It is interesting that you only use the radial curve and a   corresponding tangent to this for a model.  I'm not sure why you eliminate all the other possibilities...secants for example. I'm not an engineer but I see no reason for using this theoretical model. 
 If you take three points on a clarinet facing for example 24, 12, 6 readings this might be a good starting point to form a radial curve rather than starting from a radial curve and it's tangent.  I'm not sure of the historical basis for this approach.    
  

There are a number of facing curves that can work besides a radial curve that is tangent at the table.  But there are many more that do not work well.  I think the requirement that the curve be tangent at the table is essential.  Otherwise you will have a kink in the facing that the reed can not seal when it bends.  Air will leak out the sides and response will be poor.

You can make a curve that passes through your 24, 12, 6 points and then hand blend it into the table so there is no kink.  But then it is not a true radial curve anymore.  However it may work great.  But you can not calculate a good target for the .0015" feeler gage.  You will be hand adjusting the facing length until it blends in.  I prefer to calculate good number targets and work towards them.  You can do whatever you want. 

A radial facing curve is a good simple curve that works well on sax mouthpieces.  I do not think it is the best shape for clarinet mouthpieces.  Elliptical facing curves that are tangent to the table are good curves that give you one more variable you can adjust to add resistance to the facing curve.  I have a PowerPoint presentation on my site that was part of a clinic I gave on refacing.  You can download it to see some illustrations of these facing curves.




________________________________
From: John <john_w_price33@...>
To: MouthpieceWork@yahoogroups.com
Sent: Thu, March 4, 2010 2:11:56 PM
Subject: [MouthpieceWork] Radial Curves yet again,

  
It is interesting that you only use the radial curve and a corresponding tangent to this for a model. I'm not sure why you eliminate all the other possibilities. ..secants for example. I'm not an engineer but I see no reason for using this theoretical model. 
If you take three points on a clarinet facing for example 24, 12, 6 readings this might be a good starting point to form a radial curve rather than starting from a radial curve and it's tangent. I'm not sure of the historical basis for this approach. 


      

The curve has to be tangent to the table.  If you angle a radial curve so that the table intersects the curve (use the table as a secant instead of tangent), you have a steeper and more abrupt transition from table to curve, which experience will quickly tell you doesn't play well.

I can't speak for everybody, but when I started experimenting with refacing, I made a spreadsheet for plotting radial curves using only lenght and width because a) the table IS tangential to the curve, and b)it was the simplest way I could figure how to do it.  No trig, just some simple back-of-an-envelope geometry.

We could get into the historical reasons for and pros/cons to using a  radial curve in the first place, but that's maybe another question.  FWIW I use a radial curve pretty much never these days.


--- In MouthpieceWork@yahoogroups.com, "John" <john_w_price33@...> wrote:
>
> It is interesting that you only use the radial curve and a   corresponding tangent to this for a model.  I'm not sure why you eliminate all the other possibilities...secants for example. I'm not an engineer but I see no reason for using this theoretical model. 
>  If you take three points on a clarinet facing for example 24, 12, 6 readings this might be a good starting point to form a radial curve rather than starting from a radial curve and it's tangent.  I'm not sure of the historical basis for this approach.
>

Thanks Keith,   As I replied to Morgan I think that having a larger diameter circle will "unkink" the facing....more gradual beginning of he curve.  

--- In MouthpieceWork@yahoogroups.com, Keith Bradbury <kwbradbury@...> wrote:
>
> There are a number of facing curves that can work besides a radial curve that is tangent at the table.  But there are many more that do not work well.  I think the requirement that the curve be tangent at the table is essential.  Otherwise you will have a kink in the facing that the reed can not seal when it bends.  Air will leak out the sides and response will be poor.
> 
> You can make a curve that passes through your 24, 12, 6 points and then hand blend it into the table so there is no kink.  But then it is not a true radial curve anymore.  However it may work great.  But you can not calculate a good target for the .0015" feeler gage.  You will be hand adjusting the facing length until it blends in.  I prefer to calculate good number targets and work towards them.  You can do whatever you want. 
> 
> A radial facing curve is a good simple curve that works well on sax mouthpieces.  I do not think it is the best shape for clarinet mouthpieces.  Elliptical facing curves that are tangent to the table are good curves that give you one more variable you can adjust to add resistance to the facing curve.  I have a PowerPoint presentation on my site that was part of a clinic I gave on refacing.  You can download it to see some illustrations of these facing curves.
> 
> 
> 
> 
> ________________________________
> From: John <john_w_price33@...>
> To: MouthpieceWork@yahoogroups.com
> Sent: Thu, March 4, 2010 2:11:56 PM
> Subject: [MouthpieceWork] Radial Curves yet again,
> 
>   
> It is interesting that you only use the radial curve and a corresponding tangent to this for a model. I'm not sure why you eliminate all the other possibilities. ..secants for example. I'm not an engineer but I see no reason for using this theoretical model. 
> If you take three points on a clarinet facing for example 24, 12, 6 readings this might be a good starting point to form a radial curve rather than starting from a radial curve and it's tangent. I'm not sure of the historical basis for this approach.
>

I disagree with this 
 " (use the table as a secant instead of tangent),
you have a steeper and more abrupt transition from table to curve, which
experience will quickly tell you doesn't play well."  
    If you use a secant it will give you a steeper curve but you can then use a bigger circle to make it "unsteep". I realize how theoretical this is but since this board talks about missing cone sections etc I thought it not out of line.  thanks  
  


--- In MouthpieceWork@yahoogroups.com, "Morgan" <frymorgan@...> wrote:
>
> 
> The curve has to be tangent to the table.  If you angle a radial curve so that the table intersects the curve (use the table as a secant instead of tangent), you have a steeper and more abrupt transition from table to curve, which experience will quickly tell you doesn't play well.
> 
> I can't speak for everybody, but when I started experimenting with refacing, I made a spreadsheet for plotting radial curves using only lenght and width because a) the table IS tangential to the curve, and b)it was the simplest way I could figure how to do it.  No trig, just some simple back-of-an-envelope geometry.
> 
> We could get into the historical reasons for and pros/cons to using a  radial curve in the first place, but that's maybe another question.  FWIW I use a radial curve pretty much never these days.
> 
> 
> --- In MouthpieceWork@yahoogroups.com, "John" <john_w_price33@> wrote:
> >
> > It is interesting that you only use the radial curve and a   corresponding tangent to this for a model.  I'm not sure why you eliminate all the other possibilities...secants for example. I'm not an engineer but I see no reason for using this theoretical model. 
> >  If you take three points on a clarinet facing for example 24, 12, 6 readings this might be a good starting point to form a radial curve rather than starting from a radial curve and it's tangent.  I'm not sure of the historical basis for this approach.
> >
>

The larger the dimeter gets, the less curved the facing gets.  It starts to approach a straight line which gives you the maximum kink.  If you round off the kink, you will in effect be using a small radius at that point.




________________________________
From: John <john_w_price33@hotmail.com>
To: MouthpieceWork@yahoogroups.com
Sent: Fri, March 5, 2010 1:45:13 PM
Subject: [MouthpieceWork] Re: Radial Curves yet again,

  
Thanks Keith, As I replied to Morgan I think that having a larger diameter circle will "unkink" the facing....more gradual beginning of he curve. 


      

Ok, yes, you could do this.  As your radius gets larger the curve will approach a straight line, which as Keith observes, will give you the least smooth transition into the curve.  A few minutes' observation (with compass and straightedge if you have to) will make it clear that a curve to which the table is tangential must have the smoothest transition regardless of any other features.  Try a few curves and you will see how important a feature a smooth transition into the curve is.

That said, don't get the impression that a radial curve tangential to the table is the only way to go.  It's just easy to model and simple to machine, and is probably the least resistant possible curve.  A wide variety of curves work.  If you want to use a different model, by all means.  I do.  
  
--- In MouthpieceWork@...m, "John" <john_w_price33@...> wrote:
>
> I disagree with this 
>  " (use the table as a secant instead of tangent),
> you have a steeper and more abrupt transition from table to curve, which
> experience will quickly tell you doesn't play well."  
>     If you use a secant it will give you a steeper curve but you can then use a bigger circle to make it "unsteep". I realize how theoretical this is but since this board talks about missing cone sections etc I thought it not out of line.  thanks  
>   
> 
> 
> --- In MouthpieceWork@yahoogroups.com, "Morgan" <frymorgan@> wrote:
> >
> > 
> > The curve has to be tangent to the table.  If you angle a radial curve so that the table intersects the curve (use the table as a secant instead of tangent), you have a steeper and more abrupt transition from table to curve, which experience will quickly tell you doesn't play well.
> > 
> > I can't speak for everybody, but when I started experimenting with refacing, I made a spreadsheet for plotting radial curves using only lenght and width because a) the table IS tangential to the curve, and b)it was the simplest way I could figure how to do it.  No trig, just some simple back-of-an-envelope geometry.
> > 
> > We could get into the historical reasons for and pros/cons to using a  radial curve in the first place, but that's maybe another question.  FWIW I use a radial curve pretty much never these days.
> > 
> > 
> > --- In MouthpieceWork@yahoogroups.com, "John" <john_w_price33@> wrote:
> > >
> > > It is interesting that you only use the radial curve and a   corresponding tangent to this for a model.  I'm not sure why you eliminate all the other possibilities...secants for example. I'm not an engineer but I see no reason for using this theoretical model. 
> > >  If you take three points on a clarinet facing for example 24, 12, 6 readings this might be a good starting point to form a radial curve rather than starting from a radial curve and it's tangent.  I'm not sure of the historical basis for this approach.
> > >
> >
>

I really don't understand "kink".  if the curve is approaching a straight line there should be no kink whatsoever. ie a very smooth transition. 

--- In MouthpieceWork@yahoogroups.com, Keith Bradbury <kwbradbury@...> wrote:
>
> The larger the dimeter gets, the less curved the facing gets.  It starts to approach a straight line which gives you the maximum kink.  If you round off the kink, you will in effect be using a small radius at that point.
> 
> 
> 
> 
> ________________________________
> From: John <john_w_price33@...>
> To: MouthpieceWork@yahoogroups.com
> Sent: Fri, March 5, 2010 1:45:13 PM
> Subject: [MouthpieceWork] Re: Radial Curves yet again,
> 
>   
> Thanks Keith, As I replied to Morgan I think that having a larger diameter circle will "unkink" the facing....more gradual beginning of he curve.
>

The "kink" is where the curve breaks awy from the table.  If the curve is a straight line, then there is a sharp corner where it connects to the table.  If there is no kink, and the "curve" is straight, there is no tip opening!

