An earlier discussion raised the question of the effects of playing
different mouthpiece pitches versus changing the position of the
mouthpiece on the cork.

It is known that each can change the amount of the "effective volume" of
the mouthpiece, but that raises the question of whether the Frs  of the
mouthpiece and neck can be "tuned"  by the embouchure  while keeping the
"effective volume" of the mouthpiece closely matched to that of the
missing cone.

A first step has been to create a spreadsheet
<http://jbtsaxmusic.homestead.com/neck___mp_pitch_when_mp_moved_1_mm.pdf\
>   showing the calculated changes in missing cone + neck volume, length
, and pitch when the mouthpiece is moved on or off the cork in 1 mm
increments, keeping the embouchure the same.

A preliminary summary of the results shows that on the mouthpiece and
neck alone:

A 1 mm movement of the mouthpiece
-creates a .20 ml change in the missing cone volume
-creates a 4.7 mm change in the missing cone length
-results in a 20 cents change in the pitch (Frs) of the mouthpiece and
neck

A 5 mm movement of the mouthpiece
-creates a 1.0 ml change in the missing cone volume
-creates a 23.5 mm change in the missing cone length
-results in a 100 cents (1/2 step) change in the Frs of the mouthpiece
and neck

John

In your last missing cone volume study, the missing cone was determined by the taper of the neck, and extended from the small end of the neck to the apex.  As such, the position of the mouthpiece played no roll at all.  Is the term, "missing cone" now being used as a label for the substitution for the missing cone?

--- On Thu, 3/18/10, John <jtalcott47@...> wrote:

From: John <jtalcott47@...>
Subject: [MouthpieceWork] The calculated effects of moving the mouthpiece on or off the cork
To: MouthpieceWork@yahoogroups.com
Date: Thursday, March 18, 2010, 4:11 AM







 



  


    
      
      
      An earlier discussion raised the question of the effects of playing different mouthpiece pitches versus changing the position of the mouthpiece on the cork.

It is known that each can change the amount of the "effective volume" of the mouthpiece, but that raises the question of whether the Frs  of the mouthpiece and neck can be "tuned"  by the embouchure  while keeping the "effective volume" of the mouthpiece closely matched to that of the missing cone.

A first step has been to create a spreadsheet  showing the calculated changes in missing cone + neck volume, length , and pitch when the mouthpiece is moved on or off the cork in 1 mm increments, keeping the embouchure the same.

A preliminary summary of the results shows that on the mouthpiece and neck alone: 

A 1 mm movement of the mouthpiece 
-creates a .20 ml change in the missing cone volume
-creates a 4.7 mm change in the missing cone length
-results in a 20 cents change in the pitch (Frs) of the mouthpiece and neck

A 5 mm movement of the mouthpiece
-creates a 1.0 ml change in the missing cone volume
-creates a 23.5 mm change in the missing cone length
-results in a 100 cents (1/2 step) change in the Frs of the mouthpiece and neck

John




    
     

    
    


 



  






      

Good point.  What it means is the replication or substitution for the missing cone. I could have made that more clear in the column labels.
 
My thinking is that when the mouthpiece's effective volume is too large, the saxophone "sees" its missing cone as being longer to its apex (the base of the cone is fixed at the size of the neck opening).  When the mouthpiece's effective volume is too small, the saxophone "sees" a cone that is shorter. 

This is following up on an earlier theory of mine that the physical length of the instrument to the tip of the mouthpiece plays no direct part in the tuning of the instrument.  It is the volume inside the mouthpiece that determines the volume of the cone it is a substitution for and therefore the length to the apex of that cone.  That length in turn determines the wavelength of the soundwave and therefore the pitch.

I believe my mouthpiece insert experiments showed this to be the case, but I would be the first to agree that more tests and measurements are needed.


