Reed tongue materials - a survey

[ttonon]

Greetings,

 

1) The Known Difference

 

As far as I know, there are two materials most often used in making Western free reed tongues: steel and some Copper alloy, which is most often brass, but perhaps also bronze. It seems to be generally accepted that steel tongues sound different from brass tongues, and most people describe the sound of steel as brighter than that of brass, which is often described as softer, or even less harsh. Steel, however, seems to be the dominant material, and many people prefer it’s brighter sound because it carries further, though others like brass because it provides an instrument that doesn’t unduly dominate when accompanied by the human voice, and that may be primarily because of its lower playing volume. There are of course many nuances on this topic, including the questioned durability of brass, but my main point here is that these different materials produce distinctly different sounds, at least as observed by a great deal of the musical community.

 

To me, the fact that two different materials sound differently is extremely interesting, and one obvious question raised is, What about other materials? In the 170 odd years of Western free reed manufacture, I’m quite sure many people investigated this question, certainly experimentally, but I’m unaware of any theoretical investigation. Of course, experimentation is the final arbitrator, as long as the experimentation was properly and thoroughly done, with results reproducible by many people. But there are complications. With some technologies, certain practices are established when the results they produce are good enough, and long periods of time pass before a surprising breakthrough appears on the scene. (One interesting example here is the long bow vs. the compound bow.) There are many other issues, some involving the amount of effort it takes to explore different pathways. But suppose there’s an easier way? In this post I’d like to make some suggestions based on three things: 1) the known difference between the sound of steel and brass, 2) a fundamental physical law that describes the vibration of the reed tongue, and 3) an educated guess, based on the previous two.

 

2) The Fundamental Law

 

The earliest derived governing partial differential equation for the vibration of a cantilever is associated with the names Euler and Bernoulli. This (E- formulation neglects both rotational inertia of the cross section and shear force in the plane of the cross section. A more exacting formulation, associated with the names Timoshenko and Rayleigh, came later, and it (T-R) does include these effects. I myself, however, conclude that the difference between the predictions of these two formulations, when applied to Western free reeds in musical instruments, is negligible, and other researchers in universities concur. In fact, I calculate that the difference between these formulations is at least four orders of magnitude less than either prediction.

 

I include the above paragraph because it’s important to note that the E-B equation is so simple, one can make a very general prediction from it, without even solving it. The T-R formulation, however, is too complicated to see such a prediction, and I want to be clear that we can put confidence into the accuracy of the E-B formulation, because that’s the one I base this entire study on.

 

In the E-B formulation, the only place material properties enter into the dynamical response of the vibrating tongue is through the ratio Y/rho, where Y is Young’s Modulus and rho is density. To me, this is an astonishingly simple result, and it can be used to predict much about the effect of different materials on reed vibration. The result is also quite general. As long as the tongue has the same material throughout, this simple result includes the effect of area change along the tongue, as often happens by means of tapering and profiling.

 

The above conclusion means that two tongues with the same geometry, each made with a different material, albeit with both materials having the same Y/rho, will vibrate the same, in every way, both in vibrational response and sound. This is perhaps an astonishing statement, but I’ve thought about this for a while, and although I can come to no other conclusion, I’m open to alternative views. I don’t think we understand the details why different materials sound differently as reed tongues, although we continue to talk about it (as in the post, Why does brass sound different than steel?) But for now, I stand by this assertion, and inquire as to its consequences. There are of course many practical issues that will conspire to decide whether any alternative material is suitable as a free reed tongue. Most of such practical issues are beyond the main interest here, although I will address a couple of the most obvious; i.e., that the material be strong enough, and that it allow sufficient playing volume.

 

In order to get an intuitive feel what this all means, the ratio Y/rho has units of force-distance/mass, or energy per unit mass, and in this case, elastic energy per unit mass. Thinking in these terms, one might conjure some physical intuition why two tongues of the same geometry and elastic energy per unit mass would have the same sound. Such intuition can broaden to include forced vibration as well as free vibration.

 

3) An Educated Guess

 

Most all brass and bronze materials have a Y/rho ratio that is about one-half that of most steels, including the spring steels commonly used in making tongues. In fact, it’s remarkable how most all these brasses and steels have very close ratios among themselves. To assist our educated guess, we start with two facts: 1) steel and brass have identifiably different sounds, and 2) the tongue motion/response of different materials can be laid out in a one-dimensional scale, using units of Y/rho. For the purposes of explanation, let’s keep it simple and say that the ratio Y/rho for steel is 1.0 and that for brass is 0.5, which is approximately the case. Thus, all materials having this ratio close to unity will sound like steel and all materials having this ratio close to 0.5 will sound like brass. Thus, why does brass sound different than steel? Because it has a different ratio Y/rho.

