Saxophone mouthpiece study

Toby. Thank you for that clear explanation with the necessary foundation laid out to make it easy to grasp the higher concepts. My explanation was "tongue in cheek" and a feeble stab at humor. Yours was the real deal. May I ask where you have found your information about the effects of the helmholtz resonance of the mouthpiece that you refer to? Benade indicates the playing frequency (Frs) of the saxophone mouthpiece on its neck must come close to matching the natural resonant frequency of the missing cone calculated by the formula Frs = v/2xo where v is the velocity of sound and xo is the length of the "missing cone" including the length of the neck. The part I am still unclear on is how the "equivalent volume" of the mouthpiece which is roughly 30% larger than its geometric volume ties into the ideas about the helmholtz frequency.
 
My explanation was "tongue in cheek" and a feeble stab at humor.
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Yes, but we still love you just the same.

Relating this back to my comment about lying to you, another truism is that if you can't explain it in a sentence, you probably don't have a good enough grasp of what you're trying to talk about. The ELI5 idea is that you really should think more about the subject matter and try to distil it into something that can be understood by a 5 year old. Or a former pro musician :p.
 
jbtsax said:
Toby. Thank you for that clear explanation with the necessary foundation laid out to make it easy to grasp the higher concepts. My explanation was "tongue in cheek" and a feeble stab at humor. Yours was the real deal. May I ask where you have found your information about the effects of the helmholtz resonance of the mouthpiece that you refer to? Benade indicates the playing frequency (Frs) of the saxophone mouthpiece on its neck must come close to matching the natural resonant frequency of the missing cone calculated by the formula Frs = v/2xo where v is the velocity of sound and xo is the length of the "missing cone" including the length of the neck. The part I am still unclear on is how the "equivalent volume" of the mouthpiece which is roughly 30% larger than its geometric volume ties into the ideas about the helmholtz frequency.
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John, Fletcher and Rossing talk about the two orders of correction in their book. This jibes with Benade. We had a huge debate on SOTW about the meaning of the mpc "on its neck", but it seems clear to me that it is the resonant frequency of the interior of the mpc as it sits on the neck in the correct position, and has nothing to do with the combination of mpc and neck together.

I said I wasn't going to get into it, but you asked ;)

A classic Helmholtz resonator is a mass of air enclosed in a bulb, with a neck. A true Helmholtz resonator is notable for the fact that it has no partials--it is the fundamental or nothing. Bottles are not true Helmholtz resonators, for example, because one can overblow other frequencies, but the Helmholtz resonance is considered to be the main fundamental frequency that sounds when air is blown across the opening of the neck. Because any shading of the hole can alter the sounding frequency, a better way to measure the frequency is with a "pop" test"--tap the opening and listen for the frequency created.

The Helmholtz resonance of a given enclosed volume of air depends (apart from the usual suspects of air temperature and composition) on three geometric factors: the mass of air enclosed in the bulb or chamber, the length of the neck and the diameter of the neck opening. More air, longer neck and smaller neck opening all lower the resonance frequency.

So actually we have two parameters to play with independent of the actual volume in order to vary the frequency. But on a sax, the opening diameter is fixed for all practical purposes: it is the inner diameter of the neck. That leaves us with the question of where the bulb ends and the neck begins, because a mpc is not at all a classical Helmholtz resonator. Still, by changing the amount of volume in the chamber as compared to that in the throat, there should be the possibility of changing the resonant frequency of the mpc as it sits on the neck.

With the sax, unfortunately, the fact that we must move it on the neck makes tailoring the Helmholtz frequency difficult. On the tárogató, for instance, the throat diameter can be varied in order to change that value, but the throat diameter cannot be less than will fit on the cork. If you want to experiment, you can try temporarily reducing the neck diameter with plasticine, for instance, or reducing the diameter at the top of the throat. Unfortunately, these are not really good adjustments, because they introduce discontinuities in the bore. In the case of the neck, the reduction will only be at the very end of the neck, and in the case of the mouthpiece, the throat diameter will widen back out before it comes to the neck insertion point.