John

--- In MouthpieceWork@yahoogroups.com, MartinMods <lancelotburt@...> wrote:
>
> In your last missing cone volume study, the missing cone was determined by the taper of the neck, and extended from the small end of the neck to the apex.  As such, the position of the mouthpiece played no roll at all.  Is the term, "missing cone" now being used as a label for the substitution for the missing cone?
> 
> --- On Thu, 3/18/10, John <jtalcott47@...> wrote:
> 
> From: John <jtalcott47@...>
> Subject: [MouthpieceWork] The calculated effects of moving the mouthpiece on or off the cork
> To: MouthpieceWork@yahoogroups.com
> Date: Thursday, March 18, 2010, 4:11 AM
> 
> 
> 
> 
> 
> 
> 
>  
> 
> 
> 
>   
> 
> 
>     
>       
>       
>       An earlier discussion raised the question of the effects of playing different mouthpiece pitches versus changing the position of the mouthpiece on the cork.
> 
> It is known that each can change the amount of the "effective volume" of the mouthpiece, but that raises the question of whether the Frs  of the mouthpiece and neck can be "tuned"  by the embouchure  while keeping the "effective volume" of the mouthpiece closely matched to that of the missing cone.
> 
> A first step has been to create a spreadsheet  showing the calculated changes in missing cone + neck volume, length , and pitch when the mouthpiece is moved on or off the cork in 1 mm increments, keeping the embouchure the same.
> 
> A preliminary summary of the results shows that on the mouthpiece and neck alone: 
> 
> A 1 mm movement of the mouthpiece 
> -creates a .20 ml change in the missing cone volume
> -creates a 4.7 mm change in the missing cone length
> -results in a 20 cents change in the pitch (Frs) of the mouthpiece and neck
> 
> A 5 mm movement of the mouthpiece
> -creates a 1.0 ml change in the missing cone volume
> -creates a 23.5 mm change in the missing cone length
> -results in a 100 cents (1/2 step) change in the Frs of the mouthpiece and neck
> 
> John
>

The missing cone length is dependent on where the neck is
truncated. It is fixed and has nothing to do with the mpc
position.

Seems to me that effective volume has the effect of
volume: differing reed compliances create different
effective volumes and these will certainly affect BOTH the
effective internal volume and resonance frequency of the
mpc, as the Frs is a function of the missing volume (and
the end opening).

Toby

--- John <jtalcott47@...> wrote:

> An earlier discussion raised the question of the
> effects of playing
> different mouthpiece pitches versus changing the
> position of the
> mouthpiece on the cork.
> 
> It is known that each can change the amount of the
> "effective volume" of
> the mouthpiece, but that raises the question of
> whether the Frs  of the
> mouthpiece and neck can be "tuned"  by the
> embouchure  while keeping the
> "effective volume" of the mouthpiece closely matched
> to that of the
> missing cone.
> 
> A first step has been to create a spreadsheet
>
<http://jbtsaxmusic.homestead.com/neck___mp_pitch_when_mp_moved_1_mm.pdf\
> >   showing the calculated changes in missing cone +
> neck volume, length
> , and pitch when the mouthpiece is moved on or off
> the cork in 1 mm
> increments, keeping the embouchure the same.
> 
> A preliminary summary of the results shows that on
> the mouthpiece and
> neck alone:
> 
> A 1 mm movement of the mouthpiece
> -creates a .20 ml change in the missing cone volume
> -creates a 4.7 mm change in the missing cone length
> -results in a 20 cents change in the pitch (Frs) of
> the mouthpiece and
> neck
> 
> A 5 mm movement of the mouthpiece
> -creates a 1.0 ml change in the missing cone volume
> -creates a 23.5 mm change in the missing cone length
> -results in a 100 cents (1/2 step) change in the Frs
> of the mouthpiece
> and neck
> 
> John
> 
> 
> 

You are right.  I have since labeled the columns in the study more accurately to avoid confusion.

My hypothesis is that the pitch and volume change created by changing the embouchure pressure (mouthpiece pitch) is not going to have a one to one relationship to the pitch and volume change by moving the mouthpiece without changing the embouchure.

