Switch from Parabolic Shape to Conical

[SamJ]

Here's a brain tester for everyone. Perhaps someone can give me an answer, but I don't' know, brainstorming's good too...


Why did the saxophone shape switch from Parabolic to Conical?

[Ari]

Saxes used to be parabolic and later switched to conical???
Well you learn something new every day I guess.
When did this switch occur? what sort of models would be one vs. the other ?

[kymarto]

They never were parabolic. A parabola is not a shape that produces true octaves. There were and are slight bore variations to compensate for the vagaries introduced to the ideal cone by the addition of toneholes with their extra compliance and the truncation of the apex of the cone to put a mpc on the instrument, as well as the bow curve (among other factors such as the end correction when you have tone holes open at right angles to the bore with a certain depth that are not the size of the bore at that point). Different manufacturers empirically solve--or at least try to equalize--the problems with different bore variations, but basically saxes are and always have been conical.

Toby

[abadcliche]

i disagree with kymarto, and i disagree with the assumption that saxes are now strictly conical.

first, we have to figure out what parabolic means. as applied to the sax in the way Adolphe applied it in his patents it means: if you were to take a straight soprano sax, cut it in half lengthwise, removing all of the toneholes, lay it down on paper and trace it, the line from bell to neck opening would not be straight. instead, if you were to lay the sax down on some paper and trace the outline of your half sax, you would get a shape a lot like a parabola: (ignore the writing at the bottom of the pic, borrowed it from somewhere else)


that is, it would have a greater rate of taper for the first 1/3 of the sax than the second 2/3 (it gets wider faster at the neck end than it does at the bell end). Adolphe himself figured out that in order to get your octaves and upper register in tune, the rate of taper needed to be greater around the neck of the sax, near the octave pips. he patented his work regarding this.

there are two ways to have your bore properly "parabolic":

you can actually make the taper directly reflect this. you can see this on many a straight soprano, with the older yamaha 475 in particular really being easy to see.

you can bend the tubing, like on any neck that isn't straight. bending the tubing has the same acoustic effect as enlarging it.

so todays saxes are still "parabolic" in bore, otherwise they wouldn't play in tune. They have always been so, when built properly. Any sax that is a strict cone will play out of tune octaves.

[kymarto]

Sorry, but this is untrue. The only mathematically valid shapes for woodwind instruments are the cone and the cylinder. All other shapes create overtone series that are at mathematically (and thus musically) incorrect intervals.

Toby

[abadcliche]

Two quotes:

1. "French Patent #3226: Saxophone

(cut) This instrument is the Saxophone. The Saxophone is able to change the volume of its sounds better than any other instrument. I have made it of brass and in the form of a parabolic cone to produce the qualities which were just mentioned and to keep a perfect quality throughout its entire range.(cut)"




2. From "The Saxophone is My Voice" by Ernest Ferron
Page 18

ADOLPHE SAX'S PARABOLA

Very early on, the brilliant inventor noticed that, for the reasons stated earlier [in the book, pages 7-17, entirely too much to type out here], the bore's upper registers had a tendency to sound flat. To correct this, he had the idea of enlarging the bore on a zone of high register displacement antinodes. This zone is located in the upper third of the bore. In reality, this expansion of the bore is rarely a parabola in the geometric sense of the term, but rather a curving produced in relation to the requirements for tuning.

(Illustration of a parabola overlaid upon a cone)

THE NECK

What has just been stated concerning Adolphe Sax's "parabola" underlines the neck's importance in the construction of a saxophone.
(cut)
The famous "parabola" is clearly visible on some models of straight soprano saxophones.
Alto, tenor, baritone, and bass saxophones have curved necks. Adolphe Sax understood that a curved tube sounds differently than a straight tube, especially when the curve has a small radious. He patented his work in this area.
The wave forms and inertia of the air-column are affected by this curve. It is as if the bore were larger where it curves.
The same is true for necks. Even though the cone remains regular, the fact that the necks are curved often gives the same result as enlarging them. The curve's impact on tuning has been known by competent instrument makers for years.

