I have been thinking a lot about why reeds fail. Many people have mentioned blowing to hard and this makes intuitive sense. I decided to put some numbers to it using beam equations and fatigue theory form mechanical engineering. Below is a print from a program called MathCad that allows me to lay out equations and notes and the it will automatically update all the equations as I change numbers. I put in the equations for a cantilever beam uniformly loaded. Look at the picture and you will see this looks a lot like a harmonica reed with air pressure on it. I input values for a table for brass at the low end of the brass strength range.
I chose a length of 16mm for the reed and iterated the thickness until its first resonant frequency was about 440 Hz (concert A). I chose a width of 3mm but the width does not effect the frequency or the stress in the reed. I had a value for the stress to fail at 10,000,000 cycles (6.3 hours of playing A). I then reduced the pressure until the reed had this stress on it and found that the pressure was about 0.6 psi. I don’t have a gage handy to measure how hard blowing at 0.6 psi feels like but is seems reasonable. A party balloon inflates at 1 to 2 PSI. It takes a lot more force to blow up a balloon than I use on a harmonica.
The nature of fatigue is such that if you double the pressure you will reduce the life by much more than half and if you half the pressure you will more than double the life. Steel has what is called a fatigue limit. If you get the stress below the fatigue limit it will vibrate forever without breaking. I have a Session Steel in low D and I have, unfortunately, exceeded the fatigue stress limit a couple of times. On the bright side, I now know how to replace a reed.
Hey cool! I was wondering when a mechanical engineer would weigh in on this issue... Now, the question is does anyone have a Spirometer handy to check what "normal" breath force is? Is any one asthmatic or know anyone with breathing issues that might own a spirometer? If we could run some experiments to find out what the range of breath force is for different people blowing at different subjective levels of force ("light", "normal", "hard"), we could get some central tendencies on those subjective categories, and then crunch the numbers with STME58's model, and we could "predict" the life of reeds under different playing conditions... We'd have to also cross reference reed lengths/thicknesses for the different notes on different brands of harmonicas... I think this info may already be compiled (or in the process of being compiled) by Jim? If so, it would make the job easier! This would be a really cool set of experiments, and I could definitely see a paper being presented at SPAH... ---------- == I S A A C ==
By the way, STME58, I am unable to open the .xps file (nor does it show in my browser). I'm assuming it is some sort of graphics file? What program does it open with? And is it possible for you save it out as png or jpeg so it's web-viewable? ---------- == I S A A C ==
Just a quick google found that the highest breath pressure a typical person can exert is 1.4 PSI, and that a trained trumpet player can push out up to 1.9 PSI. I'm assuming harp players are capable of that too... STME58, can you run the numbers with those PSI inputs and see how long a typical 4 draw reed can last?
BTW, the source of this info is wikipedia, so it may not be totally correct: http://en.wikipedia.org/wiki/Orders_of_magnitude_%28pressure%29 ---------- == I S A A C ==
The frequency and mas stress calculated from these formulas are probably pretty acurate. The time to failure is highly statistical and would be very dependent on the exact alloy, manufacturing method and surface condition of the reed.
These equations are of a simple beam with constant cross section. Higher end harmonicas have reeds whos thickness varies along the length and more calculus would be required to calculate the stresses.
WARNING!!!!
Responding to this thread might get you labled as a nerd. I am beyond hope in this area. Don't worry about me, run, save yourselves!
Last Edited by on Apr 12, 2012 11:35 AM
Cool! Thanks for converting that graphic for me... Yes, the calculations could get messy, I imagine, if you were to take all variables into account... Still, I think it would be useful to know how long a "typical" brass reed of every dimension would last under "light", "normal", and "hard" breath pressure. It will, at least, let people know up front what to expect in terms of the life-expectancy of reeds, and will help keep people from blaming other things... ;) ---------- == I S A A C ==
Great stuff. I'm an engineer at heart. I often wish people would speculate less and use science more. Clearly this is an oversimplification, of course, but it is a step in the right direction. Why an oversimplification? Because we know that reeds are as likely, or more - to go bad due to attempting to bend them too far than by simply blowing or drawing too hard - and in actuality it is likely a combination of both. The forces associated with bending will be much hard to measure or calculate than simple vibration.
