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It's been a while since we've had a heated debate about Sax's "parabolic conical bore", so imagine my excitement when awholley brought to my attention that the topic is discussed in some detail in the Selmer saxophone manufacturing video originally posted by jbtsax here.

Before going further, a recap of some of our past discussions may be in order:

Switch from Parabolic Shape to Conical Bore

Buescher's "Parabolic Bore" -- What's the Deal?

Now a matter-of-fact discussion of the topic appears in the most unlikely of places - a Selmer promotional video on saxophone manufacture. Check out the first two minutes of the video (the rest is quite interesting too but not relevant to the parabolic bore issue.) I noted the following:

1) The discussion is very clear and the topic, for the most part, de-mystified.

2) That is, except for the meaning of "parabolic" in the term "parabolic conical bore." The illustration of a conic section clearly illustrates a "cone" curving inward, while the later discussion indicates the parabolic conical bore curves outward. This contradiction has been noted in the previous discussions.

3) Past discussions have focused on the outward curve of the tonehole side of the bore, while here they say the side opposite the tone holes also curves outward.

4) They point out that, since the other two sides are straight lines, the affect is that the bore becomes increasingly elliptical away from the neck receiver.

5) They mention something I don't believe I've heard before - the walls opposite the C, A and E tone holes protrude slightly, "providing yet another parabolic curve" whatever that could mean.

6) Modern saxophones have conical bores but vary in the degree of taper. A more pronounced taper results in a darker tone.

So, while this still leaves some confusion in terminology, does this convince the sceptics that the parabolic conical bore actually existed in early saxophones?
 

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The simple truth is that outside of this little forum (i.e., in the real world) it never WAS a controversy. It is well-documented that this was an integral part of Sax's original design. Personally I never doubted the existence of the infamous parabolic cone. There is also a clear, factual explanation of Sax's design in Michael Segell's recent book, "The Devil's Horn."

To me what would be most interesting is to learn when this cone was first compromised in a major way. Was it with the introduction of the Buescher Aristocrat (at least where the Buescher's were concerned), or the New Aristocrat? They say that John Edward Kelly plays a 1928 Aristocrat because, he claims, the design of subsequent models either eliminated or dramatically reduced the presence of the cone.

The "anti-cone" folks always seemed a bit fanatical in their opposition to me, as if they were driven by a secret agenda. Could it have been a deep loathing for Rascher and his disciples (such as Kelly), who almost piously swear by the existence of the parabola?
 

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Swingtone said:
... There is also a clear, factual explanation of Sax's design in Michael Segell's recent book, "The Devil's Horn." ...
Though interestingly, in Segell's discussion he cites Jap Kool's Das Saxophon and John-Edward Kelly's article on saxophone acoustics saying that the wall opposite the tone holes is straight, not curved as the Selmer video asserts.
 

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I material in the Selmer video was lifted from Jaap Kool's book, Das Saxophon. Jaap Kool was a non-saxophone player who admittedly knew very little about the saxophone.

Adolphe Sax did not make saxophones with a parabolic bore. The proof is in the surviving instruments themselves. I own 3 saxophones made by Adolphe Sax, and I have measured many others. None of them have a parabola, or anything approaching a parabola anywhere.

The "secondary parabolic curves" opposite some of the tone holes that are described by Jaap Kool simply do not exist, except in a few old saxophones where the dents were removed by an overzealous repairman.

My MYSPACE page:

http://www.myspace.com/saxpsychosis
 

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saxtek said:
I material in the Selmer video was lifted from Jaap Kool's book, Das Saxophon. Jaap Kool was a non-saxophone player who admittedly knew very little about the saxophone.

Adolphe Sax did not make saxophones with a parabolic bore. The proof is in the surviving instruments themselves. I own 3 saxophones made by Adolphe Sax, and I have measured many others. None of them have a parabola, or anything approaching a parabola anywhere.

The "secondary parabolic curves" opposite some of the tone holes that are described by Jaap Kool simply do not exist, except in a few old saxophones where the dents were removed by an overzealous repairman.