--- In MouthpieceWork@yahoogroups.com, "John" <john_w_price33@...> wrote:
>
> I really don't understand "kink".  if the curve is approaching a straight line there should be no kink whatsoever. ie a very smooth transition. 
> 
> --- In MouthpieceWork@yahoogroups.com, Keith Bradbury <kwbradbury@> wrote:
> >
> > The larger the dimeter gets, the less curved the facing gets.  It starts to approach a straight line which gives you the maximum kink.  If you round off the kink, you will in effect be using a small radius at that point.
> > 
> > 
> > 
> > 
> > ________________________________
> > From: John <john_w_price33@>
> > To: MouthpieceWork@yahoogroups.com
> > Sent: Fri, March 5, 2010 1:45:13 PM
> > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > 
> >   
> > Thanks Keith, As I replied to Morgan I think that having a larger diameter circle will "unkink" the facing....more gradual beginning of he curve.
> >
>

I don't follow your use of the word "kink" either.

The first, and most applicable to this discussion, definition of "kink" on
freedictionary.com is:

1. A tight curl, twist, or bend in a length of thin material, as one caused
by the tensing of a looped section of wire.

The change in a mouthpiece where the table meets the facing curve is most
decidedly *not* a tight curl.

It is a point of tangency. ( http://en.wikipedia.org/wiki/Tangent )

You are certainly free to impart your own personal meanings to  words, but
the end result is "babel." (see http://www.thefreedictionary.com/babel )

FWIW

Barry

> From: "Morgan" <frymorgan@...>
> Reply-To: MouthpieceWork@yahoogroups.com
> Date: Sat, 06 Mar 2010 05:32:14 -0000
> To: MouthpieceWork@yahoogroups.com
> Subject: [MouthpieceWork] Re: Radial Curves yet again,
> 
> 
>  
> The "kink" is where the curve breaks awy from the table.  If the curve is a
> straight line, then there is a sharp corner where it connects to the table.
> If there is no kink, and the "curve" is straight, there is no tip opening!
> 
> --- In MouthpieceWork@yahoogroups.com
> <mailto:MouthpieceWork%40yahoogroups.com> , "John" <john_w_price33@...> wrote:
>> >
>> > I really don't understand "kink".  if the curve is approaching a straight
>> line there should be no kink whatsoever. ie a very smooth transition.
>> > 
>> > --- In MouthpieceWork@yahoogroups.com
>> <mailto:MouthpieceWork%40yahoogroups.com> , Keith Bradbury <kwbradbury@>
>> wrote:
>>> > >
>>> > > The larger the dimeter gets, the less curved the facing gets.  It starts
>>> to approach a straight line which gives you the maximum kink.  If you round
>>> off the kink, you will in effect be using a small radius at that point.
>>> > > 
>>> > > 
>>> > > 
>>> > > 
>>> > > ________________________________
>>> > > From: John <john_w_price33@>
>>> > > To: MouthpieceWork@yahoogroups.com
>>> <mailto:MouthpieceWork%40yahoogroups.com>
>>> > > Sent: Fri, March 5, 2010 1:45:13 PM
>>> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
>>> > > 
>>> > >   
>>> > > Thanks Keith, As I replied to Morgan I think that having a larger
>>> diameter circle will "unkink" the facing....more gradual beginning of he
>>> curve.
>>> > >
>> >
> 
> 
> 
> 

So that we're using it to mean a tight bend in the facing curve isntead of "on thin material" makes this usage confusing?    

To your point that the table is tangential to the curve, whether this is necessarily so is what we are discussing.  If instead of a tangent, you consider the table a secant (as posited by John), you end up with a tight bend (a kink, if I may be so bold) where curve meets table.  The longer the radius of the curve for a given tip opening, the farther from tangential the table gets, and the tighter the curve at this point, up to the point where you have an infinite radius, a straight line, and a sharp angle instead of a curve.  

--- In MouthpieceWork@yahoogroups.com, Barry Levine <barrylevine@...> wrote:
>
> I don't follow your use of the word "kink" either.
> 
> The first, and most applicable to this discussion, definition of "kink" on
> freedictionary.com is:
> 
> 1. A tight curl, twist, or bend in a length of thin material, as one caused
> by the tensing of a looped section of wire.
> 
> The change in a mouthpiece where the table meets the facing curve is most
> decidedly *not* a tight curl.
> 
> It is a point of tangency. ( http://en.wikipedia.org/wiki/Tangent )
> 
> You are certainly free to impart your own personal meanings to  words, but
> the end result is "babel." (see http://www.thefreedictionary.com/babel )
> 
> FWIW
> 
> Barry
> 
> > From: "Morgan" <frymorgan@...>
> > Reply-To: MouthpieceWork@yahoogroups.com
> > Date: Sat, 06 Mar 2010 05:32:14 -0000
> > To: MouthpieceWork@yahoogroups.com
> > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > 
> > 
> >  
> > The "kink" is where the curve breaks awy from the table.  If the curve is a
> > straight line, then there is a sharp corner where it connects to the table.
> > If there is no kink, and the "curve" is straight, there is no tip opening!
> > 
> > --- In MouthpieceWork@yahoogroups.com
> > <mailto:MouthpieceWork%40yahoogroups.com> , "John" <john_w_price33@> wrote:
> >> >
> >> > I really don't understand "kink".  if the curve is approaching a straight
> >> line there should be no kink whatsoever. ie a very smooth transition.
> >> > 
> >> > --- In MouthpieceWork@yahoogroups.com
> >> <mailto:MouthpieceWork%40yahoogroups.com> , Keith Bradbury <kwbradbury@>
> >> wrote:
> >>> > >
> >>> > > The larger the dimeter gets, the less curved the facing gets.  It starts
> >>> to approach a straight line which gives you the maximum kink.  If you round
> >>> off the kink, you will in effect be using a small radius at that point.
> >>> > > 
> >>> > > 
> >>> > > 
> >>> > > 
> >>> > > ________________________________
> >>> > > From: John <john_w_price33@>
> >>> > > To: MouthpieceWork@yahoogroups.com
> >>> <mailto:MouthpieceWork%40yahoogroups.com>
> >>> > > Sent: Fri, March 5, 2010 1:45:13 PM
> >>> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> >>> > > 
> >>> > >   
> >>> > > Thanks Keith, As I replied to Morgan I think that having a larger
> >>> diameter circle will "unkink" the facing....more gradual beginning of he
> >>> curve.
> >>> > >
> >> >
> > 
> > 
> > 
> >
>

Since "kink" is probably not a math term, we could try "vertex" or "function discontinuity". 




________________________________
From: Morgan <frymorgan@...>
To: MouthpieceWork@yahoogroups.com
Sent: Sat, March 6, 2010 10:13:09 AM
Subject: [MouthpieceWork] Re: Radial Curves yet again,

  
So that we're using it to mean a tight bend in the facing curve isntead of "on thin material" makes this usage confusing? 

To your point that the table is tangential to the curve, whether this is necessarily so is what we are discussing. If instead of a tangent, you consider the table a secant (as posited by John), you end up with a tight bend (a kink, if I may be so bold) where curve meets table. The longer the radius of the curve for a given tip opening, the farther from tangential the table gets, and the tighter the curve at this point, up to the point where you have an infinite radius, a straight line, and a sharp angle instead of a curve. 

--- In MouthpieceWork@ yahoogroups. com, Barry Levine <barrylevine@ ...> wrote:
>
> I don't follow your use of the word "kink" either.
> 
> The first, and most applicable to this discussion, definition of "kink" on
> freedictionary. com is:
> 
> 1. A tight curl, twist, or bend in a length of thin material, as one caused
> by the tensing of a looped section of wire.
> 
> The change in a mouthpiece where the table meets the facing curve is most
> decidedly *not* a tight curl.
> 
> It is a point of tangency. ( http://en.wikipedia.org/wiki/Tangent )
> 
> You are certainly free to impart your own personal meanings to words, but
> the end result is "babel." (see http://www.thefreed ictionary. com/babel )
> 
> FWIW
> 
> Barry
> 
> > From: "Morgan" <frymorgan@. ..>
> > Reply-To: MouthpieceWork@ yahoogroups. com
> > Date: Sat, 06 Mar 2010 05:32:14 -0000
> > To: MouthpieceWork@ yahoogroups. com
> > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > 
> > 
> > 
> > The "kink" is where the curve breaks awy from the table. If the curve is a
> > straight line, then there is a sharp corner where it connects to the table.
> > If there is no kink, and the "curve" is straight, there is no tip opening!
> > 
> > --- In MouthpieceWork@ yahoogroups. com
> > <mailto:MouthpieceW ork%40yahoogroup s.com> , "John" <john_w_price33@ > wrote:
> >> >
> >> > I really don't understand "kink". if the curve is approaching a straight
> >> line there should be no kink whatsoever. ie a very smooth transition.
> >> > 
> >> > --- In MouthpieceWork@ yahoogroups. com
> >> <mailto:MouthpieceW ork%40yahoogroup s.com> , Keith Bradbury <kwbradbury@ >
> >> wrote:
> >>> > >
> >>> > > The larger the dimeter gets, the less curved the facing gets.  It starts
> >>> to approach a straight line which gives you the maximum kink.  If you round
> >>> off the kink, you will in effect be using a small radius at that point.
> >>> > > 
> >>> > > 
> >>> > > 
> >>> > > 
> >>> > > ____________ _________ _________ __
> >>> > > From: John <john_w_price33@ >
> >>> > > To: MouthpieceWork@ yahoogroups. com
> >>> <mailto:MouthpieceW ork%40yahoogroup s.com>
> >>> > > Sent: Fri, March 5, 2010 1:45:13 PM
> >>> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> >>> > > 
> >>> > >   
> >>> > > Thanks Keith, As I replied to Morgan I think that having a larger
> >>> diameter circle will "unkink" the facing....more gradual beginning of he
> >>> curve.
> >>> > >
> >> >
> > 
> > 
> > 
> >
>





      

Tell the math police we're calling it an inflection point.  But I still think of it as a kink.