@ Isaac re: "Just a quick google found that the highest breath pressure a typical person can exert is 1.4 PSI, and that a trained trumpet player can push out up to 1.9 PSI. I'm assuming harp players are capable of that too... "
NOT.
You've likely never put a trumpet to your lips. Or an oboe. I have. These instruments take TREMENDOUS pressure compared to harp. I'm willing to bet that, when measured, we'll find the pressure required to play harp is even less than the 0.6 PSI of STME's assumption.
@STME: I assume the formula at hand is generally used in structural engineering assuming much higher masses and lower resonant frequencies. Is that correct? If so, I would wonder if they apply linearly down to this scale. I know a little something (enough to be dangerous) about aerodynamics from many years spent flying radio controlled airplanes and helicopters - and there is something called the Reynolds Number, which in turn has something to do with the size of air molecules - that causes aerodynamic theories to fail dramatically at smaller sizes unless accounted for. The example I remember from studying it was that for a fly to flap its wings, would feel more to us humans like flapping in molasses. Anyway - just wondering if you can comment as to whether the Reynolds number or some other factor might might come into play for these formulas at such small sizes......
You're right there Greg, I haven't played a trumpet... but it makes sense now that I think about it... actually, you are probably right that .6 psi is too high for a minimal value. What about the pressure of.plying TOO loudly? Do you think that would approach the 1.4 psi mark? ---------- == I S A A C ==
I think that math is cool, From what I see, it would calculate the tensile strength of a reed, provided it was perfect, but reeds aren't. It's like calculating the combined strength of strands in a rope, then making a small cut in the rope. We've calculated the strength at the strong points. But, this is still a good thing. Since all reeds made have horizontal milling, it's a good way to understand how force and reed fatigue relate.
At HH, I worked most of the time in West Virginia, telecommuting, but I did spend some time working in Illinois, which is a very flat state. The first time I was up there was when Brad was working on designing reed profiles. Anytime Brad didn't like something about some reeds, he'd dump them in the floor - because if you set them aside, there's a chance of mixup - Whenever the day ended, Brad would sweep up this pile of reeds. So there were a lot of disposable reeds. I was staying with Brad and he was my ride. It all started like at 5 a.m., next thing you know it's evening, finally about 8 p.m., I'm at my limit, but Brad's still rolling - and he is my ride - so I've got a lot of time to kill, noplace to go and a lot of disposable reeds to mess with. So, I spent hours doing experiments seeing what it would take to break reeds. I held a reed with one hand and a small jewelers file with the other. I moved the file back and forth in a steady motion across the free tip of the reed. the distance of this motion was my amplitude, the speed was kept as constant as I could. I moved the file strike point down the reed, increased the amplitude, varied all kinds of stuff because I was really bored. There was a point of amplitude where I could probably have gone on forever and not had the reed break. Then as the amplitude of file movement increased, the reeds broke quicker and quicker. It appeared to be exponential. I tried a few horizontal milled reeds, subjecting them to the same high-amplitude file movement, then did the same with the lengthwise milled reeds and counted the strokes. The lengthwise milled reeds lasted about three times as many strokes. The results were pretty consistent when repeated. That ratio would probably change some with big changes in amplitude, but this wasn't that precise a test, I just tried to keep one constant speed and amplitude. I was with the company for one year. During my tenure, we had reports of two reed fatigues. They were both from the same guy. That's pretty unusual, with regular milled reeds, there's always this core group of guys who blow a reed out within two weeks , then as the months go by you get more.. then there's some like me who play them for years. If some machinist out there wanted to make something that would hit a reed back and forth like I was doing with the file, only have the ability to precisely control that speed, you could get some workable numbers to compare the strength of different reeds to see a comparison in tensile strength. You could do a good comparison with mechanical force only.
The formulas used are standard beam formulas and there is no reason they should not work at this scale. This could be verified by measuring rectangular constant cross section reed that we know the pitch of and seeing how close the frequency calculation comes. In the example given a 16mm long reed .2065 mm thick vibrates at 440hz. This seems quite in the ball park. This is the resonant frequency of the beam, the frequency it will vibrate at if plucked and released. This would be the value in a vacuum but air only adds a little damping and small amounts of damping have very little effect on the frequency. So far the model should match reality very closely without needing to consider Reynolds numbers and the like.