As to the question of the actual volume being different from the theoretical volume, there's that pesky thing called a "reed". The mechanical parameters of the reed definitely affect the sounding frequency, as do the aeroacoustics near the reed tip I imagine. I am not familiar with this stuff, and I believe it is quite complex and probably not well modeled, although I have seen papers on it. Here is a taste:

http://viennatalk.mdw.ac.at/addons/Add_01_49_Chatziioannou.pdf
 
Thanks for that information. I haven't studied Fletcher and Rossing's book as much as the others largely to their painfully brief discussion of the acoustics of the saxophone. I am going to dig in to the entire chapter on woodwinds, read between the math and try to increase my understanding. Are there any other sources that deal with the physics of what takes place inside the mouthpiece other than the Rocaboy study. Wyman's work seems to be more empirical than theoretical but contains a lot of useful information.
 
I tried really hard to read everything and comprehend but... forgive the ignorance of my follow-up questions because the math eludes me greatly. If you have a relatively large chamber mouthpiece like a vintage Otto Link and place a baffle in it reducing the inner volume of the mouthpiece will it have the same effect as playing on a smaller chamber mouthpiece? Also, does the oral chamber and opening up your throat as a player factor into the extended cone of the horn and compensating for the size/shape of the mouthpiece?
 
The effect of putting a raised baffle in an existing mouthpiece has a far more pronounced effect upon the overtones produced than on the proportionately small reduction in the overall mouthpiece volume.

In a study I did replicating a method used by Benade and Gebler, I found that the "equivalent volume" of a Rousseau 4R classical mouthpiece to be 33% greater than its measured geometric volume. The "equivalent volume" is the volume "seen" by the saxophone as its "missing cone" under playing conditions. It includes the area of the reed's travel and a portion of the oral cavity of the player just in front of the reed.

Another example of the volume added by the player's embouchure is when jazz players push the mouthpiece farther onto the cork and then open the teeth and play lower on the pitch to bring the saxophone in tune. The increased volume in the oral cavity along with the increased travel of the reed compensates for the mouthpiece volume taken away by moving the mouthpiece farther onto the cork. Fascinating stuff.
 
I don't think that the oral cavity volume has any effect on intonation except where the impedance of the tube is very weak and the upstream impedance of the oral cavity very strong. That can happen for single notes in some circumstances, but for overall playing that would mean that the player would have to expertly vary oral cavity resonance during playing and that does not happen. If a player "lips down" the pitch that is all about increasing the effective volume by less lip damping AFAIK.
 
Are you sure? On a clarinet I can "lip" a C6 down nearly an octave but I don't think my lips do all that much. It feels more like something in my throat that's very difficult to describe.

Are you sure that we aren't all "expertly varying our oral cavities" all the time? I've been switching between Boehm system and an early clarinet recently. Occasionally I get mixed up and play a completely wrong fingering for an altissimo note. When this happens, rather than just a wrong note I sometimes get an unstable sliding sound that seems to be trying to get to the right note. It just happens all on it's own, like my embouchure is set for one note and the instrument for another and there's a fight going on between them.
 
kymarto said:
I don't think that the oral cavity volume has any effect on intonation.
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Well, as I mention above, I think this would make a difference. If you take an 8 year old that can play perfectly in tune and age him to 70, will he have to make adjustments other than just holding the mouthpiece in his mouth? I'm actually asking: I haven't done study in this field, but I'd think that the answer should be, "Yes."
 
kymarto said:
I don't think that the oral cavity volume has any effect on intonation except where the impedance of the tube is very weak and the upstream impedance of the oral cavity very strong. That can happen for single notes in some circumstances, but for overall playing that would mean that the player would have to expertly vary oral cavity resonance during playing and that does not happen. If a player "lips down" the pitch that is all about increasing the effective volume by less lip damping AFAIK.
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The famous clarinet glissando at the beginning of Rhapsody in Blue is not done by lipping. The pitch is lowered using the player's oral cavity. Also see this video by Randall Clark who is both a fine classical player on saxophone as well as being a great jazz player.

