This is a follow-up question to the recent post I had..
 

 

 Upon stumbling on Theo's book, aside from the 5 feelers, I noticed that he did not put the tip rail measurements there..Is he measuring tip rails when refacing? If he does, what thickness does he use?
 

 Aside from the tip rail measurements, is he also using the Radial Facing Curve just like what we are using here?
 

 

 Thank you 

 

On 2016-08-03 1:47 pm, warren927736@... [MouthpieceWork]
wrote: 

This is a follow-up question to the recent post I had.. 

Upon
stumbling on Theo's book, aside from the 5 feelers, I noticed that he
did not put the tip rail measurements there..Is he measuring tip rails
when refacing? If he does, what thickness does he use? 

Aside from the
tip rail measurements, is he also using the Radial Facing Curve just
like what we are using here? 

Thank you


----------------------------------- 

Apparently not. 

Here is text
from an article I found, and a pdf of same which includes graphs. 

This
seems to have been pulled from the web, I couldn't find it on line,
although maybe the Wayback machine would have it. 

Barry Levine


----------------------- 

Genesis of 'The Ring' Equation for a Medium
Length Tenor Saxophone Mouthpiece Facing Curve 
 -Theo Wanne 

We
started by measuring the facing curves of over 50 original (never
refaced) tenor saxophone mouthpieces between the sizes of 5 and 10 that
played well in all registers. We used the Florida Period Otto Links of
the 1950s and 1960s as they have been the standard of the Jazz industry
for tenor saxophone and many of the Jazz Greats (Dexter Gordon, Stan
Getz, John Coltrane, etc.) played them.
 We started plotting the facing
curves using 8 points along the curve for each mouthpiece. Here, shown
in graph form, are the 8 plot points for the 7* Otto Link 'Super Tone
Master' curve. All points are shown in millimeters:

We then calculated
the break point on each mouthpiece. The break point is the point at
which the reed very first separates from the table, and states the
initial starting point of the curve. We then found the linear
relationship of the 'Break Point' to the tip opening. We found the rate
the break point increased relative to the increase in tip opening

The
actual tip opening measurement was added as the final plot point. Adding
the break point and the tip opening gave us 10 plot points in total for
each of the 50 mouthpieces. We combined the data for each tip opening to
find the average curve used by Otto Link for each tip opening in their
Florida mouthpieces. Here is an example of the 7* Otto Link 'Super Tone
Master' curve shown in millimeters:

We then combined Theo's personal
data gathered from years of maximizing the performance of Otto Link
mouthpieces. The new combined data represented an improved curve over
the original Otto link curve. Below is Theo's curve for a 7* tenor
saxophone mouthpiece based off of the data taken from the actual Otto
Link mouthpieces:

(Both vertical and horizontal scales are in mm.)
Each
curve (tip openings from 5 to 10) was then expressed in the form of a
quadratic equation (second degree polynomial). A unique quadratic
equation was created for each tip opening. Below is the curve for the 7*
tip opening using our quadratic equation to calculate the facing curve
data point:

R2 is a measure of how well an equation fits the data
points it is modeling. R2 values range from 0 (no fit) to 1.0 (a perfect
fit). Although we are showing variable place holders for our
coefficients, our R2 values are reflective of our actual data. As the R2
for the above equation is very close to 1, we have an excellent degree
of accuracy in our model.
We were then able to calculate the points for
each facing curve using their individual quadratic equations. Shown
below is a graph with all the facing curves (one for each tip opening
size) shown together.

Finally, we wanted to have one equation to
describe all the facing curves across the different tip openings. We
found that the tip opening has an accurate linear relationship to our
three coefficients (F1, F2, and F3) in our quadratic facing curve
equations. We then created a linear equation for each coefficient so
that our quadratic equation will model the change in the facing curves
as the tip opening changes: 
F1 = x2 coefficient = G1 * (Tip Opening)
+G2 (R2 = 0.968) 
F2 = x coefficient = H1* (Tip Opening) + H2 (R2 0.974) 
F3 = offset coefficient = I1* (Tip Opening) + I22 (R2 = 0.998)

As all our R2 values are very close to 1.0, we have excellent equations
to describe the change in our facing-curve equation coefficients based
on different tip opening.
'The Ring' or master equation, representing a
single quadratic equation to calculate the facing curves for all tip
opening from 5 up to 10, was then created. By simply plugging in the
desired tip opening and any desired distance from the tip, The Ring
equation will tell you its related facing curve plot point. This one
equation will show the optimal facing curve for any tenor saxophone
medium length facing curve. 