The bending part is also very straightforward. Think of the reed as you add pressure but before it starts vibrating. The load on the beam (reed) is the pressure times the area of the reed (b*l). Under this pressure the beam will take the shape shown in the diagram and the displacement and stress can be calculated for any air pressure. So far there is not much in the way of simplifying assumptions. A brass beam of modulus 97 GPa this size, with a pressure load of .676 psi on top will have a stress of 83.9 MPa at the root and the end of the beam will displace .536mm. The stress at which brass will last 10,000,000 cycles can be approximated at about ¼ of the ultimate tensile stress, in this example the ultimate tensile stress is 338MPa so the 10,000,000 cycle limit is 84.5 Mpa. I iterated the pressure until the stress on the beam was very close to 84.5 MPa and found this pressure to be .676 PSI. Now I made a big assumption, I assumed that if you initiated an airflow that created .676psi before the reed moved, the reed would vibrate at a displacement of .536mm reaching a stress of 84.5MPa at the root on each cycle, alternating in tension and compression. If this assumption is true this model would predict failure to the accuracy of the ¼ ultimate stress at 10,000,000 cycles rule. The engineering literature warns that this rule is not very accurate and it is important to test the exact alloy and shape to see exactly how it fatigues.
To analyze this further it is important to understand how a reed makes sound (I will say now that I don’t). When you pluck a reed it makes sound like a guitar string but this is very little sound. I have a hypothesis that the sound is created by the reed acting like an air valve and letting little puffs of air out at the frequency the reed is vibrating. We know that the reed can have an impact on each other by the stroboscopic and other work done in looking at reeds as a note is bent. This is where considerations of things like the Reynolds number might come in. This is likely a compressive gas fluid dynamics problem and things get a bit more complicated. In all of the fluid dynamic problems I have done (mostly in school years ago), the assumption that the fluid (air in this case) does not compress is made because it greatly simplifies the math, and has little effect on the outcome of the solution. If anyone knows of any literature on this I would love to see it.
I would not be surprised if the main mechanism for early reed failure is blowing or drawing too hard. This model shows that the pressure required to cause early failure is well within the capability of the average player. Many have asserted a correlation between over bending and reed failure and I won’t challenge the assertion, but the over bending may also go along with just blowing and drawing too hard. I wonder if people are getting bend (change in frequency of a note) confused with bend (apply force to reshape a beam). If you bend a beam too far it will break. However, if you force something to vibrate at other than its resonant frequency, the stresses are related to the maximum flexure of the beam, not how far you are away from the resonant frequency. One way I can think of to test this hypothesis would be to design a tiny and accurate relief valve that could be placed in the reed chamber that would not allow the pressure to exceed its set point. Then you could check to see if you could bend (change frequency) the reeds to try get an early failure and know you had not over pressured the reed.
Your engineering work matches, qualitativley, what is in the literature on fatgue. The cycles to failure varyies exponentialy with the stress. Stress is related to the amplitude of displacement. Standard fatigue tests are done by rotating a rod of the test material with a weight on the end in order to cycle the stress but there is not reason it can not be just as accurate, in fact more accurate if you are evaluating the material for a vibrating beem. The rotating beam test came out of the railroad industry as this is how railroad axles are loaded.
If I understand verticle milling, you make the machining scratches go the long way down the reed. This would make the reed much more fatigue resistant. Your tests seem to bear this out. The engineering literature suggest that you also consider the direction a material was rolled. In the case of a reed you would want to cut it out of the sheet in the direction the sheet was rolled so the grain goes the long way down the reed, not across it.
Did you ever try shot peening or bead blasting reeds after maching? They may be a little small for this but this is a common way to increase fatigue resitance.
I'm an aircraft engineer and know a little of gas flow and the laws involved.
So thought I'd throw this into the debate.
Should you not look at air velocity rather than pressure ? Does Bernoulli's law come into bending ?
When bending I do not change the flow of air from my lungs ,but the shape of my mouth. Narrowing the space the air is flowing through. This increases the velocity and will actually lower the air pressure going through the harp.
Reeds will fail earlier if you blow or draw too hard, but IMHO bending has nothing to do with it.
Perhaps, as a beginner, you draw/blow too hard whilst trying to bend which will overload the reeds.
But an experienced player will not have this problem.
Reeds have a finite life, the more you play a particular note, the sooner that reed will fail. ---------- The Pentatonics Reverbnation Youtube
"Why don't you leave some holes when you play, and maybe some music will fall out".