 

What about even different materials? The basic form of the guess here suggests that Y/rho provides a very convenient and simplifying method to guess what all other materials might sound like as reed tongues. For instance, would a tongue material with Y/rho = 0.75 sound somewhat intermediate between the sound of steel and the sound of brass? Would another material with Y/rho = 1.2 sound even more in contrast to brass than steel does? And finally, would a material with Y/rho = 0.3 sound even more softer or mellower than brass?

 

If such questions spark any kind of intrigue in the reader, the following discussion might prove interesting, and in the remaining discussion, I boldly assume the answer to all these questions is “yes.” Again, the intention here is not to try to sell anyone on an alternate reed tongue material, and if many readers consider all this as simply a whimsical exercise, I would agree, but I myself cannot ignore the fact that nature has seemingly provided us with a relatively simple theoretical assist to a very practical, and difficult problem, so why not see what it might predict?

 

4) The General Approach

 

Materials properties for various materials are readily obtainable, and for this study, we need to know at least three things: 1) Y, 2) rho, and for purely practical purposes, 3) a measure of the materials strength. For (3), when it comes to metals, the most useful property in this application is probably the materials fatigue limit over the lifetime of the reed, or what often amounts to the same thing, the material’s endurance limit, Se. A criterion based on Se is generally more conservative than one based on simply the yield strength of the material.

 

For non-metals, I’m not aware that the concept of fatigue strength is very well understood, or even valid, and so, I present other measures of strength, most commonly, the materials yield strength, or in some instances, it’s flexural strength (also caused modulus of rupture).

 

For both metals and non-metals, in order to have something to compare strength to, we need a measure of the maximum stress developed while the reed speaks. This can be calculated fairly accurately from the solution to the E-B equation of motion, provided we have an idea how much the tongue bends. In another post (Why do Brass Tongues Break?) I presented similar calculations, from experimental measurements I made on how far the tip of a steel tongue is displaced under maximum playing pressure. Such a parameter cannot be, as yet, calculated from theory. The maximum stress in the tongue occurs at the root of the tongue, and for this calculation, we need the curvature of the bending tongue at that point. The geometric shape of the vibrating tongue is readily obtainable from the E-B equation in the case of free vibration. With forced motion, in principle, the geometry can be different. However, Cottingham at Coe College has indeed measured the shape of the bending tongue, using a technique of laser vibrometry, and he has concluded that the shape in the actual, forced case matches very closely to the theoretical solution for free vibration, at least close enough for the purposes of calculating stress.

 

With this approach, and assuming that the amplitude of tip vibration scales as the length of the tongue, we can calculate the stress in the tongues and compare it to the strength of the tongues and make some prediction on tongue longevity. If the assumption here about vibration amplitude is in error, this error may not be too serious, simply because such amplitude is a strong function of bellows pressure, and so adjustment of bellows pressure can be part of a process that imposes the same amplitude.

 

5) The Data/Calculations/Predictions

 

Table 1 in the Attachment contains a survey for metals, Table 2 a survey for non-metals, and Table 3 presents a comparison between stress and strength for some of the more interesting materials. I don’t mean to imply these surveys are exhaustive, but I did try to focus on the more common and practical materials for which data can be found. I also tried to include enough materials of a given type, in order to get a general feel for what each type offers.

 

In Tables 1 and 2, the two left columns specify the materials, which are grouped according to major components. At the top are our two reference materials, steel and brass. The right side of the Table gives Young’s Modulus, density, and the ratio Y/rho, normalized with respect to the ratio for our reference steel material, which then becomes unity. For metals, the measure of strength is given by endurance limit, Se, calculated from the materials’ ultimate strength, using common engineering practice. For non-metals, either a yield strength or a flexural strength is given, denoted simply by “Strength.”

 

The main focus of this (whimsical?) article is contained in the last column of Tables 1 and 2. As proposed, any material with a normalized ratio near unity will sound like the standard steel reed, any material with this value near about one-half will sound like a brass reed, and materials having other values will contain appropriate mixes of tone, as predicted by this one-dimensional scale of “normalized ratio.”

 

As I explained in a previous post, brass tongues designed to last many vibration cycles should be shorter than corresponding steel tongues that are designed for the same frequency, when the lengths of these tongues are roughly around an inch or more. Smaller tongues should not experience endurance problems, providing that filing and scrapes are not excessive. Such conclusions apply strictly to tongues of constant cross section, though they should carry over to mildly profiled and tapered tongues. Thus, in Table 3, which lists only the more interesting of the materials presented in Tables 1 and 2, the column, “geo fraction,” for Geometric Fraction, shows the fraction of the steel tongue length required for the experienced stresses to be within the capability of the material in question, for the longer tongues. A geo fraction of unity indicates that the material may be as durable as steel. More of this will become clear as individual materials are discussed.

