Hi,

In a discussion on SOTW, I had a brief exchange with Keith about elliptical curves.  

As he has stated here before, he prefers radial curves, but he uses elliptical curves also.  These curves have the major axis (long axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.

I have been thinking about an elliptical curve that has the major axis tilted from the perpendicular toward the tip - so that the curve is gentler at both the break from the table AND the tip.

I have seen mouthpieces with a gentle break (or, equivalently, a longer facing), and I have seen mouthpieces with a gentler curve at the tip. 

What I would like to start a discussion on is: 

1) Does anyone regularly use facing curves that have both these features (gentler curve at the break and gentler curve at the tip), and if so, are they elliptical?  No need to post possibly proprietary formulas...  

2) If not, then does anyone regularly use just one of these features?  

30 And (for the sake of completeness!) does anyone NOT use either of these features regularly, and if so why?

Thanks!
-Steve Keller  

--- In MouthpieceWork@yahoogroups.com, "Steve Keller" <esteban_cadenza@...> wrote:

> As he has stated here before, he prefers radial curves, but he uses elliptical curves also.  These curves have the major axis (long axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.
> 

Correction: These curves have the MINOR axis (SHORT axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.

So for your facing curve experiment, you would want to rotate this ellipse the other way.  The minor axis away from the tip.

Right you are about the minor vs major axis - of course, I meant "short" when I said "long" and "minor" when I said "major"...

(Luckily I don't confuse major and minor in music... too much...)

Anyway, the curve I am envisioning is this - an ellipse with the major axis tilted FROM the break TOWARD the tip - that is, the point at which the major axis intersects the curve is halfway along curve. (This is equivalent to the rotation Keith describes below.)

My question remains - has anyone ever used such a curve?

Thanks again, and sorry for the confusion.

-Steve Keller

--- In MouthpieceWork@yahoogroups.com, "Keith Bradbury" <kwbradbury@...> wrote:
>
> --- In MouthpieceWork@yahoogroups.com, "Steve Keller" <esteban_cadenza@> wrote:
> 
> > As he has stated here before, he prefers radial curves, but he uses elliptical curves also.  These curves have the major axis (long axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.
> > 
> 
> Correction: These curves have the MINOR axis (SHORT axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.
> 
> So for your facing curve experiment, you would want to rotate this ellipse the other way.  The minor axis away from the tip.
>

Hi friends!
(sorry my english language is terrorific, i am Argentine and speak only spanish)
You not know how of utility are all that information for me!! thing that gratefully!!
Now, will be possible explain the question of AXIS with photos or so much better with pictures or simple draws adjunts? because for all interested in this item not understand sufficiently what are you speaking!!
Fraternally yours
Silverio
from Argentine Patagonian

--- El mié 24-jun-09, Steve Keller <esteban_cadenza@...> escribió:

De: Steve Keller <esteban_cadenza@...>
Asunto: [MouthpieceWork] Re: Elliptical Facing Curves
Para: MouthpieceWork@yahoogroups.com
Fecha: miércoles, 24 de junio de 2009, 6:04 pm











    
            
            


      
      Right you are about the minor vs major axis - of course, I meant "short" when I said "long" and "minor" when I said "major"...



(Luckily I don't confuse major and minor in music... too much...)



Anyway, the curve I am envisioning is this - an ellipse with the major axis tilted FROM the break TOWARD the tip - that is, the point at which the major axis intersects the curve is halfway along curve. (This is equivalent to the rotation Keith describes below.)



My question remains - has anyone ever used such a curve?



Thanks again, and sorry for the confusion.



-Steve Keller



--- In MouthpieceWork@ yahoogroups. com, "Keith Bradbury" <kwbradbury@ ...> wrote:

>

> --- In MouthpieceWork@ yahoogroups. com, "Steve Keller" <esteban_cadenza@ > wrote:

> 

> > As he has stated here before, he prefers radial curves, but he uses elliptical curves also.  These curves have the major axis (long axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.

