 

 

 

 

 

 

 

 

G3

1

196

69.2

-0.19

1.00

2.00

0.30

0.25

10.1

10.4

0.50

16.87

34.38

G3

4

784

17.3

-0.19

1.10

2.00

0.32

0.30

0.65

2.59

0.50

3.83

8.40

G3

5

980

13.8

-0.19

1.20

2.70

0.40

0.30

0.41

2.08

0.50

2.92

6.65

 

 

 

 

 

 

 

 

 

 

 

 

 

 

G4

1

392

34.6

-0.13

1.00

1.80

0.30

0.25

2.84

5.19

0.50

8.22

17.08

G4

3

1176

11.5

-0.13

1.10

1.80

0.30

0.25

0.34

1.73

0.50

2.45

5.55

G4

4

1568

8.65

-0.13

1.20

1.80

0.32

0.20

0.24

1.30

0.50

1.77

4.13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C5

1

523

25.9

-0.12

1.00

1.70

0.30

0.25

1.72

3.89

0.38

6.05

12.75

C5

3

1569

8.64

-0.12

1.10

1.70

0.32

0.20

0.27

1.30

0.38

1.77

4.13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C6

1

1046

13.0

-0.07

1.00

1.50

0.32

0.20

0.63

1.94

0.20

2.85

6.29

C6

2

2092

6.48

-0.07

1.00

1.50

0.32

0.20

0.19

0.97

0.20

1.23

3.04

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C7

1

2093

6.48

-0.08

1.00

1.25

0.32

0.18

0.24

0.97

0.15

1.25

3.05

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C8

1

4186

3.24

-0.02

0.80

1.00

0.32

0.13

0.11

0.49

0.15

0.49

1.46

Notes:

 

 

 

 

 

 

 

 

 

 

 

 

All lengths in inches

Note is nomenclature for piano keyboard, typically found in concertinas

Partial is partial number

ν is frequency of corresponding partial (Hz)

λ is wavelength of corresponding partial

Vadj is volume adjustment to orthogonal cavity structure, to account for reed volume (cubic inches)

W is orthogonal cavity width in Helmholtz model

L is orthogonal cavity length in Helmholtz model

d is aperture diameter

t is aperture length (Action Board thickness)

H is calculated orthogonal cavity height for Helmholtz resonance, Equation 2 & 3, k = 0.6

S max = 0.15λ is about maximum size of any component for Helmholtz model to remain accurate

H fixed is cavity height used for tube calculations in next two columns

L-QW is length of cavity for quarter-wave model, Equations 4 & 5, k = 0.6

L/2-FW is length of cavity for partitioned full-wave model, Equations 6 & 7, k = 0.6

BOLD numbers indicate regions on the musical scale where resonance occurs and/or where

reed choking may occur (when Partial = 1)

- - - - - - - - - - - - - - -

The notes after the table should be adequate explanation.  For the calculations in this table, I assumed what I think are typical cavity dimensions (L, W, H).  The bold numbers indicate the cavity dimensions that form resonant geometries with the reed frequencies shown.  Most often the involved resonators are Helmholtz or quarter-wave, but mostly Helmholtz.

 

Notice that as the reed frequency increases, there is a greater chance that the cavity will produce a Helmholtz frequency that is close to the reed frequency (in bold).  In these cases, the air vibration induced by the Helmholtz resonator disrupts the air oscillations that are required in the tongue's self-induced vibration.  Hence, these are areas where the reed is likely to choke.

 

For the longer reeds, the frequencies are much larger than what a Helmholtz resonator can supply, unless you consider the frequencies of the higher partials.  Since in some cases second and third partials can compete with the fundamental, there remain possibilities for choking even with these reeds.  

 

The phenomenon of choking is not new, but explanations vary.  As far as I can tell, you simply assert that the cavity length is the culprit, without any physical explanation on why that could happen.  In the light of the Helmholtz calculation, it's misleading to focus only on the length.  You say that you change the length and it does away with choking.  Why does that work?  My explanation is that when you change the length you change the cavity volume, and thus you change the natural vibration frequency of the Helmholtz resonator, moving it away from its conflict to tongue vibration.  It's very simple.