[abadcliche]

Also for physical proof, check out some straight sopranos. As I said earlier, the yss-475 (at leas the ones from the 90s, which is the model I used to own) in particular is very visibly a "parabolic" cone.

[abadcliche]

Found a picture of a yss-475 on saxpics. Check out the taper changing between the octave pips, almost directly halfway between the top of the sax and the left hand thumbrest. There is your "parabolic" cone.

[kymarto]

Sorry again, but you've got it wrong. There may be some areas of the cone that do not expand linearly and may resemble a parabola for some limited distance, but this does not mean that the overall shape is a parabola. You quoted as much:

"In reality, this expansion of the bore is rarely a parabola in the geometric sense of the term, but rather a curving produced in relation to the requirements for tuning."

As I explained, the truncation of the cone to fit the mouthpiece, and the extra compliance added by the tonehole chimneys, mean that the mathematically-ideal conic shape will not produce a true overtone series. In compensation, makers change certain areas of the bore to bring the partials somewhat into line. Those changes might result in certian local areas resembling a parabola, but the shape of the sax is by no means a geometric parabola. If you don't believe this just measure the diameter of any sax from one end of the tube to the other (excluding the bell flare) and graph it.

Toby

[Rackety Sax]

Oooh boy, SamJ, don't know if you realized it but you've opened an old can of worms. I'm going to only partially get sucked in, I hope.

This has been discussed at length before on the site. Probably search "parabola" or "cone" or such.

Just one comment to abadcliche - my understanding of your description of Sax's "parabolic cone" is just the opposite meaning that I understand from the Rascher school's characterization of this cone. Namely, the curvature of the bore is not IN, but OUT - they describe looking down the bore from the neck opening of a Buescher True Tone or New Aristocrat and seeing the tone holes swoop out of sight.

Furthermore, they say that modern horns do not have the parabolic cone, so using a Yamaha to illustrate your point is wrong.

I'm just passing on what (I think) they say, mind you, not saying they are correct.

Glenn

[Mike Ruhl]

You're both saying the same thing, but you're splitting hairs over how to say it. A saxophone is neither a true parabola nor a true cone.

[kymarto]

Maybe this will help to clarify:

"The woodwind instruments as actually built are only approximately the cylinders and cones on which they are based. The deviations form the simple shapes are quite important musically, since they affect both the intonation and tone quality of the instrument. To begin with, the basic six-hole, seven-note scale (together with the added holes for sharps and flats) is used in all the instruments for the two main registers, and by means of cross-fingerings for higher registers. This is possible only for air columns which have a cylindrical or conical shape. This fact can be demonstrated mathematically; it is also demonstrated from the practical standpoint in that only these shapes have survived in the evolution of woodwind instruments. For any other shape of air column, it is impossible to use the same series of holes for two different registers; if the holes are so placed that the scale is in tune in one register, it will be out of tune in the other. It follow that any deviatoin in the woodwind instruments from the true cylindrical or conical shape will mean that a tone hole would generally need to have two different locations to be exactly right in the two registers. Therefore, in order to use the same hole for both registers, certain compromises are necessary.

[snipped explanations for flutes and clarinets]

The oboe and bassoon have complications similar to those in the flute and clarinet. Covered holes are usually present...the cone is not complete out to the tip, bit is cut off short of the tip and the reed substituted; the bassoon would be some 30 centimeters, (12 inches) longer if it were a complete cone. These factors produce deviation of the resonance frequencies from the desired tempered scale values..."