--- In MouthpieceWork@yahoogroups.com, Keith Bradbury <kwbradbury@...> wrote:
>
> Since "kink" is probably not a math term, we could try "vertex" or "function discontinuity". 
> 
> 
> 
> 
> ________________________________
> From: Morgan <frymorgan@...>
> To: MouthpieceWork@yahoogroups.com
> Sent: Sat, March 6, 2010 10:13:09 AM
> Subject: [MouthpieceWork] Re: Radial Curves yet again,
> 
>   
> So that we're using it to mean a tight bend in the facing curve isntead of "on thin material" makes this usage confusing? 
> 
> To your point that the table is tangential to the curve, whether this is necessarily so is what we are discussing. If instead of a tangent, you consider the table a secant (as posited by John), you end up with a tight bend (a kink, if I may be so bold) where curve meets table. The longer the radius of the curve for a given tip opening, the farther from tangential the table gets, and the tighter the curve at this point, up to the point where you have an infinite radius, a straight line, and a sharp angle instead of a curve. 
> 
> --- In MouthpieceWork@ yahoogroups. com, Barry Levine <barrylevine@ ...> wrote:
> >
> > I don't follow your use of the word "kink" either.
> > 
> > The first, and most applicable to this discussion, definition of "kink" on
> > freedictionary. com is:
> > 
> > 1. A tight curl, twist, or bend in a length of thin material, as one caused
> > by the tensing of a looped section of wire.
> > 
> > The change in a mouthpiece where the table meets the facing curve is most
> > decidedly *not* a tight curl.
> > 
> > It is a point of tangency. ( http://en.wikipedia.org/wiki/Tangent )
> > 
> > You are certainly free to impart your own personal meanings to words, but
> > the end result is "babel." (see http://www.thefreed ictionary. com/babel )
> > 
> > FWIW
> > 
> > Barry
> > 
> > > From: "Morgan" <frymorgan@ ..>
> > > Reply-To: MouthpieceWork@ yahoogroups. com
> > > Date: Sat, 06 Mar 2010 05:32:14 -0000
> > > To: MouthpieceWork@ yahoogroups. com
> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > > 
> > > 
> > > 
> > > The "kink" is where the curve breaks awy from the table. If the curve is a
> > > straight line, then there is a sharp corner where it connects to the table.
> > > If there is no kink, and the "curve" is straight, there is no tip opening!
> > > 
> > > --- In MouthpieceWork@ yahoogroups. com
> > > <mailto:MouthpieceW ork%40yahoogroup s.com> , "John" <john_w_price33@ > wrote:
> > >> >
> > >> > I really don't understand "kink". if the curve is approaching a straight
> > >> line there should be no kink whatsoever. ie a very smooth transition.
> > >> > 
> > >> > --- In MouthpieceWork@ yahoogroups. com
> > >> <mailto:MouthpieceW ork%40yahoogroup s.com> , Keith Bradbury <kwbradbury@ >
> > >> wrote:
> > >>> > >
> > >>> > > The larger the dimeter gets, the less curved the facing gets.  It starts
> > >>> to approach a straight line which gives you the maximum kink.  If you round
> > >>> off the kink, you will in effect be using a small radius at that point.
> > >>> > > 
> > >>> > > 
> > >>> > > 
> > >>> > > 
> > >>> > > ____________ _________ _________ __
> > >>> > > From: John <john_w_price33@ >
> > >>> > > To: MouthpieceWork@ yahoogroups. com
> > >>> <mailto:MouthpieceW ork%40yahoogroup s.com>
> > >>> > > Sent: Fri, March 5, 2010 1:45:13 PM
> > >>> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > >>> > > 
> > >>> > >   
> > >>> > > Thanks Keith, As I replied to Morgan I think that having a larger
> > >>> diameter circle will "unkink" the facing....more gradual beginning of he
> > >>> curve.
> > >>> > >
> > >> >
> > > 
> > > 
> > > 
> > >
> >
>

I checked the results of Ferron's missing cone formulas, which use a numerical constant as a shortcut(?), against complete applicable formulas, and got some interesting results.  Maybe someone would care to check my formulas/calculations.  We'll use John's recent study as an example.

Neck tube measurements

length (l) = 173mm
radius (r) = 6.3mm
radius (R) = 11.9mm

A theoretical incomplete neck tube, with these dimensions, forms a right conical frustum, so we can use this simple formula to calculate the distance from it's top to it's theoretical apex, or the missing cone's length (mcl)

mcl  =  (l*r/(R-r))  

Compare my results with John/Ferron's

MM mcl = 194.62mm
JBT/Ferron mcl = 213.7mm

Standard cone volume calculations for missing cone using above lengths (mcv):

MM mcv = 8.08cl
JBT/Ferron mcv = 8.88cl

The cone taper (ct) is calculated from the right triangle formed by the missing cone base radius (r) and it's length measurement (mcl).  

Degrees(Atan(r/mcl)) = ct (Excel Functions)

MM ct = 1.854 degrees
JBT/Ferron ct = 1.689 degrees

Applying the formulas to John's body taper measurements resulted in similar discrepancies, however to lesser degree, so it would seem that Ferron's constant is less accurate for smaller numbers.















      

What I’ve got in mind is a marking system like this:

 

Our Super Duck tenor mouthpiece has a facing that reads 49 on a standard
gauge and a somewhat high baffle, so a .105 would be marked 105/49/1

Our Blues Blaster tenor mouthpiece has a facing that reads 48, and a low
baffle, so a .105 would be marked 105/48/3

Our Rottweiler tenor mouthpiece has a facing that reads 51 and a very high
baffle, so a .105 would be market 105/51/0

 

It might be a good idea to label the baffles A,B,C & D so as not to confuse
with the Berg Larsen system

 

From: MouthpieceWork@yahoogroups.com [mailto:MouthpieceWork@yahoogroups.com]
On Behalf Of Morgan
Sent: Saturday, March 06, 2010 1:17 PM
To: MouthpieceWork@yahoogroups.com
Subject: [MouthpieceWork] Re: Radial Curves yet again,

 

  


Tell the math police we're calling it an inflection point. But I still think
of it as a kink.

--- In MouthpieceWork@yahoogroups.com
<mailto:MouthpieceWork%40yahoogroups.com> , Keith Bradbury <kwbradbury@...>
wrote:
>
> Since "kink" is probably not a math term, we could try "vertex" or
"function discontinuity". 
> 
> 
> 
> 
> ________________________________
> From: Morgan <frymorgan@...>
> To: MouthpieceWork@yahoogroups.com
<mailto:MouthpieceWork%40yahoogroups.com> 
> Sent: Sat, March 6, 2010 10:13:09 AM
> Subject: [MouthpieceWork] Re: Radial Curves yet again,
> 
> Â  
> So that we're using it to mean a tight bend in the facing curve isntead of
"on thin material" makes this usage confusing? 
> 
> To your point that the table is tangential to the curve, whether this is
necessarily so is what we are discussing. If instead of a tangent, you
consider the table a secant (as posited by John), you end up with a tight
bend (a kink, if I may be so bold) where curve meets table. The longer the
radius of the curve for a given tip opening, the farther from tangential the
table gets, and the tighter the curve at this point, up to the point where
you have an infinite radius, a straight line, and a sharp angle instead of a
curve. 
> 
> --- In MouthpieceWork@ yahoogroups. com, Barry Levine <barrylevine@ ...>
wrote:
> >
> > I don't follow your use of the word "kink" either.
> > 
> > The first, and most applicable to this discussion, definition of "kink"
on
> > freedictionary. com is:
> > 
> > 1. A tight curl, twist, or bend in a length of thin material, as one
caused
> > by the tensing of a looped section of wire.
> > 
> > The change in a mouthpiece where the table meets the facing curve is
most
> > decidedly *not* a tight curl.
> > 
> > It is a point of tangency. ( http://en.wikipedia.org/wiki/Tangent )
> > 
> > You are certainly free to impart your own personal meanings to words,
but
> > the end result is "babel." (see http://www.thefreed ictionary. com/babel
)
> > 
> > FWIW
> > 
> > Barry
> > 
> > > From: "Morgan" <frymorgan@ ..>
> > > Reply-To: MouthpieceWork@ yahoogroups. com
> > > Date: Sat, 06 Mar 2010 05:32:14 -0000
> > > To: MouthpieceWork@ yahoogroups. com
> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > > 
> > > 
> > > 
> > > The "kink" is where the curve breaks awy from the table. If the curve
is a
> > > straight line, then there is a sharp corner where it connects to the
table.
> > > If there is no kink, and the "curve" is straight, there is no tip
opening!
> > > 
> > > --- In MouthpieceWork@ yahoogroups. com
> > > <mailto:MouthpieceW ork%40yahoogroup s.com> , "John" <john_w_price33@
> wrote:
> > >> >
> > >> > I really don't understand "kink". if the curve is approaching a
straight
> > >> line there should be no kink whatsoever. ie a very smooth transition.
> > >> > 
> > >> > --- In MouthpieceWork@ yahoogroups. com
> > >> <mailto:MouthpieceW ork%40yahoogroup s.com> , Keith Bradbury
<kwbradbury@ >
> > >> wrote:
> > >>> > >
> > >>> > > The larger the dimeter gets, the less curved the facing gets.Â
It starts
> > >>> to approach a straight line which gives you the maximum kink.  If
you round
> > >>> off the kink, you will in effect be using a small radius at that
point.
> > >>> > > 
> > >>> > > 
> > >>> > > 
> > >>> > > 
> > >>> > > ____________ _________ _________ __
> > >>> > > From: John <john_w_price33@ >
> > >>> > > To: MouthpieceWork@ yahoogroups. com
> > >>> <mailto:MouthpieceW ork%40yahoogroup s.com>
> > >>> > > Sent: Fri, March 5, 2010 1:45:13 PM
> > >>> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > >>> > > 
> > >>> > > Â  
> > >>> > > Thanks Keith, As I replied to Morgan I think that having a
larger
> > >>> diameter circle will "unkink" the facing....more gradual beginning
of he
> > >>> curve.
> > >>> > >
> > >> >
> > > 
> > > 
> > > 
> > >
> >
>

I'd only add to that, that it's not a tight bend.  A tight bend would be an
acute angle that was rounded off.