> > 

> 

> Correction: These curves have the MINOR axis (SHORT axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.

> 

> So for your facing curve experiment, you would want to rotate this ellipse the other way.  The minor axis away from the tip.

>




 

      

    
    
	
	 
	
	








	


	
	


      ____________________________________________________________________________________
¡Viví la mejor experiencia en la web!
Descargá gratis el nuevo Internet Explorer 8
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--- In MouthpieceWork@yahoogroups.com, "Steve Keller" <esteban_cadenza@...> wrote:
>
> Right you are about the minor vs major axis - of course, I meant "short" when I said "long" and "minor" when I said "major"...
> 
> (Luckily I don't confuse major and minor in music... too much...)
> 
> Anyway, the curve I am envisioning is this - an ellipse with the major axis tilted FROM the break TOWARD the tip - that is, the point at which the major axis intersects the curve is halfway along curve. (This is equivalent to the rotation Keith describes below.)
> 
> My question remains - has anyone ever used such a curve?
> 
> Thanks again, and sorry for the confusion.
> 
> -Steve Keller
> 
> --- In MouthpieceWork@yahoogroups.com, "Keith Bradbury" <kwbradbury@> wrote:
> >
> > --- In MouthpieceWork@yahoogroups.com, "Steve Keller" <esteban_cadenza@> wrote:
> > 
> > > As he has stated here before, he prefers radial curves, but he uses elliptical curves also.  These curves have the major axis (long axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.
> > > 
> > 
> > Correction: These curves have the MINOR axis (SHORT axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.
> > 
> > So for your facing curve experiment, you would want to rotate this ellipse the other way.  The minor axis away from the tip.
> >
>

I just did a job on a NY Link that JVW had previously done.  The curve he used on this one might fall into the category you describe.  It had a bit of a bulge in the middle, so you may be able to describe it as an ellipse with not much eccentricity that has been rotated a bit so that one axis is in the middle of the facing.

The effect this had was to emphasize the middle overtones(relative to a more traditional elliptical or a radial curve) without making the sound overly think.  I prefer Links to have a deeper voice than this, but I can imagine that it would have worked well with the smaller chamber that Jon had put in.

Since Morgan mentioned "the bulge", I have seen similar bulges maxed at the first 1/3rd of the facing curve.  These are fairly consistent in the WW&BW Guardala LTs (except for the newer MB2).  I do not know if a rotated ellipse will fit this bulge.  I do know that if I remove this bulge, the mouthpiece plays free-er and the low notes respond better.
 
I played around with plotting a rotated ellipse yesterday but the for I used is a long way off from being useful in generating a facing curve.  From Wikipedia:
 
General parametric form
An ellipse in general position can be expressed parametrically as the path of a point (X(t),Y(t)), where

 
 
for . Here (Xc,Yc) is the center of the ellipse, and φ is the angle between the X-axis and the major axis of the ellipse.
 
Issues include getting it centered so that it is tangent to the table and getting X(t), Y(t) spaced at the same intervals as you feelers and glass gage readings.  This can be done iteratively or some other formulation might be more useful.


      

I don't know how to put a picture in these messages, but here's a way to describe what I meant.

Think of a circle.  Now stretch that circle in one direction, so that it is more egg-shaped.  That is an ellipse.  The longest line that can fit in the ellipse that passes through the center is the MAJOR AXIS, and the shortest line that passes through the center is the MINOR AXIS.  

In a circle, these lines would be equal in length, they would both be the diameter of the circle.  In an ellipse one of the "diameter" lines is stretched.

Hope this helps.