This is from John Backus in "The Acoustical Foundations of Music." He does not deal with the saxophone as such, but the bore is an analog of those of the oboe and bassoon. A much fuller treatment of the sax bore is available in C.J. Nederveen's "Acoustical Aspects of Woodwind Instruments." Pages 82-83 have comparative graphs of bore diameters as a function of distance to the reed tip for tenor, alto and soprano saxes. Except in the area of the neck, one can see that they are almost exactly linear cones to the bell flare. I'm sorry I cannot reproduce them here, but they are unequivocal.

So I hope that this helps to convince you that saying the bore of the sax is parabolic is only a bad cliché (sorry, I couldn't resist)...

Toby

[abadcliche]

Yeah Kymarto, we are saying the same thing, as Mike said.

Thats why I kept putting "parabola" in quotes, and why i said numerous times it wasn't a true parabola or was a shape "like a parabola"- not sure why you think I believe it actually is one. Its not (and never was) a true parabola. Parabolic was just a descriptive word that Sax used for a shape that resembled a parabola more than an even cone. I never said it was a geometric parabola in my posts; I'm not blind.


chitown- I've read about the Rascher/Buescher usage of "parabola"- something about an (apocryphal?) elliptical bore cross-section getting mixed up with the "parabolic cone" of Sax's design. Rascher students say that modern saxes no longer have this elliptical cross-section bore (sometimes they call this idea a parabolic bore, just to be confusing!). THAT is what they say is no longer in use. It is a different thing than what we are talking about here.

Kymarto - The parabolic CONE though, which again is just Sax's descriptive word for the first 1/3 of the bore has a greater rate of taper than the rest of the horn (and thus is not a true cone either) and not actually describing a saxophone that is a parabola, is still in use as you can see from the yss-475. It has to be, because this is what makes them play in tune, as we have both pointed out. Kymarto, this is what me and you are both talking about. its the same thing! I am just using Sax's original nomenclature (which is what the poster was using as well), and you are not.

[Rackety Sax]

It is a different thing than what we are talking about here.

OK, but I have a feeling then that you are not talking about the same topic SamJ initially raised. Maybe he can clarify.

[abadcliche]

If he is talking about that elliptical cross section thing, then I am running away!! (like the toneholes do when you look down the body of a buescher )

[paulwl]

I hear if you do enough tokes, you can get the same effect out of a Conn...

[SamJ]

Ha Ha, look what I've started! I didn't realize I'd be starting a battle.

This is the intent of my question.

I play at a Rascher school, and we tend to play on older instruments, why? They conform more closely to Sax's specifications than the new horns, hence the parabolic shape, which my Buescher has.

Back on topic, here is the question at hand. Why was the shape of the saxophone changed from what it was (parabolic) to what it is now (conical).


My guess would be perhaps and ease of production. Sax being an accomplish acoustician knew what he was doing. Any change would have damaged the way the saxophone was intended to act.

[Ari]

Actually I've quite enjoyed this thread so far - the posters have been very sincere and knowlegeable. Saxophones are such fiddly instruments and I am always keen to learn what makes them tick.

[Rackety Sax]

SamJ, please see the following thread for a detailed discussion of this issue in the context of the Buescher line of instruments.

http://www.saxontheweb.net/vbulletin...hread.php?t=77

Specifically regarding your question of why, the following excerpt of a post by Paul Cohen is very relevant:

The parabolic cone issue was explained to me in simple practical terms years ago when I was interviewing senior workmen from the early years of saxophone production. When asked about the parabolic cone, three of them told me, unequivocally, that with the introduction of machine-based, mass produced saxophone production, specifically with the extruded tone hole process, the parabolic cone was too impractical for mass production and ceased to exist. The more mechanized, mass produced machinery came into use in the second decade of the 20th century.

[Rackety Sax]

Although now that I read that more carefully, it raises a very interesting issue. That quote implies that the "parabolic cone" in Bueschers disappeared during the 1910s. The debate has always been between placing this date in the mid-30s (New Aristocrat=yes, Series I Aristocrat=no) or later.

But like I said, I'm not going to get sucked into this discussion.