Enough. I'm not your book editor. But feel free to get in a last word :)

> From: "Morgan" <frymorgan@...>
> Reply-To: MouthpieceWork@yahoogroups.com
> Date: Sat, 06 Mar 2010 19:16:33 -0000
> To: MouthpieceWork@yahoogroups.com
> Subject: [MouthpieceWork] Re: Radial Curves yet again,
> 
>> > So that we're using it to mean a tight bend in the facing curve isntead of
>> "on thin material" makes this usage confusing?
> 

I think mouthpiece manufactures have historically shied away from giving the actual numbers for a number of reasons:

1. They did not want their competitors to know.

2. They knew 99% of their customers were not able to measure them anyway.

3. Their manufacturing tolerances were not good enough to ensure consistent measurements, therefore giving the numbers as a designation carried the risk of false advertising.

Points 2 and 3 have changed over the last decade with the wider use of computer controlled manufacture, availability of measuring gauges and better customer knowledge shared over the web.

Vandoren usefully used to give both the tip opening and the facing length but now only give the tip opening and general length (S,M,L etc)

Units: I understand the logic and history behind the Brand measuring system, but it is still kinda nutty to use two different units to measure the one object, as well as a mix of imperial and metric, both in non-standard denominations.  It would be great if tip opening and length were given in standard international measurements for distance: millimeters.

Also need to say where the length is taken from; at the 0.04mm (0.0015 inch) gauge or absolute length?  And is tip opening measured from outer or inner tip rail?

My 2 cents anyway.  Andrew


--- In MouthpieceWork@yahoogroups.com, "STEVE GOODSON" <saxgourmet@...> wrote:
>
> What I've got in mind is a marking system like this:
> 
>  
> 
> Our Super Duck tenor mouthpiece has a facing that reads 49 on a standard
> gauge and a somewhat high baffle, so a .105 would be marked 105/49/1
> 
> Our Blues Blaster tenor mouthpiece has a facing that reads 48, and a low
> baffle, so a .105 would be marked 105/48/3
> 
> Our Rottweiler tenor mouthpiece has a facing that reads 51 and a very high
> baffle, so a .105 would be market 105/51/0
> 
>  
> 
> It might be a good idea to label the baffles A,B,C & D so as not to confuse
> with the Berg Larsen system
> 
>  
> 
> From: MouthpieceWork@yahoogroups.com [mailto:MouthpieceWork@yahoogroups.com]
> On Behalf Of Morgan
> Sent: Saturday, March 06, 2010 1:17 PM
> To: MouthpieceWork@yahoogroups.com
> Subject: [MouthpieceWork] Re: Radial Curves yet again,
> 
>  
> 
>   
> 
> 
> Tell the math police we're calling it an inflection point. But I still think
> of it as a kink.
> 
> --- In MouthpieceWork@yahoogroups.com
> <mailto:MouthpieceWork%40yahoogroups.com> , Keith Bradbury <kwbradbury@>
> wrote:
> >
> > Since "kink" is probably not a math term, we could try "vertex" or
> "function discontinuity". 
> > 
> > 
> > 
> > 
> > ________________________________
> > From: Morgan <frymorgan@>
> > To: MouthpieceWork@yahoogroups.com
> <mailto:MouthpieceWork%40yahoogroups.com> 
> > Sent: Sat, March 6, 2010 10:13:09 AM
> > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > 
> > Â  
> > So that we're using it to mean a tight bend in the facing curve isntead of
> "on thin material" makes this usage confusing? 
> > 
> > To your point that the table is tangential to the curve, whether this is
> necessarily so is what we are discussing. If instead of a tangent, you
> consider the table a secant (as posited by John), you end up with a tight
> bend (a kink, if I may be so bold) where curve meets table. The longer the
> radius of the curve for a given tip opening, the farther from tangential the
> table gets, and the tighter the curve at this point, up to the point where
> you have an infinite radius, a straight line, and a sharp angle instead of a
> curve. 
> > 
> > --- In MouthpieceWork@ yahoogroups. com, Barry Levine <barrylevine@ ...>
> wrote:
> > >
> > > I don't follow your use of the word "kink" either.
> > > 
> > > The first, and most applicable to this discussion, definition of "kink"
> on
> > > freedictionary. com is:
> > > 
> > > 1. A tight curl, twist, or bend in a length of thin material, as one
> caused
> > > by the tensing of a looped section of wire.
> > > 
> > > The change in a mouthpiece where the table meets the facing curve is
> most
> > > decidedly *not* a tight curl.
> > > 
> > > It is a point of tangency. ( http://en.wikipedia.org/wiki/Tangent )
> > > 
> > > You are certainly free to impart your own personal meanings to words,
> but
> > > the end result is "babel." (see http://www.thefreed ictionary. com/babel
> )
> > > 
> > > FWIW
> > > 
> > > Barry
> > > 
> > > > From: "Morgan" <frymorgan@ ..>
> > > > Reply-To: MouthpieceWork@ yahoogroups. com
> > > > Date: Sat, 06 Mar 2010 05:32:14 -0000
> > > > To: MouthpieceWork@ yahoogroups. com
> > > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > > > 
> > > > 
> > > > 
> > > > The "kink" is where the curve breaks awy from the table. If the curve
> is a
> > > > straight line, then there is a sharp corner where it connects to the
> table.
> > > > If there is no kink, and the "curve" is straight, there is no tip
> opening!
> > > > 
> > > > --- In MouthpieceWork@ yahoogroups. com
> > > > <mailto:MouthpieceW ork%40yahoogroup s.com> , "John" <john_w_price33@
> > wrote:
> > > >> >
> > > >> > I really don't understand "kink". if the curve is approaching a
> straight
> > > >> line there should be no kink whatsoever. ie a very smooth transition.
> > > >> > 
> > > >> > --- In MouthpieceWork@ yahoogroups. com
> > > >> <mailto:MouthpieceW ork%40yahoogroup s.com> , Keith Bradbury
> <kwbradbury@ >
> > > >> wrote:
> > > >>> > >
> > > >>> > > The larger the dimeter gets, the less curved the facing gets.Â
> It starts
> > > >>> to approach a straight line which gives you the maximum kink.  If
> you round
> > > >>> off the kink, you will in effect be using a small radius at that
> point.
> > > >>> > > 
> > > >>> > > 
> > > >>> > > 
> > > >>> > > 
> > > >>> > > ____________ _________ _________ __
> > > >>> > > From: John <john_w_price33@ >
> > > >>> > > To: MouthpieceWork@ yahoogroups. com
> > > >>> <mailto:MouthpieceW ork%40yahoogroup s.com>
> > > >>> > > Sent: Fri, March 5, 2010 1:45:13 PM
> > > >>> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > > >>> > > 
> > > >>> > > Â  
> > > >>> > > Thanks Keith, As I replied to Morgan I think that having a
> larger
> > > >>> diameter circle will "unkink" the facing....more gradual beginning
> of he
> > > >>> curve.
> > > >>> > >
> > > >> >
> > > > 
> > > > 
> > > > 
> > > >
> > >
> >
>

MOUTHPICE NUMBERS THAT MEAN SOMTHING? THAT'S TOO EASY TO EVER CATCH ON! :-) I was asked the same two part question for every mouthpiece I had faced. What tip opening and what facing length do you want? It would make finding the right one easier if everyone did it.

Why do we use Metric for one measurement and inches on the other? (I missed that explanation.) All one system might be even easier to understand.

E v e r e t t  F i d l e r

--- In MouthpieceWork@yahoogroups.com, "STEVE GOODSON" <saxgourmet@...> wrote:
>
> What I've got in mind is a marking system like this:
> 
>  
> 
> Our Super Duck tenor mouthpiece has a facing that reads 49 on a standard
> gauge and a somewhat high baffle, so a .105 would be marked 105/49/1
> 
> Our Blues Blaster tenor mouthpiece has a facing that reads 48, and a low
> baffle, so a .105 would be marked 105/48/3
> 
> Our Rottweiler tenor mouthpiece has a facing that reads 51 and a very high
> baffle, so a .105 would be market 105/51/0
> 
>  
> 
> It might be a good idea to label the baffles A,B,C & D so as not to confuse
> with the Berg Larsen system
> 

One thing to keep in mind is the fact that the very end of the neck is often a radical departure from the rest of the neck and body. Many necks have an almost cylindrical end; others are "necked in", apparently. If you simply take the ratio of the radius of the two ends of then neck (or actually
 the top of the tenon and the end) you risk ending up with a very inaccurate picture of the real cone angle, which will take your careful calculations to hell and back.

I suggest that you "map" the angle by taking measurements of the neck every couple of cms or so, then graph them. If you find that the end of the neck departs from the cone angle of the rest of the neck, extrapolate the main cone angle to find what the radius of the cone angle would be at the end
 of the neck if the cone angle continued. Then use that to make your calculation of the missing apex. 

The actual difference in volume in a cone angle change at the end of the neck is rather small, but it makes a big difference if you just plug in numbers to find the missing cone volume. A cylindrical end piece on the neck would make the missing cone volume appear significantly larger than it would
 if the neck continued its conical angle to the end.

Toby

MartinMods <lancelotburt@...> wrote:                                           I checked the results of Ferron's missing cone formulas, which use a numerical constant as a shortcut(?), against complete applicable formulas, and got some interesting results.  Maybe someone would care to check
 my formulas/calculations.  We'll use John's recent study as an example.

Neck tube measurements

length (l) = 173mm
radius (r) = 6.3mm
radius (R) = 11.9mm

A theoretical incomplete neck tube, with these dimensions, forms a right conical frustum, so we can use this simple formula to calculate the distance from it's top to it's theoretical apex, or the missing cone's length (mcl)

mcl  =  (l*r/(R-r))  

Compare my results with John/Ferron's

MM mcl = 194.62mm
JBT/Ferron mcl = 213.7mm

Standard cone volume calculations for missing cone using above lengths (mcv):

MM mcv =  8.08cl
JBT/Ferron mcv = 8.88cl

The cone taper (ct) is calculated from the right triangle formed by the missing cone base radius (r) and it's length measurement (mcl).  

Degrees(Atan(r/mcl)) = ct (Excel Functions)

MM ct = 1.854 degrees
JBT/Ferron ct = 1.689 degrees

Applying the formulas to John's body taper measurements resulted in similar discrepancies, however to lesser degree, so it would seem that Ferron's constant is less accurate for smaller numbers.













        
      
                 
                 
 

Hi Lance,

Try dividing the 22.8 mm diameter by 2 again and put that radius into
your computations to see what you get.

There is nothing wrong with Ferron's slope formula.  It is not a
shortcut.  In fact, it is a clever way to eliminate some steps in the
computation of the slope of a cone.  If you are interested, PM me and I
will explain how he arrives at that formula.