[video]http://www.cannonballmusic.com/tonevideo.php[/video]
 
Years ago (back in the early 1980s) I spent quite a bit of time with a "clarinet expert" whose name escapes me at this remove, but he was a published author on the topic, and had a book with tons of observations on this particular topic.

He was adamant that the tone of an instrument was governed not only by the bore and openings, not only by the mouthpiece cavity and configuration, and not only by the oral cavity of the player, but to some degree by the entire respiratory tract. He developed this opinion from years of experimentation following his observations on the massive changes that a severe respiratory infection had, not only on air flow/volume, but on the tone overall.

I'd know the name if I saw it in an instant. I'm thinking maybe it was Stubbins, but it may have been someone else who had a minor modification of the Boehm system. I know that he is long time dead at this point.
 
Here is the definitive paper (so far) on the subject:

http://www.phys.unsw.edu.au/jw/reprints/SaxJASA.pdf

In fact, they state it is possible to bend pitch even in the normal playing range--but only down--by even several semitones. There is a caveat here: the vocal tract must be strongly tuned to the note being sounded. I find it difficult to believe that even experienced players bring the pitch up by any significant amount and then use the vocal tract to pull down the overall pitch in general playing, since the vocal tract must be strongly and precisely tuned for each different frequency being sounded. More likely, what is happening overall is that the change in oral configuration changes the embouchure, and the overall lowering of pitch is due mostly to increased effective volume in the mpc with a slight shift of embouchure. That is pretty clearly what is happening in the Cannonball video--he demonstrates lowering the jaw, but that is a lame example of relaxing the embouchure and giving no support. When Clark says he drops the tongue but holds the embouchure firm, do you really think that doesn't change the pressure on the reed? Embouchure muscles remain firm, yes, but dropping the tongue also changes the position of the jaw. Try it yourself: you can't drop the tongue without changing the position of the lower jaw.
 
In my experience as a saxophonist I have found that opening the oral cavity does not alter the firmness of the muscles around the mouthpiece we call the embouchure. If a player is "biting" and using the jaw and lower teeth to put pressure on the reed by pushing up on the lower lip, in that case opening the teeth will reduce the pressure on the reed. However with a well formed "ring of muscles" around the mouthpiece there is no change in pressure on the reed when the oral cavity is opened.

It is also important to differentiate between the front and back of the tongue. If the front of the tongue is at the bottom of the mouth, of course it can't be lowered more without dropping the jaw. However the back of the tongue can be moved up and down completely independent of the jaw. For proof, sing "EE" and then "AHH" while holding the jaw.

Using an oral cavity with an exaggerated opening along with firm embouchure allows a player to play lower on the mouthpiece pitch throughout the range of the saxophone. Of course a compensation must be made by pushing the mouthpiece farther onto the neck. This no more requires "tuning" each note with the oral cavity, than does playing with a "regular" oral cavity opening. As Randall Clark explains in his video, using a firm embouchure and increasing the opening of the oral cavity produces a fuller and richer tone compared to the "pinched" sound of a firm embouchure alone.

Developing the ability to "bend" notes down without relaxing the embouchure is invaluable, not only for jazz inflections, but also to bring in tune the ordinarily sharp notes on the saxophone such as D2, A2, and C#3 without the flabby sound of a relaxed embouchure.
 