-Steve Keller

P.S. The Wikipedia article on ellipse has way more information than this, including lots of formulas.  

http://en.wikipedia.org/wiki/Ellipse

--- In MouthpieceWork@yahoogroups.com, Silverio Potenza <silpopaar@...> wrote:
>
> Hi friends!
> (sorry my english language is terrorific, i am Argentine and speak only spanish)
> You not know how of utility are all that information for me!! thing that gratefully!!
> Now, will be possible explain the question of AXIS with photos or so much better with pictures or simple draws adjunts? because for all interested in this item not understand sufficiently what are you speaking!!
> Fraternally yours
> Silverio
> from Argentine Patagonian
> 
> --- El mié 24-jun-09, Steve Keller <esteban_cadenza@...> escribió:
> 
> De: Steve Keller <esteban_cadenza@...>
> Asunto: [MouthpieceWork] Re: Elliptical Facing Curves
> Para: MouthpieceWork@yahoogroups.com
> Fecha: miércoles, 24 de junio de 2009, 6:04 pm
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
>     
>             
>             
> 
> 
>       
>       Right you are about the minor vs major axis - of course, I meant "short" when I said "long" and "minor" when I said "major"...
> 
> 
> 
> (Luckily I don't confuse major and minor in music... too much...)
> 
> 
> 
> Anyway, the curve I am envisioning is this - an ellipse with the major axis tilted FROM the break TOWARD the tip - that is, the point at which the major axis intersects the curve is halfway along curve. (This is equivalent to the rotation Keith describes below.)
> 
> 
> 
> My question remains - has anyone ever used such a curve?
> 
> 
> 
> Thanks again, and sorry for the confusion.
> 
> 
> 
> -Steve Keller
> 
> 
> 
> --- In MouthpieceWork@ yahoogroups. com, "Keith Bradbury" <kwbradbury@ ...> wrote:
> 
> >
> 
> > --- In MouthpieceWork@ yahoogroups. com, "Steve Keller" <esteban_cadenza@ > wrote:
> 
> > 
> 
> > > As he has stated here before, he prefers radial curves, but he uses elliptical curves also.  These curves have the major axis (long axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.
> 
> > > 
> 
> > 
> 
> > Correction: These curves have the MINOR axis (SHORT axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.
> 
> > 
> 
> > So for your facing curve experiment, you would want to rotate this ellipse the other way.  The minor axis away from the tip.
> 
> >
> 
> 
> 
> 
>  
> 
>       
> 
>     
>     
> 	
> 	 
> 	
> 	
> 
> 
> 
> 
> 
> 
> 
> 
> 	
> 
> 
> 	
> 	
> 
> 
>       ____________________________________________________________________________________
> ¡Viví la mejor experiencia en la web!
> Descargá gratis el nuevo Internet Explorer 8
> http://downloads.yahoo.com/ieak8/?l=ar
>

Hi Steve...yes, all information to respect help, and very much.
 
1- Of fact, i know what is de elliptical curve; that is very simple of understand.
 
2- By my quality of technical drawer and illustrator i know well this questions;
but one thing is the literal explication and other is understand how are
applicated all on the real mouthpiece facing. In relation to your words i
will treat to draw that Axis.
 
3- For example: i know that the break point is very critical because condicionate
how and when start vibrations of the reed. I believe that the break and tip points
are the two fundamental things to keep in mind for a correct facing. 
 
4- Between this two point there are one straigh line. That is a commencement.
All radial or elliptical lines of the facing between this two points are condicionated
to the mouth or personal features of player. Nothing is strict. I believe that the
prove to sucess and error is the secret by to a good mouthpiece facing and
insist that lastest opinios neither are definitive.
 
5- The particular features of each mouth are unique and not always repeats.
 
Please send me simple coordenates (not formula) and i draw it. for ex.:
One straigh line how base line of mouthp. Other straigh angular line.
Length of this line and finally and fundamental line of facing dividided in ten
parts. Each part have a distance respect to the angular line. If you prefer
can divided in fifty or twenty parts by more correct  measurement.
 
thankful and fraternally yours
 
Silverio

--- El jue 25-jun-09, Steve Keller <esteban_cadenza@...> escribió:


De: Steve Keller <esteban_cadenza@...>
Asunto: [MouthpieceWork] Re: Elliptical Facing Curves
Para: MouthpieceWork@yahoogroups.com
Fecha: jueves, 25 de junio de 2009, 3:30 pm









I don't know how to put a picture in these messages, but here's a way to describe what I meant.