I hope this puts the matter to rest once and for all.   To answer your
other concern, the interior of the neck was measured using telescoping
bore gauges which give a highly accurate measurement when used with a
digital caliper.

John


--- In MouthpieceWork@yahoogroups.com, MartinMods <lancelotburt@...>
wrote:
>
> I checked the results of Ferron's missing cone formulas, which use a
numerical constant as a shortcut(?), against complete applicable
formulas, and got some interesting results.  Maybe someone would care to
check my formulas/calculations.  We'll use John's recent study as an
example.
>
> Neck tube measurements
>
> length (l) = 173mm
> radius (r) = 6.3mm
> radius (R) = 11.9mm
>
> A theoretical incomplete neck tube, with these dimensions, forms a
right conical frustum, so we can use this simple formula to calculate
the distance from it's top to it's theoretical apex, or the missing
cone's length (mcl)
>
> mcl  =  (l*r/(R-r))
>
> Compare my results with John/Ferron's
>
> MM mcl = 194.62mm
> JBT/Ferron mcl = 213.7mm
>
> Standard cone volume calculations for missing cone using above lengths
(mcv):
>
> MM mcv = 8.08cl
> JBT/Ferron mcv = 8.88cl
>
> The cone taper (ct) is calculated from the right triangle formed by
the missing cone base radius (r) and it's length measurement (mcl).
>
> Degrees(Atan(r/mcl)) = ct (Excel Functions)
>
> MM ct = 1.854 degrees
> JBT/Ferron ct = 1.689 degrees
>
> Applying the formulas to John's body taper measurements resulted in
similar discrepancies, however to lesser degree, so it would seem that
Ferron's constant is less accurate for smaller numbers.
>

"There is nothing wrong with Ferron's slope formula."

Thanks for checking that.  I see I confused your 23.8mm body diameter with your 22.8mm neck diameter.  Easy to do amidst all the numbers.  

You mustn't take this personal, as it is not meant to be.  I find the missing cone issue and the directly related mouthpiece design considerations fascinating.  I continuously get emails from players asking if the Benade pip will fix their sharp D2-F2 problems, and very often (tenors usually), initial testing indicates that mouthpiece volume issues are the cause.  

As comprehensive and impressive as your study is, I certainly don't think it can be considered definitive for every saxophone and every mouthpiece, nor do I consider it entirely accurate in itself, in that there are unaccounted for volumes (neck and gap) and lengths (gap). Also, FYI - the accurate simple frustum formula says the missing cone, projected on the body tube (446mm length, 23.55mm and 11.90mm radii, is 455.57mm long, compared to your 457.63mm.  Only 2 mm, but, either all the numbers are important and accounted for or non of them are. IMO. 

Formula: The exceedingly simple mcl = r*l/(R-r) formula enables attaining the missing cone volume in two simple calculations (length, then volume), compared to Ferron's three calculations (angle, then length, then volume).  If three calculations are simpler than two, then by all means, use Ferron's formula.  Knowing the taper is interesting, but not essential for finding the missing cone volume. The taper angle can be obtained from the right triangle formed by the missing cone radius and length easily enough.

Putting the matter to rest:  Though you say you welcome other similar studies, it would appear that you would not be receptive to any comparison to your results or your method, as the above mentioned issues would certainly come up, at least in my analysis.  I am preparing now, a few comprehensive studies based upon completely disassembled horns (Magna alto, The Martin Alto, Handcraft alto, Zyphyr alto, The Martin Tenor, Zephyr tenor, Conn Chu tenor, Conn Wonder Tenor, Conn 10m tenor, Martin Indiana tenor, Conn Wonder II baritone, Conn 12m baritone, The Martin Baritone, King Vol True Baritone, and a Martin (Buescher stencil) bass), which allows for direct internal caliper measurement (1/2 the margin of error compared to your method.  By the way.  I have the same telescoping gauges.  I'm confused as to how you were able to take 3 or 4 accurate internal diameter measurements, at different radial degrees of the body base (just above the bow), without
 taking the bow off.)

I'll post my studies on the MartinMods website.  As your study is published online, I will feel free to make any comparisons and analysis I feel relevant.  







      

Thanks Toby.  I was thinking along those same lines.  I appreciate your
positive comments and suggestions.  I have made another scale drawing of
the neck used in the study and have discovered some interesting
information about the design of the neck and the relationships of its
parts.

The drawing can be seen at:  Mouthpiece Detail
<http://jbtsaxmusic.homestead.com/Detailed_SBA_neck_measurements.pdf>

All of the acoustic studies I have done can be found at:  Acoustics
Studies <http://jbtsaxmusic.homestead.com/Acoustics.html>

When I find the time, I will upgrade the website to give it a more
formal look, but for now this will have to do.





John






--- In MouthpieceWork@yahoogroups.com, <kymarto123@...> wrote:
>
> One thing to keep in mind is the fact that the very end of the neck is
often a radical departure from the rest of the neck and body. Many necks
have an almost cylindrical end; others are "necked in", apparently. If
you simply take the ratio of the radius of the two ends of then neck (or
actually
>  the top of the tenon and the end) you risk ending up with a very
inaccurate picture of the real cone angle, which will take your careful
calculations to hell and back.
>
> I suggest that you "map" the angle by taking measurements of the neck
every couple of cms or so, then graph them. If you find that the end of
the neck departs from the cone angle of the rest of the neck,
extrapolate the main cone angle to find what the radius of the cone
angle would be at the end
>  of the neck if the cone angle continued. Then use that to make your
calculation of the missing apex.
>
> The actual difference in volume in a cone angle change at the end of
the neck is rather small, but it makes a big difference if you just plug
in numbers to find the missing cone volume. A cylindrical end piece on
the neck would make the missing cone volume appear significantly larger
than it would
>  if the neck continued its conical angle to the end.
>
> Toby
>
> MartinMods lancelotburt@... wrote:
I checked the results of Ferron's missing cone formulas, which use a
numerical constant as a shortcut(?), against complete applicable
formulas, and got some interesting results.  Maybe someone would care to
check
>  my formulas/calculations.  We'll use John's recent study as an
example.
>
> Neck tube measurements
>
> length (l) = 173mm
> radius (r) = 6.3mm
> radius (R) = 11.9mm
>
> A theoretical incomplete neck tube, with these dimensions, forms a
right conical frustum, so we can use this simple formula to calculate
the distance from it's top to it's theoretical apex, or the missing
cone's length (mcl)
>
> mcl  =  (l*r/(R-r))
>
> Compare my results with John/Ferron's
>
> MM mcl = 194.62mm
> JBT/Ferron mcl = 213.7mm
>
> Standard cone volume calculations for missing cone using above lengths
(mcv):
>
> MM mcv =  8.08cl
> JBT/Ferron mcv = 8.88cl
>
> The cone taper (ct) is calculated from the right triangle formed by
the missing cone base radius (r) and it's length measurement (mcl).
>
> Degrees(Atan(r/mcl)) = ct (Excel Functions)
>
> MM ct = 1.854 degrees
> JBT/Ferron ct = 1.689 degrees
>
> Applying the formulas to John's body taper measurements resulted in
similar discrepancies, however to lesser degree, so it would seem that
Ferron's constant is less accurate for smaller numbers.
>

Lance,

You may want to spare yourself some future embarrassment by checking
your own math before attacking someone else's work and asserting they
are wrong.  It is good to hear you are  doing some research of your own
for a change rather than just criticizing what others have done.  Good
luck with your efforts.  I'm looking forward to reviewing your methods
and findings and comparing them with my own.

John




--- In MouthpieceWork@yahoogroups.com, MartinMods <lancelotburt@...>
wrote:
>
> "There is nothing wrong with Ferron's slope formula."
>
> Thanks for checking that.  I see I confused your 23.8mm body diameter
with your 22.8mm neck diameter.  Easy to do amidst all the numbers.
>
> You mustn't take this personal, as it is not meant to be.  I find the
missing cone issue and the directly related mouthpiece design
considerations fascinating.  I continuously get emails from players
asking if the Benade pip will fix their sharp D2-F2 problems, and very
often (tenors usually), initial testing indicates that mouthpiece volume
issues are the cause.
>
> As comprehensive and impressive as your study is, I certainly don't
think it can be considered definitive for every saxophone and every
mouthpiece, nor do I consider it entirely accurate in itself, in that
there are unaccounted for volumes (neck and gap) and lengths (gap).
Also, FYI - the accurate simple frustum formula says the missing cone,
projected on the body tube (446mm length, 23.55mm and 11.90mm radii, is
455.57mm long, compared to your 457.63mm.  Only 2 mm, but, either all
the numbers are important and accounted for or non of them are. IMO.
>
> Formula: The exceedingly simple mcl = r*l/(R-r) formula enables
attaining the missing cone volume in two simple calculations (length,
then volume), compared to Ferron's three calculations (angle, then
length, then volume).  If three calculations are simpler than two, then
by all means, use Ferron's formula.  Knowing the taper is interesting,
but not essential for finding the missing cone volume. The taper angle
can be obtained from the right triangle formed by the missing cone
radius and length easily enough.
>
> Putting the matter to rest:  Though you say you welcome other similar
studies, it would appear that you would not be receptive to any
comparison to your results or your method, as the above mentioned issues
would certainly come up, at least in my analysis.  I am preparing now, a
few comprehensive studies based upon completely disassembled horns
(Magna alto, The Martin Alto, Handcraft alto, Zyphyr alto, The Martin
Tenor, Zephyr tenor, Conn Chu tenor, Conn Wonder Tenor, Conn 10m tenor,
Martin Indiana tenor, Conn Wonder II baritone, Conn 12m baritone, The
Martin Baritone, King Vol True Baritone, and a Martin (Buescher stencil)
bass), which allows for direct internal caliper measurement (1/2 the
margin of error compared to your method.  By the way.  I have the same
telescoping gauges.  I'm confused as to how you were able to take 3 or 4
accurate internal diameter measurements, at different radial degrees of
the body base (just above the bow), without
>  taking the bow off.)
>
> I'll post my studies on the MartinMods website.  As your study is
published online, I will feel free to make any comparisons and analysis
I feel relevant.
>

Thanks John,

I'm not the least bit embarrassed to make an honest mistake.  That's part of the process.