My MYSPACE page:

http://www.myspace.com/saxpsychosis

Your opinion is duly noted. :)
 

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I take it that there is no dispute about the cone element to the bore of a sax.

Now a curve does not have to be a complete parabola, coming from infinity and going to infinity, to be called parabolic, any more than a line has to go on forever to be called a line.

Likewise, we can chop off the small radius bottom of a parabola, and the shape of the remaining curve is "parabolic", in that the curve fits the mathematical formula for a parabola, for a certain range of values.

I hold my straight edge down the side of my sax, and the line is clearly not straight. Does this mean the sax is slightly bent? (Noting that I cannot test the other side of the instrument) Does it mean that it was made with a slight flare, conforming to a section of hyperbolic, parabolic, ellipse, cardioid, Cayley's Sextic Evolute, or some other formula? Who knows.

But most certainly, as the bow flares into the bell, and on to the rim, this is not a standard cone shape. It most definitely flares as it goes. Is that shape, in cross section, part of a parabola? I certainly don't know. Saxtec, have you done the measurement and maths on that for your saxes?

And Saxtec, Much of a parabola is very nearly straight. There are claims made that even 1/100 mm change in bore can be significant. Did your measurements determine fro sure that there were no deviations from the straight cone of this magnitude, and whether such deviations may actually conform to an almost straight section of parabola?

But I think that video does make some pretty strange statements about the ellipticalness of the cross section of the bore. Is THAT what you tested, Saxtec? On the other hand, with all that distortion of metal, mainly on one side of the tube, It is almost inevitable that the bore will finish up being a distortion from a circle in cross section.

And whether a curve bends out or in, is irrelevant. We can be looking at a section of parabola from either the concave side or the convex side, and even stand on our heads if we wish.

Methinks there are too many unknowns here to begin to have a sensible discussion. There is as much ambiguity in this topic as in the materials and finish threads. Tower of Babel stuff, again!
 

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There is a scientific way to prove or disprove this load of bull droppings. take several sax body tubes. Early Bueschers would be the likely candidate. Measure the diameter just below the tenon and just above the elbow. measure the length between the same two points. Using these measurements one could easily plot a conical bore. diameters could be calculated at preselected points, say, every inch or whatever. the same measurements would be taken from the sax and compared. If it is conical the diameter will increase evenly along its length. If it is parabolic the diameter will increase slower near the tip of the cone and faster as you appraoch the base.

If you could examine the tools used to create the early horns (if any still exist) you could also measure them. I don't know much about sax manufacturing but I assume some type of mandrel was used to create a body tube. If the bore was parabolic the the mandrel would have to be also.

This is all of course a big waste of time because all you have to do is look at any old handmade sax to see that the body is conical (except that drawn tone holes tend to have distortions along that side), the elbow tends to be somewhat elliptical most of time probably due to manufacturing processes, and the bell is the only parabolic item on the sax. The rest was just marketting hype.
 

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I think it is well known that no conical instrument is actually conical. The straight cone is a mathematically-ideal musical shape, along with the cylinder. These are the only two shapes that create harmonics in a musically-useful fashion--all other shapes mangle the harmonic series.

But....

In the real world both shapes are compromised by real-world things like truncation of the cone and tone holes, so there is actually no ideal shape in the real world that preserves the harmonic series.

So...

All manufacturers tweak the "ideal" shapes of cone and cylinder in order to try to correct for the problems introduced when shapes must become musical instruments.

Spiderjames has it 100% correct. One could easily plot the semi-angle of the cone of the sax and find out if it describes a parabola or not. My guess is that no sax would approach a true parabola, although there might be a constriction at the top of the neck. Just as Boehm's famous "parabolic head joint" is nothing like a parabola, I'll bet that the "parabolic sax bore" is nothing like a parabola, although I'm quite sure that the general bore of the sax has changed considerably from Sax's time.

Toby
 

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Sorry. I've read the above links now just to get a background, as well as reading this thread. I don't mean this insultingly but - what's the point?
 

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This is the first time I've weighed in on this topic. So here I go.

