The following is reprinted from The International Trumpet Guild Journal, Vol. 20, No. 3 Feb, 1996.
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The Asymmetric Trumpet Mouthpiece
JOHN LYNCH

Over the years numerous attempts have been made to improve the performance of trumpet mouthpieces in specific areas such as ease of playing, more desirable tone, and easier high register. These efforts have been, to my knowledge, essentially trial and error approaches, wherein improvement is determined by soliciting the opinions of various musicians. This approach to mouthpiece development has had limited success. Some progress has been made from these empirical activities, but only a few generalizations have emerged that appear to hold true. Two of these, which are usually regarded as "rules-of-thumb" and are widely accepted among mouthpiece manufacturers and trumpet players alike, are:

• A mouthpiece having a shallow (low volume) cup allows higher notes to be played more easily but produces a more metallic tone quality throughout the complete range of the instrument. Shallow cup mouthpieces are, therefore, desirable for the former property and undesirable for the latter.
• A mouthpiece having a deep (high volume) cup produces a more desirable tone but is frequently difficult to play in the extreme high register. Deep cup mouthpieces are, therefore, desirable for the former property and undesirable for the latter.

These rules have led to two distinct approaches to playing the trumpet. The more common approach, adopted by many players, is to use a mouthpiece having a cup of intermediate depth as a compromise. The other approach has been to use either a very deep cup mouthpiece or a very shallow cup mouthpiece, depending on the type of performance required by the particular performer; i.e., if all his performances require extreme high-register playing, he will use a very shallow cup mouthpiece and accept the brassy sound in the lower register. But if all his performances don't require extreme high-register playing, he will use a deep cup mouthpiece in order to obtain a more sonorous and desirable sound. These have been and are, the traditional approaches to mouthpiece selection, and both leave much to be desired.

In the case of the player who chooses the compromise of medium-depth cup, such a compromise usually produces a player of limited ability as an altissimo player and one whose tone quality is also somewhat less than ideal. And, for the player who bases his selection of mouthpiece cup depth either toward a very shallow or a very deep cup, similar limiations are seen in either high register-capability or tone quality. These limiations are a problem, because a performer's lips must become acclimated to a change in mouthpieces; this acclimation can require only a few days, but in some cases it may take weeks. Therefore, it is not generally feasible to change mouthpieces from one cup design to another to suit the immediate demands of the music. Thus, presently available mouthpieces do not offer trumpet players an effective solution to either range or tone problems.

In addition to these difficulties, others are fundamental to trumpet playing in particular. One is the great physical effort that must be exerted at and around any player's particular high limit. Another is that even the shallowest available mouthpiece can only be reliably played by many advanced student players, some of whom are proficient players in other respects, up to a modestly high limit of about C'''. Tumpet players today however, are expected to be able to consistently perform in the altissimo range, up to G and sometimes as high as C above high C. Students, therefore, often tend to be discouraged when they attempt high-register playing, because many of them experience difficulty even with a note as low as F above middle C; many, if not most, regard C above high C as unattainable. This has a tendency to dampen interest; many abandon the trumpet altogether for this reason. To summarize the current status of trumpet players in general, we might say that they fall into one of roughly four categories:

• A handful of professional specialists who can, with extreme physical effort and very shallow-cupped mouthpieces, execute the altissimo range up to C above high C, but whose tone is harsh in the lower register.
• Perhaps ten percent who can play up to about F above high C, again with extreme effort and shallow-cupped mouthpieces; these players may also have a less-than-ideal tone.
• Possibly thirty percent who can only play up to about high C, also with extreme effort.
• The remaining roughly sixty percent, mostly students, who can only reliably play up to about G below high C, and then with considerable difficulty.

Clearly then, essentially all trumpet players are limited, burdened, and/or compromised in some way by mouthpieces that are presently available to them. And, despite attempts by instrument and mouthpiece makers to solve these problems, none to date has been successful. The state-of-the-art of mouthpiece design has progressed essentially no further regarding these particular problems than the two rules-of-thumb stated earlier. What is needed is a new mouthpiece design that will reduce the difficulty of high-register playing for all trumpet players, students as well as professionals. This new design should also extend a player's upper register by a significant number of semitones, ideally five or more. And at the same time, it should impose only minimal restrictions on tone quality. The mouthpiece described in the following text has been designed to meet these demands.