--- On Mon, 3/8/10, John <jtalcott47@...> wrote:

From: John <jtalcott47@...>
Subject: [MouthpieceWork] Re: Accuracy of Ferron's Constant
To: MouthpieceWork@yahoogroups.com
Date: Monday, March 8, 2010, 4:27 AM







 



  


    
      
      
      


Lance,

You may want to spare yourself some future embarrassment by checking your own math before attacking someone else's work and asserting they are wrong.  It is good to hear you are  doing some research of your own for a change rather than just criticizing what others have done.  Good luck with your efforts.  I'm looking forward to reviewing your methods and findings and comparing them with my own.

John




--- In MouthpieceWork@ yahoogroups. com, MartinMods <lancelotburt@ ...> wrote:
>
> "There is nothing wrong with Ferron's slope formula."
> 
> Thanks for checking that.  I see I confused your 23.8mm body diameter with your 22.8mm neck diameter.  Easy to do amidst all the numbers.  
> 
> You mustn't take this personal, as it is not meant to be.  I find the missing cone issue and the directly related mouthpiece design considerations fascinating.  I continuously get emails from players asking if the Benade pip will fix their sharp D2-F2 problems, and very often (tenors usually), initial testing indicates that mouthpiece volume issues are the cause.  
> 
> As comprehensive and impressive as your study is, I certainly don't think it can be considered definitive for every saxophone and every mouthpiece, nor do I consider it entirely accurate in itself, in that there are unaccounted for volumes (neck and gap) and lengths (gap). Also, FYI - the accurate simple frustum formula says the missing cone, projected on the body tube (446mm length, 23.55mm and 11.90mm radii, is 455.57mm long, compared to your 457.63mm.  Only 2 mm, but, either all the numbers are important and accounted for or non of them are. IMO. 
> 
> Formula: The exceedingly simple mcl = r*l/(R-r) formula enables attaining the missing cone volume in two simple calculations (length, then volume), compared to Ferron's three calculations (angle, then length, then volume).  If three calculations are simpler than two, then by all means, use Ferron's formula.  Knowing the taper is interesting, but not essential for finding the missing cone volume. The taper angle can be obtained from the right triangle formed by the missing cone radius and length easily enough.
> 
> Putting the matter to rest:  Though you say you welcome other similar studies, it would appear that you would not be receptive to any comparison to your results or your method, as the above mentioned issues would certainly come up, at least in my analysis.  I am preparing now, a few comprehensive studies based upon completely disassembled horns (Magna alto, The Martin Alto, Handcraft alto, Zyphyr alto, The Martin Tenor, Zephyr tenor, Conn Chu tenor, Conn Wonder Tenor, Conn 10m tenor, Martin Indiana tenor, Conn Wonder II baritone, Conn 12m baritone, The Martin Baritone, King Vol True Baritone, and a Martin (Buescher stencil) bass), which allows for direct internal caliper measurement (1/2 the margin of error compared to your method.  By the way.  I have the same telescoping gauges.  I'm confused as to how you were able to take 3 or 4 accurate internal diameter measurements, at different radial degrees of the body base (just above the bow), without
>  taking the bow off.)
> 
> I'll post my studies on the MartinMods website.  As your study is published online, I will feel free to make any comparisons and analysis I feel relevant. 
>




    
     

    
    


 



  






      

I understand that if one uses a straight line from the tip of the mouthpiece to where the facing begins as facing then there would certainly be a "kink"...the reed would have difficulty with this.  What I was referring to is a radial curve that as it gets bigger with a larger and larger radius has no kink.  You are just flattening out the arc and approaching a perfectly flat table leading to a perfectly flat facing curve.  No kink..   

--- In MouthpieceWork@yahoogroups.com, "Morgan" <frymorgan@...> wrote:
>
> 
> Tell the math police we're calling it an inflection point.  But I still think of it as a kink.
> 
> --- In MouthpieceWork@yahoogroups.com, Keith Bradbury <kwbradbury@> wrote:
> >
> > Since "kink" is probably not a math term, we could try "vertex" or "function discontinuity". 
> > 
> > 
> > 
> > 
> > ________________________________
> > From: Morgan <frymorgan@>
> > To: MouthpieceWork@yahoogroups.com
> > Sent: Sat, March 6, 2010 10:13:09 AM
> > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > 
> >   
> > So that we're using it to mean a tight bend in the facing curve isntead of "on thin material" makes this usage confusing? 
> > 
> > To your point that the table is tangential to the curve, whether this is necessarily so is what we are discussing. If instead of a tangent, you consider the table a secant (as posited by John), you end up with a tight bend (a kink, if I may be so bold) where curve meets table. The longer the radius of the curve for a given tip opening, the farther from tangential the table gets, and the tighter the curve at this point, up to the point where you have an infinite radius, a straight line, and a sharp angle instead of a curve. 
> > 
> > --- In MouthpieceWork@ yahoogroups. com, Barry Levine <barrylevine@ ...> wrote:
> > >
> > > I don't follow your use of the word "kink" either.
> > > 
> > > The first, and most applicable to this discussion, definition of "kink" on
> > > freedictionary. com is:
> > > 
> > > 1. A tight curl, twist, or bend in a length of thin material, as one caused
> > > by the tensing of a looped section of wire.
> > > 
> > > The change in a mouthpiece where the table meets the facing curve is most
> > > decidedly *not* a tight curl.
> > > 
> > > It is a point of tangency. ( http://en.wikipedia.org/wiki/Tangent )
> > > 
> > > You are certainly free to impart your own personal meanings to words, but
> > > the end result is "babel." (see http://www.thefreed ictionary. com/babel )
> > > 
> > > FWIW
> > > 
> > > Barry
> > > 
> > > > From: "Morgan" <frymorgan@ ..>
> > > > Reply-To: MouthpieceWork@ yahoogroups. com
> > > > Date: Sat, 06 Mar 2010 05:32:14 -0000
> > > > To: MouthpieceWork@ yahoogroups. com
> > > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > > > 
> > > > 
> > > > 
> > > > The "kink" is where the curve breaks awy from the table. If the curve is a
> > > > straight line, then there is a sharp corner where it connects to the table.
> > > > If there is no kink, and the "curve" is straight, there is no tip opening!
> > > > 
> > > > --- In MouthpieceWork@ yahoogroups. com
> > > > <mailto:MouthpieceW ork%40yahoogroup s.com> , "John" <john_w_price33@ > wrote:
> > > >> >
> > > >> > I really don't understand "kink". if the curve is approaching a straight
> > > >> line there should be no kink whatsoever. ie a very smooth transition.
> > > >> > 
> > > >> > --- In MouthpieceWork@ yahoogroups. com
> > > >> <mailto:MouthpieceW ork%40yahoogroup s.com> , Keith Bradbury <kwbradbury@ >
> > > >> wrote:
> > > >>> > >
> > > >>> > > The larger the dimeter gets, the less curved the facing gets.  It starts
> > > >>> to approach a straight line which gives you the maximum kink.  If you round
> > > >>> off the kink, you will in effect be using a small radius at that point.
> > > >>> > > 
> > > >>> > > 
> > > >>> > > 
> > > >>> > > 
> > > >>> > > ____________ _________ _________ __
> > > >>> > > From: John <john_w_price33@ >
> > > >>> > > To: MouthpieceWork@ yahoogroups. com
> > > >>> <mailto:MouthpieceW ork%40yahoogroup s.com>
> > > >>> > > Sent: Fri, March 5, 2010 1:45:13 PM
> > > >>> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > > >>> > > 
> > > >>> > >   
> > > >>> > > Thanks Keith, As I replied to Morgan I think that having a larger
> > > >>> diameter circle will "unkink" the facing....more gradual beginning of he
> > > >>> curve.
> > > >>> > >
> > > >> >
> > > > 
> > > > 
> > > > 
> > > >
> > >
> >
>

Oh I forgot...thanks for all the responses. I am respectful and appreciative of all clarification on this subject. 

--- In MouthpieceWork@yahoogroups.com, "Morgan" <frymorgan@...> wrote:
>
> So that we're using it to mean a tight bend in the facing curve isntead of "on thin material" makes this usage confusing?    
> 
> To your point that the table is tangential to the curve, whether this is necessarily so is what we are discussing.  If instead of a tangent, you consider the table a secant (as posited by John), you end up with a tight bend (a kink, if I may be so bold) where curve meets table.  The longer the radius of the curve for a given tip opening, the farther from tangential the table gets, and the tighter the curve at this point, up to the point where you have an infinite radius, a straight line, and a sharp angle instead of a curve.  
> 
> --- In MouthpieceWork@yahoogroups.com, Barry Levine <barrylevine@> wrote:
> >
> > I don't follow your use of the word "kink" either.
> > 
> > The first, and most applicable to this discussion, definition of "kink" on
> > freedictionary.com is:
> > 
> > 1. A tight curl, twist, or bend in a length of thin material, as one caused
> > by the tensing of a looped section of wire.
> > 
> > The change in a mouthpiece where the table meets the facing curve is most
> > decidedly *not* a tight curl.
> > 
> > It is a point of tangency. ( http://en.wikipedia.org/wiki/Tangent )
> > 
> > You are certainly free to impart your own personal meanings to  words, but
> > the end result is "babel." (see http://www.thefreedictionary.com/babel )
> > 
> > FWIW
> > 
> > Barry
> > 
> > > From: "Morgan" <frymorgan@>
> > > Reply-To: MouthpieceWork@yahoogroups.com
> > > Date: Sat, 06 Mar 2010 05:32:14 -0000
> > > To: MouthpieceWork@yahoogroups.com
> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > > 
> > > 
> > >  
> > > The "kink" is where the curve breaks awy from the table.  If the curve is a
> > > straight line, then there is a sharp corner where it connects to the table.
> > > If there is no kink, and the "curve" is straight, there is no tip opening!
> > > 
> > > --- In MouthpieceWork@yahoogroups.com
> > > <mailto:MouthpieceWork%40yahoogroups.com> , "John" <john_w_price33@> wrote:
> > >> >
> > >> > I really don't understand "kink".  if the curve is approaching a straight
> > >> line there should be no kink whatsoever. ie a very smooth transition.
> > >> > 
> > >> > --- In MouthpieceWork@yahoogroups.com
> > >> <mailto:MouthpieceWork%40yahoogroups.com> , Keith Bradbury <kwbradbury@>
> > >> wrote:
> > >>> > >
> > >>> > > The larger the dimeter gets, the less curved the facing gets.  It starts
> > >>> to approach a straight line which gives you the maximum kink.  If you round
> > >>> off the kink, you will in effect be using a small radius at that point.
> > >>> > > 
> > >>> > > 
> > >>> > > 
> > >>> > > 
> > >>> > > ________________________________
> > >>> > > From: John <john_w_price33@>
> > >>> > > To: MouthpieceWork@yahoogroups.com
> > >>> <mailto:MouthpieceWork%40yahoogroups.com>
> > >>> > > Sent: Fri, March 5, 2010 1:45:13 PM
> > >>> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > >>> > > 
> > >>> > >   
> > >>> > > Thanks Keith, As I replied to Morgan I think that having a larger
> > >>> diameter circle will "unkink" the facing....more gradual beginning of he
> > >>> curve.
> > >>> > >
> > >> >
> > > 
> > > 
> > > 
> > >
> >
>

...so a tangent with a modified radial curve.