 

Getting back to the Table 1 and 2, one might not be very interested in materials with values in the rightmost column near unity, because we already have steel tongues that work very well. Likewise, normalized ratios near 0.5 may not spark too much interest, although there are material candidates that are much more fatigue resistant than is brass. Most interestingly, we find materials having a whole range of values, hinting at some very interesting tonal possibilities.

 

Starting with Table 1, values of Y/rho differ little among all the common steels, and so, I included here only those that show a significant deviation. One example is the invars, with normalized ratios intermediate between spring steel and brass, around 0.7, though Table 3 indicates that it’s length scale should be restricted, for long lifetime. Concerning only tone, here is a material that might satisfy the person who would prefer a concertina sound half way between that of brass and steel, with a corresponding playing volume. Unlike the invars, ductile Iron appears as durable as steel (from Table 3, geometric factor of unity, meaning no required restriction in length, for durability), yet with an intermediate normalized ratio between that of steel and brass (0.84).

 

Copper and its alloys most all have close normalized ratios around one-half, though there are notable exceptions. Beryllium Copper, Copper Nickel, and Nickel Silver all show a significant departure from brass, towards steel; however, from Table 3, Beryllium Copper is the only one of these without endurance issues for the longer reeds. Beryllium Copper is often used to make springs, because it holds up fairly well at elevated temperatures, and so its cost, availability and formability may not pose serious problems.

 

The more common Aluminum alloys do not appear useful for reed making, primarily because Aluminum has very poor fatigue strength. This is the reason why airliners must be disassembled and examined after so many hours of operation. For concertina reeds, with cycles going into the tens of millions, my guess is that the Aluminum alloys would not be practical. It is of whimsical interest to note, though, that a tongue made from these materials would probably sound like steel, until it breaks. Similar comments apply also to Magnesium and its alloys.

 

The Nickel alloys look interesting, providing a range of normalized ratios between that of brass and steel. As can be seen in Table 3, some of these have endurance issues. These materials are generally more expensive and more difficult to machine than spring steels; however, given a particular application, as in the case here, more detailed investigation would be advised before a final decision is made concerning these peripheral issues. The Carpenter alloy is notable because of it’s superior strength, and its normalized ratio suggests a sound perhaps a little brighter than steel. My guess is that this alloy is so strong because of it’s cold work hardening (65%), which is the same reason why brass can be made at least marginally strong enough for reed use. I haven’t investigated the extent to which cold working might possibly induce acceptance of other metals in Table 1 that are otherwise too weak to function as a reed tongue.

 

Titanium forms one of the most complicated families of alloys, depending not only upon composition, but also upon processing. They are generally difficult to machine and form, but as in the case of the Nickel alloys, detailed investigation would be required in order to draw final conclusions on cost and fashionability. A great deal depends upon the form in which the material can be purchased, and of course, its cost. Most interestingly, however, these alloys possess a wide range of normalized ratios, from 1.1 down to 0.3, with many intermediate values. They are also strong, and as can be seen from Table 3, most of them should hold up well as reed tongues. This family thus presents many candidates for a whole range of different reed sounds.

 

Moving to Table 2, we come to the thermoplastics, which generally have normalized ratios significantly less than brass, suggesting very mellow tones. If, along with musical tone, the normalized ratio also scales playing volume, such low values may also indicate playing volumes significantly below that of brass. If I might guess, they have a feathery sound. There are many practical issues with plastics, including their general tendency to swell from absorbing water from the air, and also their relatively high coefficient of linear expansion, as compared to metals. When we consider that good reed tongues operate with gaps around their periphery of the order of a mil, these practical issues suggest there may be problems. The temperature issue would be eliminated if the reed plates were made of the same material, and the water absorption issue would have to be investigated further. Another issue is whether a given plastic will hold its tuning, because of such instabilities, as compared to metals.

 

Apart from these practical issues, it’s interesting that, as shown in Table 3, their stress levels are generally within their strength capabilities, although I must admit to ignorance on their ability to withstand fatigue in this application.

 

The only thermosets I listed are composites incorporating carbon fiber or glass. Like the thermoplastics, these materials generally have normalized ratios less than brass, suggesting very mellow sounds, and from Table 3, they appear strong enough, although they perhaps offer low playing volume. In the literature, they are often described as “very fatigue resistant,” although any such claim must surely be application dependent, and it remains to be seen how well they would withstand the many cyclic stresses experienced as reed tongues. Incidentally, I think such a determination is quite easily made by a set-up incorporating an electric blower, with results obtainable after a couple weeks or so.