The Asymmetric Mouthpiece

To facilitate understanding of how the Asymmetric mouthpiece satisfies the design criteria just mentioned, it is necessary to review the mechanism of sound production using a brass-wind instrument mouthpiece, to which end the following remarks are given.

A popular misconception about brass instrument sound production is that because sound is produced by a performer's tensed, vibrating lips, pitch can be raised by increasing tension in this lip tissue. We can see, however, using elementary physical analysis, that increased tension alone in the performer's lip tissue is insufficient to provide the lip vibration frequency required to execute the complete range of frequencies expected from a brass-wind instrument. The horn, for example, produces about four usable octaves. Raising a pitch by one octave doubles its frequency; four octaves raises it sixteen fold. If we assume that all physical parameters such as lip elasticity, mass etc. are constants, and tension and frequency alone are allowed to vary, we can, using the elementary equation for frequency vs. tension in a simple vibrator, express the ratio of highest to lowest tension as,

so that even if the lowest tension were only a few ounces, the highest tension would be over thirty pounds and would surely rupture soft lip tissue. Thus, we can safely conclude that lip tissue tension alone cannot produce a four octave range. What then, we might ask, is the supplementary mechanism that enables four octaves to be played?

The facts are that although higher frequencies do depend to some extent on increased lip tissue tension, the major causal mechanism at work here is a reduction in the effective vibrating mass of the upper lip. This reduction is caused by the lower lip in the following way. When the performer wishes to raise the pitch - whether realizing it or not - he compresses the bottom lip upward against the top lip. This upward compression has the effect of partially immobilizing the upper lip and thus reducing its effective vibrating mass. When the mass of a vibrator is reduced, the frequency of vibration increases, and the pitch becomes higher.

This effect is seen with other vibrators, such as a violin string. To raise the pitch, a violinist shortens the string by pressing it down against the neck with his finger. The only portion that is then free to vibrate lies between his finger and the bridge; this part contains less mass than the complete string with no finger down to shorten it. Thus, the lighter, shorter string has a higher pitch. The tension in the string is essentially the same, with or without shortening. A brass player's two lips function together much like the violin string and the violinist's finger. To play the complete range of the trumpet by relying on changing lip tension alone would be like playing the violin with one open string, and constantly changing the pitch using the tuning peg only - clearly an impossibility! When we change lip tension, it's like changing violin strings. This is a gross change (there being four strings), and several pitches are available with one tension, just as several pitches are available with one string. When we push our bottom lip up when playing the trumpet, it's like pushing our finger down when playing the violin. Both a tension change and a mass change are effected, but the mass change is clearly more important. It's necessary to remember throughout this discussion, that if too much pressure is applied to the lips via the mouthpiece, control is lost and high range will be impossible, so we must concentrate on "keeping a thick lip!" i.e., keeping sufficient lip tissue between the mouthpiece and our teeth. Think of any required "pressure" as vertical pressure between the lips, rather than horizontal pressure (mouthpiece against the lips).

Experimental studies (ref. Henderson) have verified that the upper and lower lips of a trumpet player function in distinct and different ways. In these studies, the upper lip function was shown to be to vibrate back and forth (opening and closing the embouchure) so as to admit consective puffs of air into the mouthpiece, thus creating the alternating air compressions and rarefactions required for sound production. The principal function of the lower lip was shown to be to press upward against the upper lip so as to control the frequency of the upper lip's vibration by reducing, to varying degrees, its effective vibrating mass. Having discussed this concept of embouchure mechanics, I would now like to review brass-wind instrument mouthpiece geometry as it relates to the theory that was developed from systematic experimental studies, along with developmental prototypes, to arrive at and support the Asymmetric mouthpiece concept.