Where do people get this crazy idea that a saxophone can be or is or is supposed to be parabolic?? Do people actually know what the shape of a parabola is?? Here, let me remind you:

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

I'm sorry, but how does this parabolic shape have anything to do with a saxophone? If it were indeed the case that the saxophone followed the shape of a parabola then the neck of our saxophones would be incredibly wide by the neck receiver, and the diameter at the neck receiver would be relatively comparable to the diameter of the bell!

C'mon, guys. This is embarrassing. I guess I'm not too surprised that such a mythological discussion would occur in saxophone land seeing how many discussions take place around here regarding what make/model is suited for jazz/classical, effects of finish, resonators, etc.

The shape of the saxophone has always been and continues to be conical. In many cases it may not be perfectly conical for design reasons (tone hole volume compensation, etc) but parabolic NEVER. Case closed. Now go practice!!!
 

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Exactly, Gary!

Why does any of this matter? Are manufacturers depriving us of the perfect parabolic instrument as part of a larger conspiracy? Should someone make a parabolic bore instrument now and put every else out of business? The better instruments we have now are fine. Go practice.
 

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WARNING, THIS POST CONTAINS LINKS TO SOME VERY COMPLEX AND SPECIFIC SCIENTIFIC RESEARCH---THOSE WITH AN AVERSION TO SUCH DETAILED INFORMATION SHOULD STOP READING NOW AND GO IMMEDIATELY TO A MORE SUITABLE DISCUSSION IN THE SOTW FORUM LOUNGE :)

Dr. Gary Scavone has done extensive research on the "parabolic cone" of the saxophone which is summarized in his thesis beginning on page 83. ftp://ccrma-ftp.stanford.edu/pub/Publications/Theses/GaryScavoneThesis/thesis.pdf. This is a large pdf file and may take a while to download.

Dr. Scavone's credentials which are quite impressive are listed here: http://www.music.mcgill.ca/~gary/gpsvitae.pdf

Happy reading.

John
 

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Discussion Starter #15
gary said:
Sorry. I've read the above links now just to get a background, as well as reading this thread. I don't mean this insultingly but - what's the point?
Idle curiosity to some, essential saxophone issue to others. Among many of Rascher's adherents, Sax's horns are thought to be characterized by their "parabolic conical bore," and this resulted in a characteristic sound that was lost in saxophones produced after some time in the 1930s. To get a taste of how seriously John-Edward Kelly, for example, takes this issue, check out some of his comments in The Devil's Horn.
 

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SaxyAcoustician said:
... Where do people get this crazy idea that a saxophone can be or is or is supposed to be parabolic?? Do people actually know what the shape of a parabola is?? ...
Quoting Segal in The Devil's Horn: the parabolic shape of the saxophone's bore was the most distinctive feature of Sax's patent application.

However, I agree with you, the "parabola" in these discussions is no parabola at all.
 

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jbtsax said:
WARNING, THIS POST CONTAINS LINKS TO SOME VERY COMPLEX AND SPECIFIC SCIENTIFIC RESEARCH---THOSE WITH AN AVERSION TO SUCH DETAILED INFORMATION SHOULD STOP READING NOW AND GO IMMEDIATELY TO A MORE SUITABLE DISCUSSION IN THE SOTW FORUM LOUNGE :)

Dr. Gary Scavone has done extensive research on the "parabolic cone" of the saxophone which is summarized in his thesis beginning on page 83. ftp://ccrma-ftp.stanford.edu/pub/Publications/Theses/GaryScavoneThesis/thesis.pdf. This is a large pdf file and may take a while to download.

Dr. Scavone's credentials which are quite impressive are listed here: http://www.music.mcgill.ca/~gary/gpsvitae.pdf

Happy reading.

John
Thank you very much, John. That's why I love this forum. I don't mind being corrected if I misunderstood. In this case I admit that I weighed in too soon. It's not that the parabola is "blown into" but rather spun around to outline the cone which is then parabolic. So another way of looking at it is an infinite number of parabolas intersecting at one point to create this parabolically shaped cone-like surface.