If this is the case, then the effective mouthpiece volume could be negotiated with the embouchure pressure to meet both of Benade's requirements for the missing cone volume and the Frs of the mouthpiece and neck.

--- In MouthpieceWork@yahoogroups.com, <kymarto123@...> wrote:
>
> The missing cone length is dependent on where the neck is
> truncated. It is fixed and has nothing to do with the mpc
> position.
> 
> Seems to me that effective volume has the effect of
> volume: differing reed compliances create different
> effective volumes and these will certainly affect BOTH the
> effective internal volume and resonance frequency of the
> mpc, as the Frs is a function of the missing volume (and
> the end opening).
> 
> Toby
> 
> --- John <jtalcott47@...> wrote:
> 
> > An earlier discussion raised the question of the
> > effects of playing
> > different mouthpiece pitches versus changing the
> > position of the
> > mouthpiece on the cork.
> > 
> > It is known that each can change the amount of the
> > "effective volume" of
> > the mouthpiece, but that raises the question of
> > whether the Frs  of the
> > mouthpiece and neck can be "tuned"  by the
> > embouchure  while keeping the
> > "effective volume" of the mouthpiece closely matched
> > to that of the
> > missing cone.
> > 
> > A first step has been to create a spreadsheet
> >
> <http://jbtsaxmusic.homestead.com/neck___mp_pitch_when_mp_moved_1_mm.pdf\
> > >   showing the calculated changes in missing cone +
> > neck volume, length
> > , and pitch when the mouthpiece is moved on or off
> > the cork in 1 mm
> > increments, keeping the embouchure the same.
> > 
> > A preliminary summary of the results shows that on
> > the mouthpiece and
> > neck alone:
> > 
> > A 1 mm movement of the mouthpiece
> > -creates a .20 ml change in the missing cone volume
> > -creates a 4.7 mm change in the missing cone length
> > -results in a 20 cents change in the pitch (Frs) of
> > the mouthpiece and
> > neck
> > 
> > A 5 mm movement of the mouthpiece
> > -creates a 1.0 ml change in the missing cone volume
> > -creates a 23.5 mm change in the missing cone length
> > -results in a 100 cents (1/2 step) change in the Frs
> > of the mouthpiece
> > and neck
> > 
> > John
> > 
> > 
> >
>

You are right.  The "ideal" missing cone is what you described.  My paper has to do with the missing cone substitution which is the effective volume of the mouthpiece.  I have corrected the terminology in the paper to avoid confusion.

I am thinking there might be a way to test whether or not changes in the Frs resulting from changes in embouchure pressure (mouthpiece pitch) are in a direct one to one relationship with changes in the Frs by just adding or taking away mp effective volume without a change in embouchure.

John

--- In MouthpieceWork@yahoogroups.com, <kymarto123@...> wrote:
>
> The missing cone length is dependent on where the neck is
> truncated. It is fixed and has nothing to do with the mpc
> position.
> 
> Seems to me that effective volume has the effect of
> volume: differing reed compliances create different
> effective volumes and these will certainly affect BOTH the
> effective internal volume and resonance frequency of the
> mpc, as the Frs is a function of the missing volume (and
> the end opening).
> 
> Toby
> 
> --- John <jtalcott47@...> wrote:
> 
> > An earlier discussion raised the question of the
> > effects of playing
> > different mouthpiece pitches versus changing the
> > position of the
> > mouthpiece on the cork.
> > 
> > It is known that each can change the amount of the
> > "effective volume" of
> > the mouthpiece, but that raises the question of
> > whether the Frs  of the
> > mouthpiece and neck can be "tuned"  by the
> > embouchure  while keeping the
> > "effective volume" of the mouthpiece closely matched
> > to that of the
> > missing cone.
> > 
> > A first step has been to create a spreadsheet
> >
> <http://jbtsaxmusic.homestead.com/neck___mp_pitch_when_mp_moved_1_mm.pdf\
> > >   showing the calculated changes in missing cone +
> > neck volume, length
> > , and pitch when the mouthpiece is moved on or off
> > the cork in 1 mm
> > increments, keeping the embouchure the same.
> > 
> > A preliminary summary of the results shows that on
> > the mouthpiece and
> > neck alone:
> > 
> > A 1 mm movement of the mouthpiece
> > -creates a .20 ml change in the missing cone volume
> > -creates a 4.7 mm change in the missing cone length
> > -results in a 20 cents change in the pitch (Frs) of
> > the mouthpiece and
> > neck
> > 
> > A 5 mm movement of the mouthpiece
> > -creates a 1.0 ml change in the missing cone volume
> > -creates a 23.5 mm change in the missing cone length
> > -results in a 100 cents (1/2 step) change in the Frs
> > of the mouthpiece
> > and neck
> > 
> > John
> > 
> > 
> >
>

