If you have read any of my other blogs concerning saxophone mouthpieces you have seen that when it comes to discussing mouthpieces and mouthpiece baffles the conversation quickly becomes confusing. Part of the confusion comes from the nomenclature, which isn't really agreed upon between makers, players, re-facers, etc. Part of the confusion comes from just plain confusion. Like the confusion of equating fluid dynamics with acoustic dynamics. That's where I'm going to start. Not with confusion (hopefully), but with trying to explain how fluid dynamics and acoustical dynamics get muddled together.
Let's start with a common picture of "what's going on inside" a mouthpiece. You can enlarge by clicking on the pictures.
You find pictures like this at several places on the web and from several books about woodwind mouthpiece design. These pictures, and usually the accompanying text, shows the air/sound entering at the tip of the mouthpiece and passing through, sometimes glancing off of the mouthpiece at various places as it passes through. Usually, the way that the sound arrows ricochet around is claimed to effect the harmonics.
Here, the tiny lip under the table of the mouthpiece is claimed to be an impediment, creating chaotic inharmonics, as opposed to a cleanly bouncing virgin sound arrows which produce neat and tidy harmonics (because neat and tidy is always better??). Simple enough. In fact, it is way too simple. In fact, so simple as to be misleading. Actually, so misinformed and misleading as to be ridiculous.
Where to start? First, this "ping-pong" theory of sound isn't even close to accurate. Here is the basic idea of ping-pong theory acoustic reflection. It shows how tiny particles of sound (soundicules?) are reflected. Angle of incidence equals angle of reflection. Just like a ping-pong ball. Picture the soundicules "raining down" on this incline and reflecting off.
But sound isn't particles. A sound wave is more like a wave created by dropping a pebble in a pond. The wave spreads out simultaneously in all directions, including back inside the mouth of the player (more on that later). Sound waves do not reflect in a straight line like tiny particles of sound. They also don't bounce like a ping-pong ball. Here's the general idea of a reflecting sound wave.
The sound is emanating from point A and reflecting back off of a barrier shown in the middle of the diagram. The "B" side of the diagram just helps us understand how the reflection of sound "A" is calculated. In this diagram, the initial sound wave has been reflected back (an echo) and is approaching the source (A). If there were a reflective surface on both sides of A, the reflected waves would then bounce back again, their force somewhat reduced. The waves would intermingle to create a jumble of sound waves. That's not going to be neat and tidy. Truth is, the sound wave reflections in a mouthpiece never have been and never will be neat and tidy.
Without getting too complicated, here is a more accurate representation of what is going on.
The diagram on the left shows the first couple of pulses represented as sound waves and how they would begin to reflect inside of the mouthpiece depicted in only two dimensions.
Here are a couple of other wave diagrams that show the complexity of wave patterns. These are pictures of actual waves created in a shallow pan of water.
In this diagram, B shows the first several wave pulses emanating from more than a single point source. You can see how the waves begin to overlap and reflect back upon themselves. Diagram C shows the nodal points or "standing waves" that are created once a frequency is held constant for a moment. This is a photograph, so it stops time. What you would be viewing in real time is that the complex pattern would be constantly shifting.
It looks kind of confusing, right? Well, that's nothing. Remember that these diagrams are two dimensional representations made by waves on the surface of water. Inside of a woodwind mouthpiece, the sound waves are doing this in three dimensions. From that complex jumble, some waves are exiting the mouthpiece into the saxophone and their resultant shape and frequency will produce the pitch and unique tonal characteristics of this mouthpiece/horn/player combination. Those waves could have a "primary" frequency based on a combination of the effective tube length and the fluctuation of the reed. We would hear that as a "note."
The 3D jumbled wave idea is much more difficult to get our heads around than the super-simple super-silly ping-pong directional-arrow diagrams. But wait, there's more. The complexity is happening on both sides of the reed tip. There is also a three-dimensional fuzzy jumble of sound waves inside of your mouth, throat, lungs, and nasal cavity. Yuck. Sorry, but that's what's going on.
Again, forget about the arrows. Yes, the air is traveling out when you exhale and blow through the mouthpiece. But sound waves, being much faster, are also traveling back in and reflecting off of your interior surfaces.
When you blow through the mouthpiece, it's easy to think of "speeding up the air" in order to get a certain tone on the saxophone. Or "using warm air." I'm sure that there are other analogies used in describing how it feels to change your embouchure to get certain tonal qualities. But what you are actually doing is changing the shape and volume of the reflective area on the "front side" of the reed. i.e., in your mouth, throat, and maybe even your lungs.
That concept is too confusing to teach to children, so terms like "speed up the air," etc. are used. But promoting the speedy air theory, the ping-pong theory, the warm air theory, etc., ends up being really confusing. Unfortunately, that confusion stays with us and is even promoted by some. Sure, we can hit a certain note by "pretending that there is honey under our tongue," but what we are doing in part is changing the shape and increasing the volume of our oral cavity. The same is true by hitting a note by "speeding up the air," which is a changing the shape and decreasing the volume of the oral cavity.
These common descriptions get the player to the right physical position, but what we are actually doing is changing the reflective quality of our oral cavity and maybe beyond. We are changing the sound coming out of the mouthpiece by changing the sound going in, although the sound coming out is the goal and what we hear.