If we examine currently available brass-wind mouthpieces, we find without exception, that they are radially symmetric. This suggests that manufacturers may currently believe that although the top and bottom lips have apparently different physical structure, and although they perform strikingly different functions, a mouthpiece can function well without taking this into account; i.e., all commercially available, radially symmetric mouthpieces do not acknowledge either physical or functional differences between upper and lower lips. We note, in contrast, that this is decidedly not the case with reed instruments, such as the clarinet or saxophone. With these instruments, the mouthpieces are highly asymmetric and are designed specifically to accommodate both physical and functional upper and lower lip differences. Another possible explanation for brass mouthpiece symmetry is that manufacturers may possibly not be aware of, or place any importance on, the embouchure mechanics discussed above. But the most likely explanation might be that mouthpieces have always been made this way. Historically, the first "horns" were, in all likelihood, animal horns with the small tip cut off. Since then, the natural symmetry of the animal horn has prevailed. Also, mouthpieces are turned on lathes, and this mode of manufacture possibly tended to perpetuate the notion of symmetry as being required or even ideal. At any rate, radial symmetry has never been questioned, with specific regard to the differing lip functions explained above, until now.

Conjecturing that a mouthpiece cup could possibly respond differently to top and bottom lips as well as to cup depth, prototypes were made and experiments were performed using an orthogonal composite fractional factorial regression model (refs. Davies and Lynch) in which the curvature of the top half of the cup, the curvature of the bottom half of the cup, and the cup depth were treated as independent variables. Optimization of the resulting performance response equation showed the ideal mouthpiece to have a concave upper half and a convex lower half. These experiements, along with several subsequent prototypes made to explore and develop this configuration, let to the following theoretical explanation for the experimental results.

Let us assume that at some arbitrary frequency, a player's bottom lip is exerting an upward force sufficient to ensure that the effectively correct mass of upper lip tissue will be vibrating to produce this frequency. As the player attempts higher and higher frequencies, eventually he attains the maximum amount of upward push that he is capable of exerting and at that point is playing the highest pitch that he is capable of producing. We now consider the bottom lip in more detail.

The portion of the bottom lip tissue that lies inside the boundary of the mouthpiece rim surface is rigidly constrained on one side by the player's lower teeth. This portion is also further rigidly constrained on its lateral and bottom sides by the mouthpiece rim surface. It is not, however, constrained on its front surface, which faces into the mouthpiece cup, nor is it rigidly constrained on its top surface, which is being pushed upward by the player against his top lip. This upward push is caused by contracting the lip muscles, especially those muscles that control the lower lip. The lip tissue then is bulging upward and forward, the only directions in which it is not rigidly confined. The upward component of the bulge is producting the required upper lip immobilization, and the forward component of the bulge is causing lower lip tissue to enter the mouthpiece. This forward bulge is contributing no constructive or significant action except to reduce the cup volume slightly, which is producing a slight to negligible effect on intonation and tone quality. With this in mind, we now consider an alernative geomtery for the bottom half of the cup.

If the lower half-cup surface edge nearest to the bottom lip were made sufficiently convex, that portion of the lower lip tissue intruding into the cup would now tend to be pushed backward toward the player when it encountered this convexity. The lower lip tissue then, being an elastic container (lip tissue) filled with an essentially incompressible fluid (blood), would act much like a balloon filled with water and would accommodate this additional compression by bulging even further in the only remaining unconstrained direction (that direction for which there is no rigid constraint), namely toward the upper lip. This additional upward push would then result in additional upper lip immobilization and therefore in an increase in upper lip vibration frequency; i.e., highter pitch. Prototypes have shown a typical increase in range due to this mechanism of as much as seven semitones. Furthermore, because of the generally convex contour of the leading edge of this lower convex half-cup, the action of the mechanism is a progressive and continuously increasing one with pitch; i.e., it has little to no effect in the middle and low registers where lip intrusion is negligibly small, and a gradually increasing effect with frequency into the higher range where air pressure is higher and the associated increased mouthpiece pressure against the lips and increased muscular contraction normally causes larger lower lip intrusions. Thus, the leading convex lower surface not only extends a player's high-range capability but makes all high-range playing easier.