--- On Mon, 3/8/10, John <john_w_price33@...> wrote:

From: John <john_w_price33@...>
Subject: [MouthpieceWork] Re: Radial Curves yet again,
To: MouthpieceWork@yahoogroups.com
Date: Monday, March 8, 2010, 5:39 PM







 



  


    
      
      
      I understand that if one uses a straight line from the tip of the mouthpiece to where the facing begins as facing then there would certainly be a "kink"...the reed would have difficulty with this.  What I was referring to is a radial curve that as it gets bigger with a larger and larger radius has no kink.  You are just flattening out the arc and approaching a perfectly flat table leading to a perfectly flat facing curve.  No kink..   



--- In MouthpieceWork@ yahoogroups. com, "Morgan" <frymorgan@. ..> wrote:

>

> 

> Tell the math police we're calling it an inflection point.  But I still think of it as a kink.

> 

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

> >

> > Since "kink" is probably not a math term, we could try "vertex" or "function discontinuity" . 

> > 

> > 

> > 

> > 

> > ____________ _________ _________ __

> > From: Morgan <frymorgan@>

> > To: MouthpieceWork@ yahoogroups. com

> > Sent: Sat, March 6, 2010 10:13:09 AM

> > Subject: [MouthpieceWork] Re: Radial Curves yet again,

> > 

> >   

> > So that we're using it to mean a tight bend in the facing curve isntead of "on thin material" makes this usage confusing? 

> > 

> > To your point that the table is tangential to the curve, whether this is necessarily so is what we are discussing. If instead of a tangent, you consider the table a secant (as posited by John), you end up with a tight bend (a kink, if I may be so bold) where curve meets table. The longer the radius of the curve for a given tip opening, the farther from tangential the table gets, and the tighter the curve at this point, up to the point where you have an infinite radius, a straight line, and a sharp angle instead of a curve. 

> > 

> > --- In MouthpieceWork@ yahoogroups. com, Barry Levine <barrylevine@ ...> wrote:

> > >

> > > I don't follow your use of the word "kink" either.

> > > 

> > > The first, and most applicable to this discussion, definition of "kink" on

> > > freedictionary. com is:

> > > 

> > > 1. A tight curl, twist, or bend in a length of thin material, as one caused

> > > by the tensing of a looped section of wire.

> > > 

> > > The change in a mouthpiece where the table meets the facing curve is most

> > > decidedly *not* a tight curl.

> > > 

> > > It is a point of tangency. ( http://en.wikipedia .org/wiki/ Tangent )

> > > 

> > > You are certainly free to impart your own personal meanings to words, but

> > > the end result is "babel." (see http://www.thefreed ictionary. com/babel )

> > > 

> > > FWIW

> > > 

> > > Barry

> > > 

> > > > From: "Morgan" <frymorgan@ ..>

> > > > Reply-To: MouthpieceWork@ yahoogroups. com

> > > > Date: Sat, 06 Mar 2010 05:32:14 -0000

> > > > To: MouthpieceWork@ yahoogroups. com

> > > > Subject: [MouthpieceWork] Re: Radial Curves yet again,

> > > > 

> > > > 

> > > > 

> > > > The "kink" is where the curve breaks awy from the table. If the curve is a

> > > > straight line, then there is a sharp corner where it connects to the table.

> > > > If there is no kink, and the "curve" is straight, there is no tip opening!

> > > > 

> > > > --- In MouthpieceWork@ yahoogroups. com

> > > > <mailto:MouthpieceW ork%40yahoogroup s.com> , "John" <john_w_price33@ > wrote:

> > > >> >

> > > >> > I really don't understand "kink". if the curve is approaching a straight

> > > >> line there should be no kink whatsoever. ie a very smooth transition.

> > > >> > 

> > > >> > --- In MouthpieceWork@ yahoogroups. com

> > > >> <mailto:MouthpieceW ork%40yahoogroup s.com> , Keith Bradbury <kwbradbury@ >

> > > >> wrote:

> > > >>> > >

> > > >>> > > The larger the dimeter gets, the less curved the facing gets.  It starts

> > > >>> to approach a straight line which gives you the maximum kink.  If you round

> > > >>> off the kink, you will in effect be using a small radius at that point.

> > > >>> > > 

> > > >>> > > 

> > > >>> > > 

> > > >>> > > 

> > > >>> > > ____________ _________ _________ __

> > > >>> > > From: John <john_w_price33@ >

> > > >>> > > To: MouthpieceWork@ yahoogroups. com

> > > >>> <mailto:MouthpieceW ork%40yahoogroup s.com>

> > > >>> > > Sent: Fri, March 5, 2010 1:45:13 PM

> > > >>> > > Subject: [MouthpieceWork] Re: Radial Curves yet again,

> > > >>> > > 

> > > >>> > >   

> > > >>> > > Thanks Keith, As I replied to Morgan I think that having a larger

> > > >>> diameter circle will "unkink" the facing....more gradual beginning of he

> > > >>> curve.

> > > >>> > >

> > > >> >

> > > > 

> > > > 

> > > > 

> > > >

> > >

> >

>





    
     

    
    


 



  






      

John,

The curve you are describing is the equivalent of an eliptical facing, with
all of its advantages and disadvantages.

Jeff

-----Original Message-----
From: MouthpieceWork@yahoogroups.com [mailto:MouthpieceWork@yahoogroups.com]
On Behalf Of John
Sent: Monday, March 08, 2010 9:39 AM
To: MouthpieceWork@yahoogroups.com
Subject: [MouthpieceWork] Re: Radial Curves yet again,

I understand that if one uses a straight line from the tip of the mouthpiece
to where the facing begins as facing then there would certainly be a
"kink"...the reed would have difficulty with this.  What I was referring to
is a radial curve that as it gets bigger with a larger and larger radius has
no kink.  You are just flattening out the arc and approaching a perfectly
flat table leading to a perfectly flat facing curve.  No kink..   

Ah, I see what we're getting at now.  Thanks for pointing that out, Jeff.

John, it does sound like you are describing an elliptical curve.  Most of the curves I have seen on good playing vintage pieces can be modeled very closesly like this, and I use one variety of this or another for my own mouthpieces and refacing. I think they play better and sound better than radial curves, but tastes vary.  There is a spreadsheet in the files section somewhere that models an elliptical curve, you may find it useful to toy around with.

--- In MouthpieceWork@yahoogroups.com, "Jeff Chan" <reedman@...> wrote:
>
> John,
> 
> The curve you are describing is the equivalent of an eliptical facing, with
> all of its advantages and disadvantages.
> 
> Jeff
> 
> -----Original Message-----
> From: MouthpieceWork@yahoogroups.com [mailto:MouthpieceWork@yahoogroups.com]
> On Behalf Of John
> Sent: Monday, March 08, 2010 9:39 AM
> To: MouthpieceWork@yahoogroups.com
> Subject: [MouthpieceWork] Re: Radial Curves yet again,
> 
> I understand that if one uses a straight line from the tip of the mouthpiece
> to where the facing begins as facing then there would certainly be a
> "kink"...the reed would have difficulty with this.  What I was referring to
> is a radial curve that as it gets bigger with a larger and larger radius has
> no kink.  You are just flattening out the arc and approaching a perfectly
> flat table leading to a perfectly flat facing curve.  No kink..
>

Hi John, 

I find Joyour adaptation of Benade's Mouthpiece Equivalent Volume (reed compliance) very interesting and essential for understanding these elusive volume issues. 



I have some difficulty understanding or interpreting your results however. Hopefully you can clear that up for me.



In your MEV study the MEV added 2.78cc or 28% to the physical mouthpiece chamber volume used.



In your MCV study, MEV added only 1.28cc or 18.63% to the physical mouthpiece chamber volume used.



The same mouthpiece was used for both tests.  



Benade's conclusions to his similar MEV study showed that the MEV was
quite constant over a considerable portion of the instrument's range.
Understandable since, also being termed "reed compliance" one might see
it as a property of the reed and the mouthpiece facing, rather than the
changing mouthpiece chamber volume (used) and tube air column length.



Can you explain how you were able to get from 28% in the first study to 18.63% in the second study?
		
		

		

		
		

		

		

		

		
			 


      

Each step in the mathematical computation for each study is clearly spelled out in the document.  Close attention to the details should provide the answers to these and any other questions one might have about the results.  Of course, anyone is free to interpret the findings of the studies in any manner they see fit.

John

--- In MouthpieceWork@yahoogroups.com, MartinMods <lancelotburt@...> wrote:
>
> Hi John, 
> 
> I find Joyour adaptation of Benade's Mouthpiece Equivalent Volume (reed compliance) very interesting and essential for understanding these elusive volume issues. 
> 
> 
> 
> I have some difficulty understanding or interpreting your results however. Hopefully you can clear that up for me.
> 
> 
> 
> In your MEV study the MEV added 2.78cc or 28% to the physical mouthpiece chamber volume used.
> 
> 
> 
> In your MCV study, MEV added only 1.28cc or 18.63% to the physical mouthpiece chamber volume used.
> 
> 
> 
> The same mouthpiece was used for both tests.  
> 
> 
> 
> Benade's conclusions to his similar MEV study showed that the MEV was
> quite constant over a considerable portion of the instrument's range.
> Understandable since, also being termed "reed compliance" one might see
> it as a property of the reed and the mouthpiece facing, rather than the
> changing mouthpiece chamber volume (used) and tube air column length.
> 
> 
> 
> Can you explain how you were able to get from 28% in the first study to 18.63% in the second study?
> 		
> 		
> 
> 		
> 
> 		
> 		
> 
> 		
> 
> 		
> 
> 		
> 
> 		
> 			 
>

The thin material that is being bent sharply is the line on the graph, not the actual facing. Seeing the line of pencil lead (or many, close dots on the screen) as a thing that can be bent or shaped should be easy for artistic types who might give a hoot about a woodwind mouthpiece. 