Mouthpiece baffles add more baffling complexity to this. But first, another detour. Air doesn't enter the mouthpiece just over the tip rail and then travel straight down through the chamber. Neither does sound. Figure #1 showed a diagram of the common ping-pong sound particle theory.
If you click on the diagram you can read on the left side that:
Put a reed on your mouthpiece and look at it. When that reed vibrates, you can see that air will also enter over the side rails. Air doesn't pass straight down the piece. It also spills over the side rails. Those side rails may be thick or thin. They may be undercut (as in vintage large chamber pieces). The may be straight sided (as with Brilhart, etc.). Everyone concentrates on the thickness of the tip rail and the shape of the baffle right inside the tip.
But the reed is also vibrating along the rail and air is spilling over the rails in pulses similar to the actual tip. How can the rails not affect the sound? And the opening/closing is taking place from the tip on back along the rail. Since the note produced is based on the length of the air column, from where would we measure? This "inexact" length may be what gives a particular woodwind it's recognizable sound, so it's not a bad thing that the source of the pulse is not an exact distance.
Sure, the tip of the reed creates sound producing vibrations. But it creates vibrations not as a single pebble in a pond, but along a curved sound producing area the width of the tip. The pulses created at the reed are also produced to some extent along the side rails. Both air and sound "slip over" the mouthpiece rails to add to the complexity. Clearly, those sound waves are not "aimed at" any possible under-table obstruction, as they would be pointed "sideways" when using the soundicules arrow theory.
So now we have wave pulses emanating from the general tip area of the mouthpiece traveling in all directions inside of the mouthpiece. There are sound waves traveling from one side of the mouthpiece opening to the other side of the chamber, which may be a straight walled Brilhart mouthpiece or a scooped wall Link mouthpiece. The characteristics of those reflective surfaces would also effect the wave pattern inside of the piece and ultimately the sound sent down the neck tube.
The mouthpiece sidewalls would comprise close to 50% of the reflective surfaces inside of the mouthpiece. The surface of the reed (kind of a constant flat surface) would comprise an additional 25%. Any little "interference bump" under the table shown in the second picture in Figure # 2 and #6 is minuscule in comparison to the rest of the surfaces. So then why does that tiny area have such a huge effect on the harmonics as claimed in the text? The long answer is because we can see that little surface. The short answer is that it doesn't make any difference.
If you look closely at the diagrams, the two mouthpieces used as the test have interiors that are quite different. So is it the little flat spot or the complete changing of the mouthpiece interior shape that makes the difference in the harmonics of the two different pieces? You can be the judge.
Here for your consideration is my experiment with effectively increasing the size of the obstruction under the table. I started with an early model of a Sumner Acousticut (they changed a lot over the years). This particular piece had a fairly blunt end to the window, much like the one depicted in Figure 1.
I'd used and really liked this piece, having never really looked down inside to see the terrible inharmonious, resistant, and imprecise response caused by the little ping-pong sound particles being aimed right at it. Prior owners for the last 60 years had also missed this horrible defect because they hadn't looked. And Sumner mouthpieces have a good reputation despite this restriction to soundicules.
First, I made the flat area 200% worse by adding a piece of plastic as a further "obstacle to soundicule arrows." Now you can't even sight from the tip straight through the piece. Certainly all of the tractor beam soundicules are aimed right at this newly enlarged obstruction.
Here is the resultant sound spectrum diagram with the increased obstacle to sound wave transmission.
Okay, I don't have the equipment for creating a sound spectrum (I suspect that neither did the original author, he simply didn't fabricate a picture as nice as mine). As I suspected, there were differences in the harmonics of my modified mouthpiece. The added obstacle made the Acousticut sound a bit dull and with less volume, as would be expected, but harmonics? I think that the unicorn is actually quite representative of the visual, oops, I mean the perceived harmonic differences.
The original little bump at the bottom of the table is about 1% of the chamber surface area and is deep inside the mouthpiece. A tiny change there makes no difference. True that I can make a readily apparent difference in harmonics by altering 5% of the interior shape right at the tip of the mouthpiece, but claiming that a tiny bump deep in the mouthpiece makes a huge difference requires one to adopt the ping-pong tractor beam particle theory of mouthpiece design. I believe that my unicorn theory is just as likely.
The distance(s) from the general source of the wave to the first open tone hole on the saxophone creates a sound frequency or pitch. By general source, I'm referring to the fact that we are not dealing with a point source and an accurate distance. As we have seen, the general source of the vibration is a curved tip and extends down the mouthpiece rails. We might think of the tip rail as the source, as when adjusting the mouthpiece to adjust the pitch, but the tip and rails form a general source of the wave and that distance is + or - a centimeter or more.
Whether the first open tone hole is C, D, Eb, it is the pitch that we first notice. The jumble of reflected sound waves created by different mouthpiece chambers ultimately produces a surprisingly uniform sound (discussed in another blog not yet published). The initial jumble created inside the mouthpiece effects the tonal quality of the pitch, but not the actual pitch.
You may have noticed that I never got around to discussing baffles. Sorry. I got distracted by the visuals of ping-pong acoustics, as have many others. I'll link to the further baffle blog when it is written.