I have been studying, plotting and calculating the facing curves from this article (I believe I got a copy from Mojo) to get a feel for the general range of curve types in mouthpieces from this sample. 

 I'll post two spreadsheets of data in the Misc. folder for anyone that is interested. So far, I have only plotted and calculated curves for saxophone mouthpieces from the sample. I have a few specific questions along the way, but would be interested to hear any comments or suggestions regarding what I'm trying to do.
 

 I assumed the tip rail is .030 in all cases and used the solver to calculate elliptical curves. The curves in this sample have error sums anywhere from .06 to 23.67. If I look at the calculated curves with the largest error sums (over 9) it seems that there are two main reasons for the large error sum (am I missing other reasons?):
 

 1)The curve is nearly FLAT, with a sharp turn near to the table, and almost a straight line to the tip. (In this case I tried removing the constraint that the ellipse ratio be >= 1. This significantly improved the calculated curve fit in one case. Comments or suggestions?) Do these types of curves ever play well?
 

 OR
 2)The actual curve has one or more "outlier" plotted points that I believe to be a mistake--most likely in the measurement but possibly in the creation of the facing curve. (Comments or suggestions?)
 

 So from this sample ellipse ratios are from +1 to +12, with the vast majority being radial curves, and only a fifth or so with ratios higher than +3. It seems that higher elliptical ratio curves (+4 to +10) are becoming more and more common in modern mouthpieces. (But I haven't measured 100's of mouthpieces yet. Probably closer to 50.) Do you find this to be true generally? 

I have not found data from this article to be useful. I did a few spot checks comparing some vintage Woodwind mouthpieces that looked almost new and they did not compare well to the numbers in the article. 

There are several reasons why this is so.  In addition to the ones you mentioned there is manufacturing variation, typos, specs changing.  

As for the curves that become more flat near the tip, I think these grew out of a clarinet facing mentality.  These variations on a parabolic curve shape play better on clarinet IMO than sax.  

I think there has been a much better awareness of elliptical facings in the last 12 years or so thanks to this group.  Several manufacturers use a machining fixture that sweeps a radius to machine the facing curve.  There is a video showing Lebayle doing this on YouTube.  Since he does a little hand finishing near the tip rail, his mouthpieces often measure a little off radial, but they are close.  Same thing with Runyons and Jody Jazz DVs (though the DV facings are probably done on a CNC machine).

> On Apr 17, 2014, at 1:05 PM, <mike@...> wrote:
> 
> I have been studying, plotting and calculating the facing curves from this article (I believe I got a copy from Mojo) to get a feel for the general range of curve types in mouthpieces from this sample.
> 
> 
> I'll post two spreadsheets of data in the Misc. folder for anyone that is interested. So far, I have only plotted and calculated curves for saxophone mouthpieces from the sample. I have a few specific questions along the way, but would be interested to hear any comments or suggestions regarding what I'm trying to do.
> 
> I assumed the tip rail is .030 in all cases and used the solver to calculate elliptical curves. The curves in this sample have error sums anywhere from .06 to 23.67. If I look at the calculated curves with the largest error sums (over 9) it seems that there are two main reasons for the large error sum (am I missing other reasons?):
> 
> 1)The curve is nearly FLAT, with a sharp turn near to the table, and almost a straight line to the tip. (In this case I tried removing the constraint that the ellipse ratio be >= 1. This significantly improved the calculated curve fit in one case. Comments or suggestions?) Do these types of curves ever play well?
> 
> OR
> 2)The actual curve has one or more "outlier" plotted points that I believe to be a mistake--most likely in the measurement but possibly in the creation of the facing curve. (Comments or suggestions?)
> 
> So from this sample ellipse ratios are from +1 to +12, with the vast majority being radial curves, and only a fifth or so with ratios higher than +3. It seems that higher elliptical ratio curves (+4 to +10) are becoming more and more common in modern mouthpieces. (But I haven't measured 100's of mouthpieces yet. Probably closer to 50.) Do you find this to be true generally? 
> 

The parabolic/compound arc facing is advantageous on clarinet.  The considerable amount of reed damping by the lip/embouchure pressure required to get a characteristic professional sound, reduces the amount of embouchure corner/vocal tract control over the reed's resonance to the point where the player simply can't place that resonance correctly (to provide optimal tone and response) on a radial facing.  The more pronounced "springy" curve just after the table break provides the needed extra control.  

Since the modern saxophone schools promote, "less reed damping is more better",  which is also acoustically the case for that instrument, the extra sensitivity associated with a parabolic/compound arc facing become problematic over-kill when used on saxophone mouthpieces.  Optimal results are achieved usually, with a plain, radial facing.
On Thursday, April 17, 2014 1:56 PM, Keith Bradbury <kwbradbury@...> wrote:
 
  
I have not found data from this article to be useful. I did a few spot checks comparing some vintage Woodwind mouthpieces that looked almost new and they did not compare well to the numbers in the article. 

There are several reasons why this is so.  In addition to the ones you mentioned there is manufacturing variation, typos, specs changing.  

As for the curves that become more flat near the tip, I think these grew out of a clarinet facing mentality.  These variations on a parabolic curve shape play better on clarinet IMO than sax.  

I think there has been a much better awareness of elliptical facings in the last 12 years or so thanks to this group.  Several manufacturers use a machining fixture that sweeps a radius to machine the facing curve.  There is a video showing Lebayle doing this on YouTube.  Since he does a little hand finishing near the tip rail, his mouthpieces often measure a little off radial, but they are close.  Same thing with Runyons and Jody Jazz DVs (though the DV facings are probably done on a CNC machine).


On Apr 17, 2014, at 1:05 PM, <mike@mikewilkens.com> wrote:


  
>I have been studying, plotting and calculating the facing curves from this article (I believe I got a copy from Mojo) to get a feel for the general range of curve types in mouthpieces from this sample.
>
>
>I'll post two spreadsheets of data in the Misc. folder for anyone that is interested. So far, I have only plotted and calculated curves for saxophone mouthpieces from the sample. I have a few specific questions along the way, but would be interested to hear any comments or suggestions regarding what I'm trying to do.
>
>
>I assumed the tip rail is .030 in all cases and used the solver to calculate elliptical curves. The curves in this sample have error sums anywhere from .06 to 23.67. If I look at the calculated curves with the largest error sums (over 9) it seems that there are two main reasons for the large error sum (am I missing other reasons?):
>
>
>1)The curve is nearly FLAT, with a sharp turn near to the table, and almost a straight line to the tip. (In this case I tried removing the constraint that the ellipse ratio be >= 1. This significantly improved the calculated curve fit in one case. Comments or suggestions?) Do these types of curves ever play well?
>
>
>OR
>2)The actual curve has one or more "outlier" plotted points that I believe to be a mistake--most likely in the measurement but possibly in the creation of the facing curve. (Comments or suggestions?)
>
>
>So from this sample ellipse ratios are from +1 to +12, with the vast majority being radial curves, and only a fifth or so with ratios higher than +3. It seems that higher elliptical ratio curves (+4 to +10) are becoming more and more common in modern mouthpieces. (But I haven't measured 100's of mouthpieces yet. Probably closer to 50.) Do you find this to be true generally?