A couple questions- Would an unnatural curve or kink in the reed multiply the forces like a lever? Can mechanical resonance add any destructive effects?
While observing the reeds in a mirror while draw bending, I've noticed the the deeper you go in the bend, the larger the amplitude of the swinging blow reed. Also the draw reed sucks up to the slot and appears to nearly just stall there, which would redirect most of the airflow through the blow reed. So "to the floor" bending would seem to expose the blow reed to higher air forces than a straight blown note (where the draw reed is open and relieving some of the air). Just a mechanic's point of view:) Enjoying this thread-
If you go to google scholar and type in a few key words, you can get a list of other related articles.. including one on physics of overblows where they got levy in to the lab. if you need to get at some of the references and cannot, i might be able to through my university account, so let me know.
one of the assumptions here is that there is no torsion.. a perfect reed should have no torsion, but i bet there is some
"Many have asserted a correlation between over bending and reed failure and I won’t challenge the assertion..."
I always find that interesting as most skilled overbend players talk about how they DON'T break a lot of reeds compared to others. ---------- Mike VHT Special 6 Mods Quicksilver Custom Harmonicas - When it needs to come from the soul...
So far I have only looked at the mechanics of the reed. The only reason I used air pressure is to get an idea of the load on the reed. To look at the whole system of course the fluid dynamics will come into play. I doubt the load on the reed can really be represented by the simple pressure times area method I used but it is a starting point.
I analyzing the airflow through the harp, do you think one would have to take into account the compressibility of air or would the standard simplifying assumption of an incompressible fluid yield realistic results in this case? Not that I have the wherewithal to do this analysis. :-)
Last Edited by on Apr 13, 2012 11:53 AM
A kink or bend in the reed would change the stresses there are tables that show how much different kinds of notches in a beam affect the stress.
There is also something engineering students struggle with and usually forget after graduating called Castigliano's Theorem that is used to calculate the stress in a curved beam. I may need to look that up to see if it would make a difference in the stress at the small curves placed in a harmonica reed when it is setup properly.
As far a mechanical resonance, that is where musical instruments operate. Without the resonance there would be little sound. If the instrument can't handle it, things break. It is not like a bridge that can handle all kinds of heavy traffic and does its job well, until any army marches across in step at its resonant frequency and brings it down.
@Walterharp, Thanks for the links. I have bookmarked them and will look at them in detail when I get more time. In skimming them, I did see a comparison of a harmonica reed to a siren, I had been wondering if this was part of how the sound is produced in a harp.
Unfortunately, the measurements of reed excursion with a transducer are only relative and cannot be used for calibration of the beam calculations shown in this thread.
I have a Bawu, which is mentioned in one of the articles and I was wondering how the reed vibrates at different frequencies based on which holes are covered. I look forward to reading the article and hopefully understanding more.
Last Edited by on Apr 13, 2012 12:01 PM
None of this appears to deal with the dual nature of harp reeds and the way that the two reeds' vibrations interact - surely that makes it a much more complex system to model theoretically?
@MrVerylongusername, You are quite right that a full model of the sounding of a harmonica is much more complex than this. What I was going after is getting a feel for the stresses in the reed and how that relates to fatigue failure. As a starting point I looked at how far the reed would flex under a steady pressure and used this as a point to and from which the reed might vibrate to estimate the fatigue effects. I have really appreciated all the comments because it has gotten me thinking about this in ways I would not have come up with on my own.
Using the model presented in this thread, which shows how far a reed would bend under a given pressure if no air leaked past, I calculated the following. Air Pressure to yield 0.2016mm x 16mm reed……….1.0 psi Air pressure to break 0.2016mm x 16 reed……………2.7 psi That means it takes 1.0 psi to permanently bend the reed and 2.7 psi to break it all the way off. That’s a lot of math to state the obvious, if you blow too hard you will break it, but it helps me to gain an understanding.
This reminds me of the argument about whether you need to understand theory to play good music. Do you need to understand mechanics of materials in equation form to build a good harp? Of course not! However, the theory just might yield an insight that leads you to doing something better. On the other hand even if you don’t know the equations you might have a better handle on the theory than you think. The anecdote shared by @ElkRiverHarmonicas above about testing the reeds shows this. @ElkRiverHarmonicas may know his way around the math, but in the story he doesn’t mention using it or needing it to gain the insight that he did by just playing around with the parts.