Introducing the convexity into the lower half cup surface, by itself, would reduce normal overall cup volume. Without compensating for this reduction, tone would tend toward the brassiness of shallow conventional-cup mouthpieces. This cup volume reduction can be compensated for, however, by enlarging the upper concave portion of the cup. For example, if we know that a particular symmetric cup volume will produce a particularly desirable tone quality, then instead of reducing that volume by making the cup shallower in order to obtain high-range capability (as is currently done, and thereby destroying the tone), we instead spatially redistribute this particular cup volume by making the bottom surface convex and the top surface sufficiently concave. This conforms with the experimentally derived ideal having concave upper and convex lower half-cups. It has been shown that total cup and backbore volume, rather than the particular shape of a cup, tends to determine tone quality and playing properties for a given player (ref. Benade). Thus, in this case, the Asymmetric cup would have essentially the same total cup volume as the symmetric cup, and the tone quality would remain unimpaired. But, increased range and an overall ease of high playing would be gained over the symmetric cup mouthpiece.

It should be noted that any symmetric form of lower lip restrictor would also restrict the upper lip and inhibit vibration of this lip. And, even if such a restrictor were relatively small in width, it would also reduce the span of the cup for the upper lip. But the full span of the cup is required for the upper lip lest the vibrating mass be over-restricted and clean attack compromised. Both calculations and prototypes have shown that even with mouthpiece vertical respositioning, the tradeoff is such that bottom lip performance is enhanced by the restrictor, but simultaneous top lip restriction would impair its performance. Thus, asymmetry is required. It should also be noted that players using incorrect mouthpiece vertical positioning (other than the generally accepted 1/3 on the top lip and 2/3 on the bottom lip) will be unable to use the Asymmetric mouthpiece successfully. Players who position the mouthpiece "half on each lip" for example or more on the top than the bottom will experience the convexity as an obstruction to the air stream. Most players, however, use the "2/3 bottom, 1/3 top" position, this having been experienced for the last hundred years (see, for example, Arban's method) as more advantageous for higher register playing. Although the reason for this is clearly that much less top lip has to be immobilized, this was only known by experience prior to the last 50 years. Other positions decidely handicap the player unnecessarily.

Summary

The Asymmetric's cup design can add up to one-half octave of high range capability and make all notes in the high range generally easier to produce, and do this with no loss of tone quality. The Asymmetric cup mouthpiece discussed herein is therefore significantly and undeniably superior to radially symmetric mouthpieces. Furthermore, the theory underlying this concept is substantiated by prototypes and systematically obtained experimental data and does not rely on cut-and-try efforts.

The Asymmetric mouthpiece is used in exactly the same manner as a symmetric mouthpiece with one small but important exception; the Asymmetric must be inserted into the trumpet with the convex portion of the cup surface down, so as to be substantially nearer the bottom lip than the top lip of the performer. Once installed with this orientation, no other special consideration is required because the mouthpiece does not rotate in the instrument when playing. Tests showed that as much as ten degrees of rotation, clockwise or counterclockwise could be tolerated without appreciably impairing the Asymmetric mouthpiece's efficacy. Also, the orientation of the trumpet's slides, valves, and other structure vis-a-vis the mouthpiece's axial orientation provides the player with an instant visual confirmation of the mouthpiece's axial orientation when playing. This orientation will remain essentially constant, because the performer's hand positions when playing must remain essentially constant to ensure unimpaired valve manipulation.

References

Henderson, H.W. An Experimental Study of Trumpet Embouchure. J.A.S.A., Vol. 13, pp. 58-64, July 1942.

Davies, O.L. The Design and Analysis of Industrial Experiments. Hafner Publishing Co., 1956.

Lynch, J.H. A Systematic Approach to Model Development by Comparison of Experimental and Analytical Regression Coefficients. NASA TM-X 1797, May 1969.

Benade, A.H. Fundamentals of Musical Acoustics. Oxford University Press, pp. 414-418, 1976