I figured it out - the equivalent missing cone.

If you understand why the f = c / l * 2 formula works for both an open cylinder and an open, straight sided cone, then you can see why it does not provide accurate results for any similar, though irregular shape - for example, your irregularly tapered, bent neck tube with a 21mm long cylindrical section on the end.  

A cylinder has the same diameter at the midpoint compression anti-node as it does at the 2 end displacement anti-nodes.  While the open cone's end diameters are larger and smaller than the midpoint, they differ by the same amount, and thus their differences cancel each other out.  That applies for the fundamental resonant frequency and the higher resonant modes forming the regime.

If the walls are anything but straight, the degree of diameter difference in the vicinity of the ends will not be proportional to the midpoint, causing the played pitch to differ from the calculated pitch.

Keeping the length of the walls of your neck unchanged and straightening it, results in an open quasi-conical tube with the large end sliced off at an angle.  The long side will be almost an inch longer than the short side.  The resultant planar surface area of the open end, which is now a lopsided oval, is considerably larger than that of the tube, were it sliced straight across and circular.   More + pitch change here.  Averaging the length by measuring down the middle does not give accurate results due to volume effects near the end, as the long side expanded more than the short side.  The cylindrical tenon would reduce this effect some but not eliminate it.

These same errors apply to measurements of this latest equivalent missing cone + neck pitch calculations.  As soon as it is shortened or extended, it is no longer a straight sided cone (based on the neck taper), and calculated results using f = c/2*l will be inaccurate.



      

Also, if you apply end correction for played tube results, you must do so consistently.  That would include the Mouthpiece Equivalent Volume tests.



      

I think your point is well taken on the effect of the midpoint diameter.
I did a quick check on my measured alto mouthpiece and found the average
of the larger and smaller diameters to be 17.8 mm.  However, in finding
by extrapolation the diameter at the midpoint of the neck (including the
tenon), I found it to be only 17.2.

In the second part of your "theory" I think you are missing something
important.  That is that in a toroidal bend in a tube the length lost in
the inside of the curve is made up for by the added length of the
outside curve.  As a result, the length of a center line through the
tube gives the average of the two lengths and therefore the actual
geometric and acoustic length.  Also in the real world, the ends of the
neck are never "lopsided" ovals, nor do they behave as such. At least
that's how I interpret it.

All your valid point proves is that it is difficult to come up with an
accurate calculated resonant frequency of a neck alone that agrees
completely with its played frequency.  It does not cast doubt on the
accuracy of the calculated pitch of the mouthpiece plus neck using the
formula   Frs  =  c/2(xo + .6 r) ---where Xo is the calculated length of
the missing cone added to the measured length of the neck including the
tenon.