Last Edited by on Apr 13, 2012 2:13 PM
hey mike, actually the second link I put up is the best one on overbending and overblowing, and it should be available for free.. my favorite quote from the article is in the conclusions and follows all the physics
In the final analysis, the music created by the harmonica consists of more than the acoustic and physical function of the reeds. There is a synergy which causes the whole to be greater than the sum of the component parts and an artistry which cannot be quantified—dynamics which give personality to the instrument, reflecting individuality of the musician. As with speech which varies from person to person, there are certain tonal elements of harmonica playing which are similarly individualized. This dynamic interaction allows the player to speak with his instrument perhaps as with no other. Just as no two voices are exactly alike, each player imparts his own timbre, and one cannot expect to emulate exactly the musical tonality of another. This helps keep the harmonica interesting, and indeed has helped to sustain its enduring prominence throughout the world
@STME58 "do you think one would have to take into account the compressibility of air or would the standard simplifying assumption of an incompressible fluid yield realistic results in this case?"
The kids of today and those to come are one day going to be playing harmonicas that are "MAGNIFICENT"...By then the rest of us will be to old to give a shit about the harmonica, hashahahaha
Last Edited by on Apr 15, 2012 9:21 AM
I hope right anbout the progress but it may not come that fast.
A new Kia or Hundai could run circles around the Marmon Wasp that won Indy in 1911 and probably costs less in constant value dollars. Can the same be said of a modern low cost harmonica vs. the best available in 1911?
This may not be a fair comparison. My trombone is not much different than the ones made 100 years ago. I have, however, spent more repairing harmonicas in 3 years of playing than I have spent on my trombone in 30 years.
Can anyone tell me if any of the above pictured descriptions of reed milling is hat is refered to as "Verticle Milling" ? My guess is that it would be C. This would give machining marks down the lenght of the reed in a way the would create the least stress risers and woud give a curve rather than a step up to the root of the reed which would also reduce stress.
Having never been in a harmonica factory, I don't know how things are done.
Last Edited by on Apr 18, 2012 3:45 PM
Now on the one where the cutter is on its end... the cutter is not making a lengthwise cut. The cut is still horizontal, although the marks will have a little curve. By the way, horizontal milling was a revolution when it was introduced in Klingenthal in 1878. It was what made mass production possible for the first time. BTW, in regular horizontal milling, reeds aren't milled individually, a strip of brass is. It's ground to the profile of the reeds, then another machine cuts them out, spitting them out like bullets from a machine gun. It's pretty fast.
Yeah, let's lobby all the major manufacturers about this... after all, what we all really need right now is a huge increase in the cost of production being passed on us at the retail end.
I wouldn't mind paying $10 a harp for 1878 technology than I could buy a six pack of each key and I could keep playing for a couple months.A professional strength reed ,is a vertical milled reed,period,is anybody listening?Get Brads machine and sell me some vertical milled reeds,just gimmee da reeds,I'll make em fit into something.I'm tired of wait'n!.
No you're paying $45 for 1878 technology and it isn't going to get cheaper.
Wasn't one of the issues with Harrison, that Brad was rejecting a huge number of the reeds his machine was making?
Hohner know about vertical milling. Suzuki know. Seydel know. Tombo know. I guarantee all the major manufacturers were watching Harrison with interest, but:
1) Tooling. It won't just magically appear, it costs a fortune and will undoubtedly have teething problems. Its installation will disrupt production and could well have knock-on effects for the workforce. Retooling of this nature doesn't just happen overnight - it is planned years ahead and phased in.
2) The sales model - inbuilt obsolescence. A longer lasting harmonica is going to reduce the number of repeat sales. The price will increase.
and the killer...
3) Patents. Brad was canny and took out patents. Those patents were probably the most attractive part of his business to the mysterious bail-out buyer. Perhaps the buyer was one of the big company? I dunno. Its all gone very quiet.
I would like to see these technologies implemented as much as you, but reality and economics doesn't work like that.
A quick search of the USPTO ( http://appft1.uspto.gov/netahtml/PTO/search-bool.html ) found this using Harrison and Harmonica as search terms. My computer won't load the images so I cant make sense of what is patented here. It looks like a cover plate patent. Patents are sopposed to describe the invention so that anyone "skilled in the art" can reproduce it. You are trading a few years of exclusive production for sharing you invention with society at large. In practice it is usually very hard to figgure out how to build the invention from the patent decription. I did not find a patent with the name Herrison that mentions reeds.
