### The Asymmetrical Mouthpiece Page

To go to Lynch's site, follow this link. Ohterwise, scroll on down for my discussion on how I have interpreted the physics that would justify this design.

Nicholas Drozdoff ndrozdoff@hotmail.com

# The Basic Physics Behind A Lynch Asymmetrical Trumpet Mouthpiece

### by Nick Drozdoff

John Lynch, the designer of the asymmetric trumpet mouthpiece, wrote an article in the International Trumpet Guild Journal for the February Edition in 1996. Anyone really interested in finding out more about his design ideas and theories about high note trumpet playing should get a copy and study it for themselves. What is presented here is an "interpretation" of the ideas set forth in his writing.

Many trumpet and physics teachers will blithely say that lip tension is the factor that determines the pitch that a trumpeter plays. They will say that as one plays higher, the lips must somehow be stretched tighter. I myself have made that same statement. While the lips do increase in tension for most players as they ascend in pitch, the notion that this is primary determinant of pitch is mistaken. Lynch points this out very nicely in his article, but I want to take a more direct look at it here.

Let's begin with the most rudimentary vibrating device that changes pitch with tension, a vibrating string. The accepted equation for the frequency of a vibrating string fixed at both ends is as follows:

##### f = (n/2L)(T/m)^.5

Now the symbol ^.5 simply means "the square root." The variable "n" refers to the number of the harmonic. For example, the fundamental, or the lowest resonant frequency of the string has n=1. The variable "L" refers to the length of the string. The variable "T" refers to the tension of the string. Last, the variable "m" refers to the linear mass density, or mass per unit length.

Now that that is on the table, let's make a first order approximation of how the lips work. Let's assume that they behave very much like a vibrating string and follow a similar equation. What does this mean to the trumpeter? Lynch's interpretation goes like this. Most good lead players can cover a range of four octaves or more. Octaves are multiples of powers of 2. That is, one octave is twice the original frequency, two octaves is 4 times the original, 3 octaves is 8 (two cubed) times the original and 4 octaves is 16 (2 to the 4th power) times the original.

Now if we assume that all of the basic parameters are held constant (the length, and the mass density) and vary only the tension and the frequency we can see that we are comparing n=1 to n=1 with a new fundamental frequency established by the higher frequency. Let's now take the ratio of the frequencies created when we do this.

##### f2/f1 = [(1/2L)(T2/m)^.5]/[ (1/2L)(T1/m)^.5]

Now we can see that the length and mass densities, which are all equal, cancel out, as will the coefficient of 2 on the L. We are left with the following:

##### f2/f1 = [T2^.5]/[T1^.5] = 16

Now this is exactly what Lynch has on page 53 of the ITG journal article. What does this end up meaning? Consider only the tension side, [T2^.5]/[T1^.5] = 16. If we square both sides, we get the following:

##### T2/T1 = 256

This means that in order to produce a note four octaves higher that the trumpeter would have to stretch his lips to a tension 256 times greater than he started with. "…Even if the lowest tension were only a few ounces, the highest tension would be over thirty pounds," says Lynch. Have you ever tried to pick up a thirty-pound bag with just your lips? Even for the most brutal trumpeter, this isn't a likely scenario.

Now Lynch goes on to say that the main factor in what drives the pitch up is the mass. Let's explore that a little more here. If we consider the same equation and control everything but the mass density we will end up with the following:

##### f2/f1 = [m1^.5]/[m2^.5] = 16

By the same analogy, we can conclude that by reducing the mass density by a factor of 256, we can achieve the four-octave skip. This is much easier to achieve than the 30+ pounds required to do it with tension.

Now it is very important to note here that this analysis is at BEST only an approximation. To me, it seems very unlikely that the equations that will result from the differential equations describing the forces in the lips will be the same, but it does seem likely that tension won't be the main factor in pitch determination.

Now the way I achieve higher frequencies is outlined in my book, "Embouchure Design", but I'll include a discussion here fitting this context.

As I ascend in pitch I am very aware of doing a couple of things. First, I very deliberately reduce the "aperture" size. I think of myself reducing the "hole" that the air is escaping through between my lips as I play. This will reduce the vibrating mass. Next, I have always, regardless of whom I have been studying with, raised my lower lip towards the upper lip. This assists in my closing up the "aperture". Lynch refers to "immobilizing the upper lip" thereby reducing the vibrating mass. This way of thinking is very consistent with what I find myself doing as I play higher notes. In any case, the motion that my lips tend to go through as I play higher is up and down (vertical) not side to side. In other words, I don't stretch my lips tighter with some sort of a smile. This, I'm sure you will find, is consistent with most contemporary trumpet instruction (never stretch the lips thin, but "pucker" more with firm corners, etc.).

Now with a conventional mouthpiece, as your lower lip comes up, it also bulges slightly into the cup. This forces the lower lip muscles to work harder to keep the general motion upward to reduce the vibrating mass. The asymmetric mouthpiece assists this process in the following manner. As your lower lip comes up, the asymmetric forces it straight up without bulging into the mouthpiece. It can't go anywhere but up! This reduces the need for muscular activity in also keeping the lower lip in.

Another component here that helps this mouthpiece sound good is the fact that the depth of the upper part is significant. It is not a shallow mouthpiece. There is plenty of room for the upper lip to vibrate. This will ensure a good tone in all registers. Now, we all know that mouthpieces with small volume cups and tight backbores favor the upper partials thus resulting in a very bright sound all the time. Well, the asymmetric can produce a good tone because, while the volume of the cup is smaller by virtue of the thick lower rim, it is still deeper. Also, the throat and backbore are designed to compliment the smaller cup volume.

Now, in using one of these mouthpieces I have found that the lead model does not have as nice a low register as a Laskey 81D, but it does hold its own quite nicely. The reason for this could be that the lower lip does contribute more to the vibrating in the lower register. In the high register, I feel that my upper lip is the primary vibrating surface, but I'm not prepared to make the same claim from low C on down. Lynch has designed two other models for playing more varied styles. His 3C and his Opera models incorporate the same asymmetry to good advantage but with sufficient cup volume to allow the player to navigate the lower register more effectively.

In conclusion, let me reiterate that the "analysis" show above is very approximate in nature and is intended only to attempt to explain in a little more detail what I see as the theory behind the asymmetric mouthpiece. You should do your own study to see if you agree. Above all, you should review Lynch's original article.

I do have another article on "How to Use A Lynch Asymmetric" elsewhere on this site. If you are interested in trying one of these mouthpieces, you should also read this.

The equation shown above was taken from Dr. Tom Rossing's book, "The Science of Sound", page 55. This is an excellent reference book for the physics layman. It is thorough yet understandable.

##### QED

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