> 

 

hmmmmm... 

 

 So he uses a quadratic curve...
 

 

 

 Is there a formula for this in excel? 
 

 

 I read the article but I did not notice the formula that they use (or maybe I don't know how to translate it to excel formula)
 

 

 Do you have an idea how? 
 

 

 Thank you :)

 

I don't think Theo intended to totally to give away the shop on
this. 

Because the article seems to have been pulled from the web,
perhaps even the graphs are telling more than he'd like. But they're so
low resolution, I don't see how useful they could be. 

Barry Levine


On 2016-08-04 11:53 am, warren927736@... [MouthpieceWork] wrote:


> hmmmmm... 
> 
> So he uses a quadratic curve... 
> 
> Is there a
formula for this in excel? 
> 
> I read the article but I did not notice
the formula that they use (or maybe I don't know how to translate it to
excel formula) 
> 
> Do you have an idea how? 
> 
> Thank you :) 
>


 

Links:
------
[1]
https://groups.yahoo.com/neo/groups/MouthpieceWork/conversations/messages/12598;_ylc=X3oDMTJxZDA0aXR2BF9TAzk3MzU5NzE0BGdycElkAzYyODI5MDAEZ3Jwc3BJZAMxNzA1MDMyMTk4BG1zZ0lkAzEyNTk4BHNlYwNmdHIEc2xrA3JwbHkEc3RpbWUDMTQ3MDMyNjAzNw--?act=reply&messageNum598
[2]
mailto:warren927736@...?subject=Re%3A%20Tip%20Rail%20and%20Radial%20Facing%20Curve
[3]
mailto:MouthpieceWork@yahoogroups.com?subject=Re%3A%20Tip%20Rail%20and%20Radial%20Facing%20Curve
[4]
https://groups.yahoo.com/neo/groups/MouthpieceWork/conversations/newtopic;_ylc=X3oDMTJlMmhmNGZrBF9TAzk3MzU5NzE0BGdycElkAzYyODI5MDAEZ3Jwc3BJZAMxNzA1MDMyMTk4BHNlYwNmdHIEc2xrA250cGMEc3RpbWUDMTQ3MDMyNjAzNw--
[5]
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[6]
https://yho.com/1wwmgg
[7] https://yho.com/1wwmgg
[8]
http://groups.yahoo.com/group/MouthpieceWork
[9]
http://groups.yahoo.com/mygroups
[10]
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[13]
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[14]
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Ohhh i see... 

 

 Hmmm
 

 

 What is the purpose of the equation really? I mean the quadratic and radial curve.
 

 

 Which is widely/generally used, the quadratic or the radial curve?
  

You need a large data set to define the constants in Theo's curve formulation.  I think his brother may have actually done the math work.  

Quadratic safe great at fitting a variety of shapes.  But they can be unruly too.  They do not extrapolate well.  The formulation is not forced to be tangent to the table.  

His curve shapes are a little more parabolic than radial.  They curve more where the Reed is thick and less near the tip.  This is the opposite of the elliptical formulation many of us use.  Though an ellipse can be formulated to work this way too.  Many vintage Links have this facing curve shape which I suppose Theo had many readings of these facings.  They work fine but I do not think they are superior to radial and elliptical curves.

> On Aug 4, 2016, at 12:05 PM, warren927736@... [MouthpieceWork] <MouthpieceWork@yahoogroups.com> wrote:
> 
> Ohhh i see...
> 
> 
> 
> Hmmm
> 
> 
> What is the purpose of the equation really? I mean the quadratic and radial curve.
> 
> 
> Which is widely/generally used, the quadratic or the radial curve?
>  
>