United States Patent 7,847,172 Harrison December 7, 2010
Abstract The harmonica may include a cover, a comb, reed plates and reeds. In one embodiment, the harmonica may include an upper button and/or a lower button which may allow the cover to be removed from the comb. In another embodiment, the harmonica may include one or more side buttons which allow the cover to be removed from the comb. In another embodiment, the cover may be allowed to pivot relative to the comb so that the cover can be rotated away from the comb. In another embodiment, the harmonica may include one or more inserts and openings in the comb in order to improve the sound of the harmonica. In another embodiment, the harmonica may include one or more side vents which allow air to escape or to enter the harmonica which may improve the sound of the harmonica.
-------------------------------------------------------------------------------- Inventors: Harrison; Bradley A. (Chicago, IL) Appl. No.: 12/139,825 Filed: June 16, 2008
WHat you described sounds like a progressive die using a pre-machined coil of brass. I have not been working closely with sheet metal for a while, but 20 years ago there were prog dies that could run 900 strokes per minute. They flowed out of the machine like a stream of water! These were typiclaly making the little brass contacts that go in to computor connectors.
I wonder if something could be achived if Suzuki and Hohner were to talk with AMP and Molex?
Last Edited by on Apr 16, 2012 9:50 AM
I just did a google search on "How to make a Harmonica" and fund some video of the Hohner reed making process.
http://www.youtube.com/watch?v=3tk5f8cPY0A
The reed milling machine is closer to a shaper someone might have in their garage, than the CNC Mill I had envisioned.
This is much smaller scale than I had envisioned. I can see the barriers to changing to a new technology, even if it has a chance to be a lot better. This is not a stamping house where $50,0000 die sets are run in $1,000,000 presses.
To take advantage of the technology possible today the harmonica companies would have to contract the work out to a stamping house and then they would loose the control they have of an in house process.
The progressive die that makes the covers was impressive for a small in house operation.
I now really think Hohner could benifit by visiting ( if they have not already) a stamping house where electrical connector contacts (about the size of reeds) are made by the millions per day. Some of the best tooling for this is made in Germany.
All that video shows is how someone fails at making a professional quality reed.One hundred years of milling reeds in the wrong direction.Thanks Brad for bringing that to my attention!
I can understand your frustration but there is really not a conspiracy to deliver inferior harp reeds, nor do I think Hohner is just being cheap by not retooling. That simple machine they are using to mill reed stock is serving many musicians well. It is just hacks like me that need a more durable reed until I can learn to play right. The way the mill is set up now it can do the sheet in one swipe with the cutter only rotating. If you turn the cutter 90 degrees to get the machining marks in a preferable direction, it will now need to translate back and forth as the material is moved from side to side. Even with the milling going the “wrong” way, making the cut as smooth as possible will reduce the stress risers. I’ll bet the engineers at Hohner have optimized the speeds feeds, cutter materials, tool sharpening regimens etc. to get the smoothest, most durable reed they can. When they switch to milling the other direction they will have a more complicated machine, and all kinds of new process problems to sort out. It could take years to get it running a smoothly as the current process. For all we know they are part way thought that development now. If they are working on it I would expect them to keep it secret until the products hit the market.
The idea of a custom brass material intrigues me. When I approached sheet metal suppliers for a special plating for steel for a stamping die that would produce several hundred thousand parts a month that were much bigger than a harmonica, I was told that my quantity was much too small for anything custom and I would have to select from the stock materials and platings. Of course even if Hohner does not get a custom alloy made from them by the rolling mill, but selects the best from the readily available, they would still do well to keep exactly which of the many available alloys they are using a secret.
What I have taken away from this exercise is that there are some improvements that could be made to the manufacture of Harmonicas, the best improvement, and the one that I can realize the fastest, will come through better breath control and playing with less pressure. I have been concentrating on this and have noticed an unexpected benefit of better note clarity, and the ability to play fast passages with better definition between the notes. I find this ironic because when I was in college there were a couple of garage bands near where I lived that played loudly and badly. I gave them the unsolicited advice to turn if down, listen to each other and get the intonation and timing right so that when they turned up the amps it would be worth listening to. They , of course, ignored me but I now find myself taking my own advice.