Think of a circle. Now stretch that circle in one direction, so that it is more egg-shaped. That is an ellipse. The longest line that can fit in the ellipse that passes through the center is the MAJOR AXIS, and the shortest line that passes through the center is the MINOR AXIS. 

In a circle, these lines would be equal in length, they would both be the diameter of the circle. In an ellipse one of the "diameter" lines is stretched.

Hope this helps.

-Steve Keller

P.S. The Wikipedia article on ellipse has way more information than this, including lots of formulas. 

http://en.wikipedia .org/wiki/ Ellipse

--- In MouthpieceWork@ yahoogroups. com, Silverio Potenza <silpopaar@. ..> wrote:
>
> Hi friends!
> (sorry my english language is terrorific, i am Argentine and speak only spanish)
> You not know how of utility are all that information for me!! thing that gratefully!!
> Now, will be possible explain the question of AXIS with photos or so much better with pictures or simple draws adjunts? because for all interested in this item not understand sufficiently what are you speaking!!
> Fraternally yours
> Silverio
> from Argentine Patagonian
> 
> --- El mié 24-jun-09, Steve Keller <esteban_cadenza@ ...> escribió:
> 
> De: Steve Keller <esteban_cadenza@ ...>
> Asunto: [MouthpieceWork] Re: Elliptical Facing Curves
> Para: MouthpieceWork@ yahoogroups. com
> Fecha: miércoles, 24 de junio de 2009, 6:04 pm
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> Right you are about the minor vs major axis - of course, I meant "short" when I said "long" and "minor" when I said "major"...
> 
> 
> 
> (Luckily I don't confuse major and minor in music... too much...)
> 
> 
> 
> Anyway, the curve I am envisioning is this - an ellipse with the major axis tilted FROM the break TOWARD the tip - that is, the point at which the major axis intersects the curve is halfway along curve. (This is equivalent to the rotation Keith describes below.)
> 
> 
> 
> My question remains - has anyone ever used such a curve?
> 
> 
> 
> Thanks again, and sorry for the confusion.
> 
> 
> 
> -Steve Keller
> 
> 
> 
> --- In MouthpieceWork@ yahoogroups. com, "Keith Bradbury" <kwbradbury@ ...> wrote:
> 
> >
> 
> > --- In MouthpieceWork@ yahoogroups. com, "Steve Keller" <esteban_cadenza@ > wrote:
> 
> > 
> 
> > > As he has stated here before, he prefers radial curves, but he uses elliptical curves also. These curves have the major axis (long axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.
> 
> > > 
> 
> > 
> 
> > Correction: These curves have the MINOR axis (SHORT axis) perpendicular to the table, so that the curve is gentlest at the break from the table, and sharpest at the tip.
> 
> > 
> 
> > So for your facing curve experiment, you would want to rotate this ellipse the other way. The minor axis away from the tip.
> 
> >
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> ____________ _________ _________ _________ _________ _________ _
> ¡Viví la mejor experiencia en la web!
> Descargá gratis el nuevo Internet Explorer 8
> http://downloads. yahoo.com/ ieak8/?l= ar
>

















      ____________________________________________________________________________________
¡Viví la mejor experiencia en la web!
Descargá gratis el nuevo Internet Explorer 8
http://downloads.yahoo.com/ieak8/?l=ar

Why not a double exponential curve? Something like this one:

y = A1*exp(-x/t1) + A2*exp(-x/t2) + y0

It fits any link I measured, modern and old ones... moreover scientists know that if we use a theoretical curve with a lot of parameters (6, 7, 8...) it will fit even better :) of course the problem is the physical meaning of these parameters. I am writing this because I noticed Link curves are not really radial neither exponential but they play in any case great. What I usually do is to start with an elleptical facing (thanks Mojo 4 sharing your knowledges) and finish it using my ears and my (few) skills as saxophone player to adapt the mouthpiece to the player needs. We should not forget a mouthpiece should play in spite of all the math we are using.

DannyG