 

Many times in technology development, people come up with intuitive ideas to explain what they observe.  Then along comes a theory that explains things very well, and this theory is based on a much broader body of knowledge, adding confidence to the theory.  I think this is the case here. 

 

Despite it's complexities, the free reed is still subject to Fluid Mechanics and Acoustics, not magic.  As an acoustic source, it can couple to other acoustic sources, something that you cannot understand unless you invoke those valuable and proven physical principles.  That's why theory is so strong, when it works.  Especially very simple theories, like this one.  

 

Best wishes and stay well,

Tom

www.bluesbox.biz

 

 

 

 

 

 

 

 

 

 

 

 

 

Edited by ttonon
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Posted (edited)

Hi Alex, my guess is that the valve enables a larger body of air to vibrate with the tongue, thus causing a higher inertial load to the vibration.  It "cups" the tongue with a larger air mass, forcing more air to participate in the vibration.  In addition it adds its own mass to the vibration.  With any single parameter spring-mass vibration, larger mass results in lower natural frequency.  

 

One reason for the absence of leather valves on the high pitched reeds is to lessen the tendency to choke.  At least with accordions, when two tongues share the same cavity, the lack of a leather on the one reed provides air leakage as the other speaks.  This leakage lessens the effect of the Helmholtz vibration on the speaking reed.    

 

For my work, I sometimes need valves on all reeds and when I installed valves for the highest reeds, they tended to choke.  As I mention in my PICA article, a similar solution is to drill a small hole through the cavity wall or the reed plate.  Thus, the air vibration caused by Helmholtz is not concentrated solely on the playing reed.  In other words, leakage through the hole lessens the acoustic coupling to the cavity. 

 

Incidentally, this is another phenomenon that you cannot explain with Lukasz's "length theory." 

 

Best regards,

Tom   

Edited by ttonon
Signature, and "In addition it adds its own mass to the vibration."
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I know this table and I know Helmholz model. What I try to tell you is that you can make the reed work perfectly well with non-orthogonal cavities that do not follow this model, thus the model is overly simplistic. Another example - I’m currently trying to solve the following problem: I have two F3 reeds in the box I’m building, both cavities have exact same geometries (classic Helmholz orthogonal), one causes beating, the other does not. The problem is not reed related nor valve related, as it doesn’t follow the reed when swapped. It is also not air leak decoupling related as you imply above in similar context. What is different between those sides is position on the reedpan relative to outer border and surrounding endplate geometry. Since you seem to understand reed physics way better than I do, maybe you can point me in a proper direction here? I have encountered the same problem in the other box and have indeed thought at first that introducing cavity leak will solve it, but it didn’t. This particular case has different reed, different valve, different cavity dimensions (coincidentally it is the same note, F3) and the spectrum is ok up until I secure the enbox screws. Any suggestions?

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Might I add a small thought:

 

This is all very admirable trying to quantify this stuff scientifically but if the aim is to make a musical instrument, or reeds for one: should such sounds not be judged aesthetically, or artistically? In how it feels and sounds to play? To get too bogged down in the science of it we might end up missing the point. 

 

I am pretty sure that most people who make musical instruments are not usually thinking about things in such a scientific way or imagining fluid mechanics, rather they have a physical knowledge of how things are supposed to be and feel. Charles Jeffries was supposedly illiterate, though apparently was a performing musician if sources are to be trusted.

 

What is actually the aim here?

Edited by Auldfellowmelad
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2 hours ago, Łukasz Martynowicz said:

I know this table and I know Helmholz model. What I try to tell you is that you can make the reed work perfectly well with non-orthogonal cavities that do not follow this model, thus the model is overly simplistic.

