FREE REED PHYSICS - 4

[ttonon]

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

[Johann]

2 hours ago, ttonon said:

 

 

"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."

 

As i think you should know i did make sample reeds years ago with titanium and the measured  and heard sound is as you described it here.

 

 

 

[ttonon]

3 hours ago, Johann said:

As i think you should know i did make sample reeds years ago with titanium and the measured  and heard sound is as you described it here.

Hi Johann, if you have recordings of those sounds, it might be interesting to look at the Fourier spectrums and compare them to my results.

 

Best regards,

Tom