Nice try, but no cigar.   [;)]


--- In MouthpieceWork@yahoogroups.com, MartinMods <lancelotburt@...>
wrote:
>
> I figured it out - the equivalent missing cone.
>
> If you understand why the f = c / l * 2 formula works for both an open
cylinder and an open, straight sided cone, then you can see why it does
not provide accurate results for any similar, though irregular shape -
for example, your irregularly tapered, bent neck tube with a 21mm long
cylindrical section on the end.
>
> A cylinder has the same diameter at the midpoint compression anti-node
as it does at the 2 end displacement anti-nodes.  While the open cone's
end diameters are larger and smaller than the midpoint, they differ by
the same amount, and thus their differences cancel each other out.  That
applies for the fundamental resonant frequency and the higher resonant
modes forming the regime.
>
> If the walls are anything but straight, the degree of diameter
difference in the vicinity of the ends will not be proportional to the
midpoint, causing the played pitch to differ from the calculated pitch.
>
> Keeping the length of the walls of your neck unchanged and
straightening it, results in an open quasi-conical tube with the large
end sliced off at an angle.  The long side will be almost an inch longer
than the short side.  The resultant planar surface area of the open end,
which is now a lopsided oval, is considerably larger than that of the
tube, were it sliced straight across and circular.   More + pitch change
here.  Averaging the length by measuring down the middle does not give
accurate results due to volume effects near the end, as the long side
expanded more than the short side.  The cylindrical tenon would reduce
this effect some but not eliminate it.
>
> These same errors apply to measurements of this latest equivalent
missing cone + neck pitch calculations.  As soon as it is shortened or
extended, it is no longer a straight sided cone (based on the neck
taper), and calculated results using f = c/2*l will be inaccurate.
>

"Also in the real world, the ends of the neck are never "lopsided" ovals,
 nor do they behave as such. At least that's how I interpret it."

You are examining the wrong part of the logical formula again.  That is not my point at all.  

The point is, your perfect, straight sided theoretical formula can not describe a "real world", bent and irregular shape accurately.  One must then, either modify the formula, or find the equivalent and applicable perfect real world shape to apply it to.  Choosing the latter, if you make your bent shape as close to your theoretical illustration (straight), without altering any of it's dimensions, then you get what I described earlier.  Finding the point of averaged length, proportional volume, and equal planar opening surface area on the large end, and compensating for proportional end/midpoint diameter differences, may give you more accurate calculated results.

Are you sure you can add the lengths of dissimilar geometric shapes using that formula?


 



  






      

You are examining the wrong part of the logical formula again.  That is
not my point at all.
The point is, your perfect, straight sided theoretical formula can not
describe a "real world", bent and irregular shape accurately.

In the first place it is not my formula it is Benade's and is based upon
a fundamental principle of physics.  Let's get that straight.  Saying
that since the the resonant frequency of the bent cone of the neck when
sounded apart from the mouthpiece and body does not exactly match that
formula that it means that formula is therefore invalid when calculating
the Frs of the missing cone plus the neck is comparing apples and
oranges.  When the neck becomes the extension of another cone or
mouthpiece substitution there is one important difference.  That is
there is but one end correction on the open end.

In Nederveen's writing he clearly states that the bend in the neck "does
not exercise any appreciable influence".  There is no need for the neck
to be a "perfect straight sided cone" in order to add its length and end
correction of  .6 times the radius of its open end to accurately
calculate the Frs of the missing cone + the neck.   Further support of
this statement is found in Nederveen's book on p.120.  The
"Dalmontophone" is hardly a perfect, straight sided cone and yet it
replicates the bore of a saxophone in its sound, and one would presume
the pitch of the fundamental based upon its end to end length +
correction.

One must then, either modify the formula, or find the equivalent and
applicable perfect real world shape to apply it to.  Choosing the
latter, if you make your bent shape as close to your theoretical
illustration (straight), without altering any of it's dimensions, then
you get what I described earlier.  Finding the point of averaged length,
proportional volume, and equal planar opening surface area on the large
end, and compensating for proportional end/midpoint diameter
differences, may give you more accurate calculated results.

This is not necessary, in my opinion.

Are you sure you can add the lengths of dissimilar geometric shapes
using that formula?

Yes.  I am sure because the calculated frequency using that formula
matches closely the played pitch with the mouthpiece in that position in
many empirical trials in my study of the SBA alto neck.   When time
permits I'm going to replicate that missing cone study using my Yamaha
Custom tenor to see if there is a similar match between the played pitch
and that calculated from the missing cone length.

John
>