Using this term - kink- for curves on a graph should make sense to visual learners.

E v e r e t t

> > > --- In MouthpieceWork@ yahoogroups. com, Barry Levine <barrylevine@ ...> wrote:

I don't follow your use of the word "kink" either.

The first, and most applicable to this discussion, definition of "kink" on
 freedictionary. com is:
 
 1. A tight curl, twist, or bend in a length of thin material, as one caused
by the tensing of a looped section of wire.
 
The change in a mouthpiece where the table meets the facing curve is most
decidedly *not* a tight curl.

It is a point of tangency. ( http://en.wikipedia.org/wiki/Tangent )

Yes I see now.  Thank-you.  So your opinion is, that the added effective mouthpiece volume (reed compliance + whatever else) is proportional to the amount of chamber volume used on this mouthpiece X 28%.  If you push in, the added volume gets smaller.  If you pull out, it gets larger.

Another test with the brass tube, inserted into the mouthpiece to 28.2mm would verify that.



--- On Tue, 3/9/10, John <jtalcott47@...> wrote:

From: John <jtalcott47@...>
Subject: [MouthpieceWork] Re: Mouthpiece Equivalent Volume
To: MouthpieceWork@yahoogroups.com
Date: Tuesday, March 9, 2010, 3:58 AM







 



  


    
      
      
      



Each step in the mathematical computation for each study is clearly spelled out in the document.  Close attention to the details should provide the answers to these and any other questions one might have about the results.  Of course, anyone is free to interpret the findings of the studies in any manner they see fit.



John



--- In MouthpieceWork@ yahoogroups. com, MartinMods <lancelotburt@ ...> wrote:

>

> Hi John, 

> 

> I find Joyour adaptation of Benade's Mouthpiece Equivalent Volume (reed compliance) very interesting and essential for understanding these elusive volume issues. 

> 

> 

> 

> I have some difficulty understanding or interpreting your results however. Hopefully you can clear that up for me.

> 

> 

> 

> In your MEV study the MEV added 2.78cc or 28% to the physical mouthpiece chamber volume used.

> 

> 

> 

> In your MCV study, MEV added only 1.28cc or 18.63% to the physical mouthpiece chamber volume used.

> 

> 

> 

> The same mouthpiece was used for both tests.  

> 

> 

> 

> Benade's conclusions to his similar MEV study showed that the MEV was

> quite constant over a considerable portion of the instrument's range.

> Understandable since, also being termed "reed compliance" one might see

> it as a property of the reed and the mouthpiece facing, rather than the

> changing mouthpiece chamber volume (used) and tube air column length.

> 

> 

> 

> Can you explain how you were able to get from 28% in the first study to 18.63% in the second study?

> 		

> 		

> 

> 		

> 

> 		

> 		

> 

> 		

> 

> 		

> 

> 		

> 

> 		

> 			 

>





    
     

    
    


 



  






      

Hi, no i'm not describing an elliptical curve...it is just a radial curve with an expanding radius.  As it gets larger the curve approaches a straight line.   

--- In MouthpieceWork@yahoogroups.com, "Jeff Chan" <reedman@...> wrote:
>
> John,
> 
> The curve you are describing is the equivalent of an eliptical facing, with
> all of its advantages and disadvantages.
> 
> Jeff
> 
> -----Original Message-----
> From: MouthpieceWork@yahoogroups.com [mailto:MouthpieceWork@yahoogroups.com]
> On Behalf Of John
> Sent: Monday, March 08, 2010 9:39 AM
> To: MouthpieceWork@yahoogroups.com
> Subject: [MouthpieceWork] Re: Radial Curves yet again,
> 
> I understand that if one uses a straight line from the tip of the mouthpiece
> to where the facing begins as facing then there would certainly be a
> "kink"...the reed would have difficulty with this.  What I was referring to
> is a radial curve that as it gets bigger with a larger and larger radius has
> no kink.  You are just flattening out the arc and approaching a perfectly
> flat table leading to a perfectly flat facing curve.  No kink..
>

A radial curve, by definition, has a constant radius and is a first order
curve.  A curve with changing radius is at least second order, and may be
elliptical or parabolic.  You might want to look at a mathematics textbook.

-----Original Message-----
From: MouthpieceWork@yahoogroups.com [mailto:MouthpieceWork@yahoogroups.com]
On Behalf Of John
Sent: Tuesday, March 09, 2010 10:26 AM
To: MouthpieceWork@yahoogroups.com
Subject: [MouthpieceWork] Re: Radial Curves yet again,

Hi, no i'm not describing an elliptical curve...it is just a radial curve
with an expanding radius.  As it gets larger the curve approaches a straight
line.   

--- In MouthpieceWork@yahoogroups.com, "Jeff Chan" <reedman@...> wrote:
>
> John,
> 
> The curve you are describing is the equivalent of an eliptical facing, 
> with all of its advantages and disadvantages.
> 
> Jeff
> 
> -----Original Message-----
> From: MouthpieceWork@yahoogroups.com 
> [mailto:MouthpieceWork@yahoogroups.com]
> On Behalf Of John
> Sent: Monday, March 08, 2010 9:39 AM
> To: MouthpieceWork@yahoogroups.com
> Subject: [MouthpieceWork] Re: Radial Curves yet again,
> 
> I understand that if one uses a straight line from the tip of the 
> mouthpiece to where the facing begins as facing then there would 
> certainly be a "kink"...the reed would have difficulty with this.  
> What I was referring to is a radial curve that as it gets bigger with 
> a larger and larger radius has no kink.  You are just flattening out 
> the arc and approaching a perfectly flat table leading to a perfectly flat
facing curve.  No kink..
>

Hmm... it sounds like you're describing a catenary (eg. one formed by a very
long chain or rope)

> Hi, no i'm not describing an elliptical curve...it is just a radial curve with
> an expanding radius.  As it gets larger the curve approaches a straight line.
> 
> --- In MouthpieceWork@yahoogroups.com, "Jeff Chan" <reedman@...> wrote:
>> 
>> John,
>> 
>> The curve you are describing is the equivalent of an eliptical facing, with
>> all of its advantages and disadvantages.
>> 
>> Jeff
>> 
>> -----Original Message-----
>> From: MouthpieceWork@yahoogroups.com [mailto:MouthpieceWork@yahoogroups.com]
>> On Behalf Of John
>> Sent: Monday, March 08, 2010 9:39 AM
>> To: MouthpieceWork@yahoogroups.com
>> Subject: [MouthpieceWork] Re: Radial Curves yet again,
>> 
>> I understand that if one uses a straight line from the tip of the mouthpiece
>> to where the facing begins as facing then there would certainly be a
>> "kink"...the reed would have difficulty with this.  What I was referring to
>> is a radial curve that as it gets bigger with a larger and larger radius has
>> no kink.  You are just flattening out the arc and approaching a perfectly
>> flat table leading to a perfectly flat facing curve.  No kink..
>> 
> 
> 
> 

You're talking about a curve for which the radius of the circular section increases with distnce from the tip, right?  If not, I'm afraid I still don't get you.  If the above is what you're talking about, the more circles you use the more nearly you approximate an ellipse.  

--- In MouthpieceWork@yahoogroups.com, "John" <john_w_price33@...> wrote:
>
> Hi, no i'm not describing an elliptical curve...it is just a radial curve with an expanding radius.  As it gets larger the curve approaches a straight line.   
> 
> --- In MouthpieceWork@yahoogroups.com, "Jeff Chan" <reedman@> wrote:
> >
> > John,
> > 
> > The curve you are describing is the equivalent of an eliptical facing, with
> > all of its advantages and disadvantages.
> > 
> > Jeff
> > 
> > -----Original Message-----
> > From: MouthpieceWork@yahoogroups.com [mailto:MouthpieceWork@yahoogroups.com]
> > On Behalf Of John
> > Sent: Monday, March 08, 2010 9:39 AM
> > To: MouthpieceWork@yahoogroups.com
> > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > 
> > I understand that if one uses a straight line from the tip of the mouthpiece
> > to where the facing begins as facing then there would certainly be a
> > "kink"...the reed would have difficulty with this.  What I was referring to
> > is a radial curve that as it gets bigger with a larger and larger radius has
> > no kink.  You are just flattening out the arc and approaching a perfectly
> > flat table leading to a perfectly flat facing curve.  No kink..
> >
>

maybe it was another radial curve with a different radius...

Dan

--- In MouthpieceWork@yahoogroups.com, "Jeff Chan" <reedman@...> wrote:
>
> A radial curve, by definition, has a constant radius and is a first order
> curve.  A curve with changing radius is at least second order, and may be
> elliptical or parabolic.  You might want to look at a mathematics textbook.
> 
> -----Original Message-----
> From: MouthpieceWork@yahoogroups.com [mailto:MouthpieceWork@yahoogroups.com]
> On Behalf Of John
> Sent: Tuesday, March 09, 2010 10:26 AM
> To: MouthpieceWork@yahoogroups.com
> Subject: [MouthpieceWork] Re: Radial Curves yet again,
> 
> Hi, no i'm not describing an elliptical curve...it is just a radial curve
> with an expanding radius.  As it gets larger the curve approaches a straight
> line.   
> 
> --- In MouthpieceWork@yahoogroups.com, "Jeff Chan" <reedman@> wrote:
> >
> > John,
> > 
> > The curve you are describing is the equivalent of an eliptical facing, 
> > with all of its advantages and disadvantages.
> > 
> > Jeff
> > 
> > -----Original Message-----
> > From: MouthpieceWork@yahoogroups.com 
> > [mailto:MouthpieceWork@yahoogroups.com]
> > On Behalf Of John
> > Sent: Monday, March 08, 2010 9:39 AM
> > To: MouthpieceWork@yahoogroups.com
> > Subject: [MouthpieceWork] Re: Radial Curves yet again,
> > 
> > I understand that if one uses a straight line from the tip of the 
> > mouthpiece to where the facing begins as facing then there would 
> > certainly be a "kink"...the reed would have difficulty with this.  
> > What I was referring to is a radial curve that as it gets bigger with 
> > a larger and larger radius has no kink.  You are just flattening out 
> > the arc and approaching a perfectly flat table leading to a perfectly flat
> facing curve.  No kink..
> >
>