Lukasz, you confuse me greatly.  Why do you assume that the Helmholtz model requires orthogonal cavities?  The Helmholtz model assumes that all acoustic wavelengths are much larger than any of the resonator dimensions.  This allows us to treat the three separate components, Volume, Aperture Area, and Aperture (effective) Length as parts of a "lumped parameter" system.  That means the shape of the volume doesn't matter.  Spherical, cubical, rectangular, cylindrical, etc. doesn't matter.  Only the Volume of the cavity matters.  I mention "orthogonal" in my article only to make the volume calculation simple.

Thus you're assumption that my model for choking reeds requires orthogonal cavities is erroneous. 

Concerning your F3 reed problem, what do you mean by "beating?"  In acoustic terminology, beating usually refers to the interference of two sounds that are separated by small frequency differences.  What is that one F3 reed beating against?  It's also difficult for me to visualize the construction, and maybe a picture would help.  I have some ideas, but I want to be sure I'm understanding the issue. 

Best regards
Tom

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1 hour ago, Auldfellowmelad said:

What is actually the aim here?

Auldfellowmelad, I think I made my aim clear.  I'm intending to understand the physics behind the tongue vibration in the free reed.  As far as I know, no one has done this before.  It's a challenge, and it brings me great pleasure in going about the process.  I hope I succeed to some degree, at least to be able to publish it for the world to see.  

 

Is that enough?

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I agree that „beating” is confusing. What I mean is that one higher partial is so emphasized that the reed burrs.

 

I only ever encountered Helmholz calculations in free reed context in orthogonal form, so my bad here, but in this case it is even less acurate for free reed physics because cavity shape matters and matters a lot. Sorry, but you are trying to convince me, that when theory contradicts experience I should rely on theory instead of practice. When working to improve my largest reeds’ response I had to work within confines of available space, so I had to work with shapes I could fit in. Simply creating a cavity of calculated (and then verified on variable length cuboid tuning chamber) volume and mounting the reed on it did not work well. The response was better (but still not ideal) than small volume, but the sound was muted and nasal. Reshaping the cavity (with near constant volume) changed the tone completely, with different shapes having different exact result, ranging from soft and muted to powerful and deep). Moreover, changing the angle of completely constant cavity (to fit another one) relative to action board/padhole also significantly changed the response and tone. So I’ll stick to my experience for now and wait for a model that can explain those variations.

Edited by Łukasz Martynowicz
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Lukasz, you take me from "beating" to "buzzing," and I don't understand either.  But your claim that a higher partial is overly emphasized intrigues me because such an event is rare, in my experience.  Sometimes with free reeds the second partial (one above the fundamental) can have a little greater amplitude than the fundamental, but I don't know if it's really noticeable by ear.

I suggest you first verify that what you say is true, and that's easy to do.  Make a digital recording of the tone with an audio recorder and feed the data in a spectrum analyzer, such as Audacity, free software available on the web. You can then see very clearly whether there's a partial with an abnormally high amplitude.  If that's the case, we'd know the frequency of that partial and that could be a clue in determining what cavity dimension is involved, if any. 

I may be wrong but I think you totally misunderstand the purpose of the table I presented.  I'm not trying to design reed cavities using Helmholtz theory.  I'm suggesting that the choking we observe, especially with the higher frequencies, is when the air resonance in the cavity matches close enough the fundamental of the musical tone.  Air resonance happens in most all musical instruments, although the free reed is exceptional in that it occurs only sporadically, without a well understood benefit to the musical tone.  I also suggest that a match with one of the lower partials can also cause problems.  Once you understand the self-excited vibration of the tongue you will see the sense to this suggestion. 

For a builder like you, there's no need to even think about this or do any calculations.  If you experience reed choking, all you do is try one of your trusted remedies and it will work, whether or not you understand why.  Being human, you come up with your own theory on why, without any need to compare it with established acoustical principles. 

For me, there's value in identifying the underlying physics, but you don't really care about that and there's no reason you need to care.  I offer this information only for those curious enough in this way.


Best regards,
Tom

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