Interesting to note that Wolfe et al found that experienced players nearly always play with an almost-closed glottis. What you say makes no acoustic sense, since to influence pitch without a change in embouchure would mean adjusting the resonance of the vocal tract very precisely for each note, in order that Z-tract would be strong enough to influence Z-bore. The most obvious conclusion is that the embouchure IS affected, no matter that you feel that it isn't. It's like the materials debate: geometry is a strong influence, material is a weak influence. Just because one horn in silver looks exactly like another in brass does not mean that it is. The real way to answer the question is obviously with an artificial embouchure; that would clearly separate the question of embouchure from that of resonance. I'd be willing to bet dollars to dimes that if embouchure is held really steady pitch would only be affected within a very narrow and precise resonance range that would have to be varied for each note or at best group of several notes.
 
Just did an experiment with my thumb. Try it. With your thumb substituting for that slant Link, make a nice firm embouchure. Form "eee" and then move to "ohh". The cavity is increased in the back, which pulls the lower jaw down moving the chin forward and rolling the teeth further back on the lay. Even if the mouth muscles do not move, it increases compliance inside the mpc. That is what is dropping the pitch, not the change in oral cavity resonance. A very different story than simply dropping the jaw as the Cannonball guy does. Firm embouchure and control are maintained, but more of the reed is free to vibrate.

Update: just pulled out my alto. Impossible to change the volume of the oral cavity by dropping the back of the tongue without major changes to the embouchure. The jawbone does not stretch. You can pull the tongue back without changing embouchure, but that does not change the actual volume of the oral cavity; it just redistributes it.
 
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Toby, what you are describing in your physiology is simply not true for me. The back of my tongue moves up and down independently from the muscles that move the jaw. What's more the obicularis oris muscles around the mouth that form the embouchure are also independent of the movement of the tongue. If that were not the case every note one tongues would be distorted by movement of the embouchure.

I agree that the formation of the vowel sound "OHH" tend to cause the jaw to drop. That's why I used the vowel sound "AHH" which lowers the back of the tongue but does not open the teeth and drop the jaw. Saxophonists refer to the proper "voicing" of notes to produce the desired timbre and pitch. This is done by shaping the oral cavity quite independent of the embouchure tension. In the video when Randal plays palm D and then lowers the pitch a C#, C, and B with D's fingering, it is not done by relaxing the embouchure, but by changing the oral cavity. If it is possible to adjust the pitch this far, then doesn't it make sense that the same mechanism can be used to "tune" a sharp note by dropping the pitch several cents without loosening the embouchure?
 
There's another way to change the volume of the oral cavity: puff out your cheeks. kymarto, I think that the problem is that you're saying that the oral cavity is always has a consistent size. That would only be true if the oral cavity was a closed system. It's not. You can say that each individual has a maximum oral cavity volume and that volume will vary from person to person.
 
The air hitting the reed at a downward angle causes the pitch to go down? C'mon, that's simply ludicrous. Now please pitch bend and tell me that your embouchure position doesn't change at all.

Let's get more precise. Leaving puffed cheeks aside, since that is not a normal means of changing voicing, we have a space defined by bone, apart from the underside of the lower jaw and whatever happens back near the glottis. No matter what the shape of the tongue, it is of a fixed mass.

Of course it is possible to change the resonance of the oral cavity without changing jaw position, as whistling through clenched teeth demonstrates. Mostly this has to do with the space left in the front of the oral cavity. But to think that pitch bends depend primarily on the weak passive impedance of the oral cavity strongly affecting the very dominant impedance of the tube is strange, to say the least. Pitch bends are always done primarily by changing the mechanical forces acting on the reed. That doesn't mean a slack jaw, but quite fine adjustments to pressure (mostly) on the reed, while keeping lip damping nearly constant. It is important to understand that the embouchure consists of both pressure variations dependent on the muscles of the jaw through the teeth, coupled with lip damping controlled by the muscles of the mouth. Oral cavity resonance effects are special cases, which have to be tailored to single notes and cases such as in multiphonics, bugling, altissimos and the like, and even in those cases they are always coupled with embouchure adjustments.
 
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