Having said that, Adolphe Sax's intention in using the parabolic surface was to maximize the reflection of the sound out of the instrument, or the acoustic output, which I can agree with in theory. However, the parabolic shape inherent in Sax's design is so subtle in the conical bore that its effect is minimal in this regard. Also, I was curious as to how the harmonics would be affected by a parabolically shaped bore and this is shown in the thesis. The effect is absolutely minimal (this is stated as such in the thesis).

There are so many greater factors than what shape the conical bore assumes. The greatest of these factors is the player. Give different horns to the same player and he may or may not sound different, but any differences can be arguable as to what is causing it. However, you give the same horn to different players and it will sound different.

So to me, while it's a worthwhile exercise to some to investigate such matters, it's all about making beautiful music on the saxophone. And great players have done it on practically every make of saxophone, parabolic or not.
 

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chitownjazz said:
Idle curiosity to some, essential saxophone issue to others. Among many of Rascher's adherents, Sax's horns are thought to be characterized by their "parabolic conical bore," and this resulted in a characteristic sound that was lost in saxophones produced after some time in the 1930s.
Rant button turned on:

I'm sorry but this just leaves me scratching my head. Like I said above, typical forest-for-the-trees fixations more appropriate to meaningless doctoral studies over insignifica than in the real world of performance music. What counts is THE MUSIC.

Is someone really going to tell me that if Bozza or Glazanov or any number of composers for the saxophone heard one of their pieces played by sax player X, they're going to give one iota of a damn whether or not it was played on a parabolic instrument? It's the artistic expression that counts. And what is the end? Expressing the music as the composer intended or playing it on an instrument that is sanctioned by a handfull of true believers?

Furthermore, does Kelly for example, actually believe that he can't get the same sound on other saxes? If he can't then I challenge all the "it's the player not the sax" devotees to rally to the cause.

And using this same kind of purist, authenticity-centered thinking, it would then follow that no one should play Corelli on a Steinway, Haydn on a Bach or Mozart on an Alexander. Are these the rules we want to play by?


Caveat - as a purist-hobbyist, learning about and seeking the very specific instruments for music from specific eras can be a lot of fun and a world unto itself. I've got a Baroque flute and a modern one and I prefer playing the Bach sonatas on the former. And if the subject is purely one of a scientific discourse in and of itself - why not; have fun.

But when it crosses the line as to what kind of saxophones one can or cannot play to express a composer's musical and artistic wishes that IMO that's just pure rubbish.
 

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SaxyAcoustician said:
...Where do people get this crazy idea that a saxophone can be or is or is supposed to be parabolic?? Do people actually know what the shape of a parabola is?? Here, let me remind you:

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

I'm sorry, but how does this parabolic shape have anything to do with a saxophone? If it were indeed the case that the saxophone followed the shape of a parabola then the neck of our saxophones would be incredibly wide by the neck receiver, and the diameter at the neck receiver would be relatively comparable to the diameter of the bell!

C'mon, guys. This is embarrassing. I guess I'm not too surprised that such a mythological discussion would occur in saxophone land seeing how many discussions take place around here regarding what make/model is suited for jazz/classical, effects of finish, resonators, etc.

The shape of the saxophone has always been and continues to be conical. In many cases it may not be perfectly conical for design reasons (tone hole volume compensation, etc) but parabolic NEVER. Case closed. Now go practice!!!
So how do you respond to this quote from my post further up?

"Now a curve does not have to be a complete parabola, coming from infinity and going to infinity, to be called parabolic, any more than a line has to go on forever to be called a line.

Likewise, we can chop off the small radius bottom of a parabola, and the shape of the remaining curve is "parabolic", in that the curve fits the mathematical formula for a parabola, for a certain range of values."


See photo.
 

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chitownjazz said:
...However, I agree with you, the "parabola" in these discussions is no parabola at all.
So how do you respond to this quote from my post further up. (Some parts of a parabola can be very, very close tot straight.):

"Now a curve does not have to be a complete parabola, coming from infinity and going to infinity, to be called parabolic, any more than a line has to go on forever to be called a line.

Likewise, we can chop off the small radius bottom of a parabola, and the shape of the remaining curve is "parabolic", in that the curve fits the mathematical formula for a parabola, for a certain range of values."
 
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