This brass alloy thing is true. It's very hard to find somebody to run batches small enough to make adjustments. I don't think theres anybody at all left to do it Europe.I talked at length to Brad about thus, he was able to get small enough batches to dial in his alloy in the U.S. And he tried all kinds of stuff. but as a rule, alloy adjustments are tough. The amount of brass you need to make reeds for a bazillion harmonicas is still relatively small in the grand scheme of things. ---------- David Elk River Harmonicas
Can we resize the images a bit? I'm having to scroll to left/right to read everything.
One of the reasons reed material could be so important is that different materials worry differently. Most metals worry every time you flex them, but a couple, steel and titanium, don't start to worry until they flex past a certain point. If a harmonica reed were to stay below that point they theoretically would never worry. My math cuts out about there though. I couldn't tell you how that applies to a single point versus a bend along a longer surface. Does the thickness of the reed matter? In my head it actually seems that side of a reed, that for lack of a better word, is extended, would be slightly more flexed, and for materials close to the threshold where the worry or don't worry that could make a difference in reed life. Might a thinner reed last longer?
The other place it would be interesting to see a little math applied is the width/depth of the gaps in between the tines in a comb. In the hypothetical model in my head it seems to me that if you shrink that area a smaller change in pressure applied to it would change the pressure in that space quicker, giving you quicker reed response, although compared to the volume of air coming out of your lungs whether the amount of air it takes to fill that cavity would be make any practical difference is anyone's guess.
Thickness... Good question. You'd think thickness would make it stronger, in some ways, that's true, I suppose. But increased thickness increases compression and tension stress when bent at the same amplitude. Remember those thicknesses vary along the reed. It's far more important how the stress is distributed along the reed. If it's concentrated more in one place than another, it will break in that place. Applying all this math is fun, but by doing so you are calculating the average strength of a chain, even though it's going to break at it's weakest link. The only way I think you can calculate anything would be to factor in the distribution of force. The distribution of force, more than quantity of force itself is why reeds break when they do. Distribution of force is key. Even without milling marks, there would still be a focus of force. Why do you think reeds always break in the same place? Even though there's milling marks all along the reed. When I reshape reed profiles for my customs, when they go out, the crack is in a slightly different place on the reed than a stock reed, that's because I've changed the way in which that force is distributed. I do draw just a little bit on longbow building experience for custom reeds.
The equations shown are for a constant cross section reed with a sharp step at the root. The highest stress is at the root. I have a broken Seydel reed on my desk that broke about 2mm from the root. When I looked closly at the profile it does not have a step but rather tapers from the root to the main reed thickness. This is a more complex calculation but I will take a caliper and get the profile and see if this reed broke where the math says it will. If I fand the calculus too dificult I will build the reed in CAD and do a Finite Element analysis to see if it predicts the failure at the point it actually failed. 20 years ago this would have taken weeks but now I can do it on my lap top in about 20 minutes.
I don't know as they have accelerometers to the right scale for harmonica work yet, but they do have them in some pretty tiny devices now. I wonder if someone could scale up a harmonica and some large bellows and get some data!
On a side note, another one of my projects I wanted to try but have never gotten around to was a giant mock harmonica, but instead of blowing the reeds I was planning on striking them. If you've ever taken a metal ruler and set it on a table with one end hanging off and twanged it, it makes an interesting noise (wooden rulers do to, but I like the sound of metal ones better). I was figuring that with measuring marks on them already I could make a giant percussive harmonica. Then I went to the store and saw that instead of being a couple bucks each they started at $10, which turned the math of 20 reeds into a little bit more daunting a project.
"HDK America Inc. unveiled what it touts as the smallest piezoresistive three-axis accelerometer with a 3-by-3-by-1mm footprint." That's from an article that's 6 years old.
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Last Edited by on Apr 18, 2012 8:08 PM
I re-solved some of the equations in order to have constant frequency at various lengths by changing the thickness (the widths does not effect the frequency). This is still a constant section reed but you can see the effect of changing thickness. These graphs are for constant pressure. If I get a chance I will re- solve for constant displacement as David suggested so we can see how that plays out as thickness changes.
Nate, these are the equations you would use to determine the lengths of the cantilever chimes you described. The equations will work for 6mm thick plate as well as for thin reeds. If you use steel instead of brass you would have to change "E" (modulus of elasticity) and "p" density form the values here for brass to the values for steel.