 

In Table 2, we now come to the woods, which interestingly show a wider range of normalized ratio than do the plastics, some even perhaps sounding more steel-like than does brass, and from Table 3, some look quite strong. With all woods, the direction of the grain is an important consideration. The performance of bamboo appears anomalous. This is perhaps not surprising, since bamboo is sometimes used to make Asian free reed tongues. Its normalized ratio of 7.2 suggests a very bright sound and perhaps a high playing volume, and from Table 3, it’s plenty strong enough to withstand its own generated stresses. Interestingly, its high normalized ratio is obtained not only by its relatively high modulus, but even more by means of it’s very low density. Perhaps it would be interesting to talk about this material with an experienced Asian free reed maker, and maybe this is what you really need to compete with those guitars.

 

Carbon fiber is interesting in many ways. If one can successfully make a reed tongue out of a bundle of long carbon fibers, with their unmatched strength and modulus, it promises an extremely bright tone, with possibly high playing volume.

 

6) Summary

 

In summary, the primary reason for this survey is to suggest to the curious what many hitherto unused materials might sound like, if they were successfully fashioned into free reed tongues. In working through it, we see how unique spring steel is, and perhaps why most other materials have a hard time competing with it for use as tongue material. But then again, there are people who may prefer brass, even accepting its potential drawbacks. Perhaps then the survey has identified an open-ended question with regard to some other possible contenders for tongue material; most notably, Beryllium Copper (1.9%), certain Nickel alloys that have been cold worked, various Titanium alloys, and maybe even a non-metal such as a composite, or even bamboo. These additional materials admit the possibility of a wider spectrum of tone and playing volume, although not completely without some unknown complications.

 

I’d be very interested in hearing from anyone who has made reed tongues from any of these alternative materials, so that we might compare notes.

 

Best regards,

Tom

www.bluesbox.biz

Free Reed Tongue Materials Survey Table.doc

[JimLucas]

1) The Known Difference

As far as I know, there are two materials most often used in making Western free reed tongues: steel and some Copper alloy, which is most often brass, but perhaps also bronze.

No equations, no tables, but a smattering of personal experience, augmented with hearsay:

• I have played one concertina with what I believe were nickel reeds, though I suppose "nickel silver" is a possibility. Its maximum volume was the least of any concertina I've played, and increasing the bellows pressure -- even suddenly -- didn't increase the volume, yet it didn't result in "choking", either. A lovely instrument for singing.
  
• I believe it's been reported that some of the earliest concertinas had gold reeds. A gold alloy, perhaps? Gold itself is very soft. In any case, that seems to have been an experiment that was quickly abandoned.
  
• As your table indicates, there are many different varieties of steel, brass, and other alloys, and it's certain that more than one of each (of steel and brass, anyway) have been used in concertinas.
  
  • At least some of the "non-ferrous" special orders made by Wheatstone long after steel reeds became standard are reported to be of brass which is more durable than the brass reeds which were once standard in cheaper instruments.
    
  • And I remember a comment made by Steve Dickinson back in the 1970's -- an over-generalization, I'm sure, but to make a point -- that with one file he could tune one Wheatstone or five Lachenals (before the file was worn enough to need replacing). I'm sure he was referring to differences in the hardness of steel most commonly used by the two firms.
    

[Chris Ghent]

Tom,

 

This is very interesting, frustrating too because for reasons coming from that other life, the one where concertinas are not as important, I do not have the time to put into it that I would like.

 

A table like this, and I understand, I think, the assumptions and compromises you have made in compiling it, is the sort of practical tool I always hope exists when I need a reference. None of my research is academic, it is looking for a specific result as quickly as possible, and as such I am not the perfect foil for you in these discussions.

 

A quick look at your table shows a couple of things, firstly materials are very shy of the middle ground in the SE column. Second, of the ones that are in the intermediate range where experimentation might most profitably (ie. we know a little of the sound of brass and of steel, can we find something half way in between so as not to be trying to detect small differences) occur, some have immediate isues. Beryllium is a significant hazard, especially if the dust is inhaled, always a danger when filing.

 

The Invar steel looks to fit the bill for a test. If it was to be available in a useable form without needing to buy a tonne I would be tempted to do the experiment, though it wouldn't happen soon. Added later, seems available here

 

You ask if anyone might have experience already with some of the materials. I understand some form of nickel, perhaps nickel/copper was not uncommon in early days of concertina making. Such a concertina was mentioned here recently, it was interpreted as part of tropicalising an instrument heading for warmer climes. The people with the most experience are likely to be Colin and Rosalie Dipper, as they make a wonderfully diverse range of concertinas. Colin told me he once made an instrument with titanium reeds, no alloy specified, his only comment was he would not do it again and I think it related to difficulty of manufacture rather than performance.

[Johann]

Hi ttonon,

 

I think you kow that did meke a few sampels of reeds with one type of

Titanium alloys.

 

And of corse the sound is diffent.

 

Johann