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Greetings. In my first post in this series, I forgot to mention the fact that in the comparison plots between brass and steel, the tongue lengths are adjusted so that the brass and steel vibration has the same frequency. In my second post comparing carbon and steel, the two tongues have equal length, and in this post, I give results for carbon and steel tongue lengths having the same frequency. The amazing thing in this comparison is that the carbon normalized harmonics are enormously larger than those for steel. I honestly didn’t expect such dramatic results. And they show large difference even for the smallest bellows pressure. For me, this increases my curiosity over what a carbon fiber reed tongue would sound like. Notice also the dominance of the 5th harmonic over the 4th, for all but the lowest bellows pressures. I've noticed before the contentious battle between these two harmonics, and here it's well displayed. The docx file for this case is the same: https://app.box.com/folder/79305691686 Best regards, Tom
Greetings again. Here we compare steel to a titanium/tantalum alloy, Ti/Ta 70/30 Beta, which is used in surgical equipment and prosthetics. It interests me, not so much to propose it as tongue material, but because the tantalum increases the density well above the neat material. The modulus is only a third of that for steel, but its density is a little above that for steel, resulting in a modulus-to-density ratio about 0.3 that of steel. We can compare these results to those comparing Titanium to steel and find that the higher harmonic amplitudes in comparison to steel are very much less in the Ti/Ta alloy. The behavior with increasing bellows pressure shows the harmonic amplitudes making up the difference – just what happens in the Titanium/steel comparison; however, since the higher harmonics of the alloy start with such low values, they don’t catch up to those of steel nearly as quickly or as completely as in the case of the neat material. Comparing these plots with the plots for brass/steel, we see an enormous difference. If we can discern an audible difference in timbre between brass and steel, according to these plots, and if our basic assumptions are correct, there should be an enormous difference in timbre between either Ti or its Ti/Ta alloy and either brass or steel. Another interesting outcome in the case of the alloy is that I couldn’t get a convergence with a solution for bellows pressure less than about 2.2 inch w.c. On the other hand, solutions continue further on for the higher bellows pressure than they do for steel and other materials. This might indicate a material that may not be able to play at very low bellows pressures, but may perform better than other materials at the highest bellows pressures. The last plot in these calculations show that the trend of increasing harmonic amplitude with bellows pressure continues for even the highest bellows pressures, for those above solutions for steel become impossible. We can make such plots for most any feasible tongue material, though at some point, the usefulness tapers off, at least if we are in search of a practical tongue material. The theoretical interest continues, as a way of getting a good intuitive feel for the effect of material properties on musical tone. At this point, I think we need wait for experimentalists to compare information they have from work already accomplished or from new work. There might be other materials I'd like to do calculations on, such as glass, and other geometric factors, such as tongue thickness and plate thickness. A docx file showing these plots are at: https://app.box.com/folder/79305691686 Best regards, Tom
Greetings again to this series showing results of free reed response from an analytical treatment of free reed physics based on a fluid mechanical model. Titanium interests me because it has close to the same ratio of Young’s modulus to density as does steel, but the Young’s modulus and density are each roughly half that of steel. It thus can shed light on the question whether the ratio of these two material properties is all one needs to make a good educated guess about what a given material will sound like when it’s used as tongue material for a free reed. Others have wondered about using titanium as tongue material, and hopefully, the information presented here can assist in evaluating possible rewards from its use. On the acoustic results, to sum up, no, in the case of titanium, there are important influences on harmonic amplitude caused by individual contributions from modulus and density, and the ratio itself cannot describe all key effects. The docx file linked to below presents instructive plots comparing the harmonic amplitudes of titanium and steel. The results are most interesting in that, for low bellows pressure, titanium harmonic amplitudes are in general significantly less than those of steel, suggesting, if these amplitudes translate to the acoustic sound we hear, that titanium should have a mellower or less bright sound than steel. The prediction is that the sound should be even mellower than that of brass, in comparison to steel. However, as bellows pressure increases, this relationship changes, and the titanium harmonic amplitudes become comparable to those of steel, leading to the conclusion that titanium might sound similar to steel at these amplitudes. At the highest bellows pressure, there are a significant number of titanium amplitudes that surpass those of steel. This is the first example I’ve seen where the character of the sound has such a dynamic nature, with markedly different timbre occurring at high bellows pressure. In previous postings in this series, we’ve seen that brass should sound mellower than steel, with the effect increasing with increasing bellows pressure. Here we see similar behavior, only it’s the titanium that becomes bright, starting from a mellow beginning, in comparison to steel. If this is all true (that these harmonic amplitudes translate to the musical tone), I think it would be advantageous for the timbre of the sound to change so much with increasing volume. Such is the case with many other instruments. In general, any aspect of the musical tone that adds complexity to the sound can often be used as an expressive vehicle. Also, the direction of timbre movement with volume - from mellow to bright - is particularly advantageous and natural. Take for example the tenor sax. Low volume notes can be very mellow, with tender association, whereas loud sounds can be plaintive and attention-getting. As with the other documents in this series, the titanium results can be found at: https://app.box.com/folder/79305691686 Best regards, Tom