The thinner the reed is the more moves for a given pressure and the higher the stress. The thick reeds may have less stress but the low displacment means they won't be making much sound. Note the sharp knee in these curves. The "sweet spot" would be just to the right of the bend. I am not a harmonica designer but from the graphs I would start with a reed with a thickness of between .1mm (~11 mm long from the first graph) and .2mm (~16mm long).
Last Edited by on Apr 18, 2012 9:21 PM
STME58, I was going to tune the first one by ear and then use the same ratios you'd use on guitar frets to tune the rest. I guess the math ends up working the same. I was really good at math as a kid, but I had a string of terrible teachers starting around 8th grade so aside from baseball statistics I stick more to math as this sort of theoretical elephant in the next room.
How bad could they have been, you ask? Well, one of them was arrested in the park wearing a dog collar and a diaper, carrying a paddle and asking bystanders to spank him. He was even stranger in the class room, and he was not the worst of them. :(
I can still get pretty good at understanding math theories, but the details make my brain hurt.
Funny, I looked up on Google and found a link for plastic rulers that already have the notes marked off on them! They don't let you copy the picture. I guess they figured out that it would be too easy for someone to just look at the picture and use the numbers on the ruler to figure it out. :)
Have you even noticed it is generally acceptable to say you are no good at math but if a person can't read, they will often go to great lengths to hide the fact? There are people who can’t read and or have little knowledge of math that have accomplished more than I ever will. Formal learning is just a tool and if you don’t have one tool you can often use another if you have the will to get things done.
Math can be tough and a good teacher can go a long way towards helping people get it. I am sorry you did not have one of those inspirational teachers. I know different people learn in different ways but I can imagine a leash and a diaper inspiring very many people to great achievement. One never knows though.
There is nothing wrong with using equations already solved out, like the guitar frets, as a short cut to a solution without the paper and pencil math. Before computers engineers used to solve differential equations of masses springs and dampers (which in turn modeled beams in bridges or mechanisms)by using their electrical equivalents of inductance, capacitance and resistance in a electrical circuit and take the answer to their structural equation off an oscilloscope (a device that shows voltages changing with time on a screen).
If you would like, I can put the formulas from my Mathcad sheet into and Excel spreadsheet so that anyone could enter the length , width, density and elastic modulus of a beam and get the free vibration frequency. I could even past a table of moduli and densities of common materials into the spreadsheet.
On the topic of a xylophone like instrument, I have heard that if you lay a set of good quality mechanics end wrenches on a foam pad and strike them with a mallet, you can play tunes. Anyone tried this?
This is more simpler,"Give us a better quality reed that doesn't develop microscopic fractures and this industry may have a chance.They've had a hundred years to work the bugs out,it's not rocket science."THE guilt trip about playing to hard is bogus.Play hard ,play soft,its called dynamics,its how we express ourselves to the max.Don't fall for the reverse sigh-kol-ogee.Peace and tranquility to all.
I hear you on not falling for the "blame the customer" mentality. I also have to work with the harmonica I have in my hand, and if I blow it hard, its gonnna break. There seems to be a differnce in how soon things break even on harps of the same make and model. I think much of this is manufacturing inconsistancy but some of it is playing inconsistancy (speaking only for myself).
It does appear, from the limited data we have, that there is a tecnological improvement in reed durability available that no one is taking advantage of. From here I can not tell if the barriers to implementation are technical, economic, cultural, politcal, or some combination of these and others. I hope that some of what is written in this forum will inspire someone to chip away at the barrier, whatever it may be, and whether they are a 150 year old company, or a brand new startup.
I have seen a shift in the last 25 years in the little part of the design and manufacturing world that I live in, to the side of the pendulum that puts short term cost reduction above all else. The idea seems to be that if several products meet the basic minimum of what the product is supposed to do, the customer will always choose the cheapest among them. If you want to stay in buisness you had better be the cheapest, whatver it takes. Gone is the idea that if you build a product that works better for the customer in a real and productive way, the customer will be willing to pay a little more for it. I do see some rays of light that the pendulum is starting to swing back in the direction of providing higher quality for a premium, in addition to providing a low cost adequately functioning product.
Last Edited by on Apr 13, 2012 3:02 AM
Last Edited by on Apr 18, 2012 9:21 PM