The mouthpiece of the trumpet is the interface between instrument and musician, and represents one of the brass instrument's most sensitive parts. Besides the influence of the embouchure, the form of the mouthpiece has a great effect on the intonation of the entire instrument. In order to observe the influence of varying mouthpiece forms on the input impedance-and consequently the intonation- of the trumpet, the resonant frequencies of a trumpet with varied mouthpieces were calculated with the help of a computer model (Simulation PMP).
Using the standard Viennese mouthpiece as a point of departure, the following factors were successively varied:
Fig.1: Standard mouthpiece, x axis length [m], y axis radius [m]
During all variations, except for the cup variation with constant cup volume, the total length, the initial radius, and the terminal radius were held constant.
Figure 2 shows the examined cup form. Figures 3 and 4 show the influence of mouthpiece and trumpet resonance resulting from the variation in the cup form.
Fig.2: The different cup forms
Fig.3: Changes to the mouthpiece resonance relative to the standard mouthpiece through variation of the cup form
Fig.4: Changes to the trumpet resonance relative to the trumpet with a standard mouthpiece through variation of the cup form
Enlargement of the cup volume results in a decrease in the trumpet resonance, while decreasing the cup volume raises it. Resulting shifts vary as much as 30 cent (the extreme variable of the cylindrical cup was as much as 180 cent). Nevertheless, this effect is not the sole influence of cup volume! In order to clarify this point, a further series of cup form variables with constant volume was studied. The mouthpiece forms are shown in Figure 5.
Fig.5: Mouthpiece with different cup form but constant volume
As seen in Figure 5, one cylindrical cup form and various conical cup forms were examined. Despite their purely theoretical basis, these forms illustrate clearly that trumpet resonance is not only influenced by the cup volume, but also the cup form. It should be noted that the length of the mouthpieces were varied. This shortening of the cylindrical portion was compensated so that the overall length of the instrument would be held constant.
Fig.6: Changes in the trumpet resonance relative to the trumpet with cylindrical cup during variation of the cup form
Figures 7& 8 show the influence of bore variation on the resonance of the mouthpiece and trumpet.
Fig.7: Displacement of mouthpiece resonances by varying the bore
Fig.8: Displacement of trumpet resonances by varying the bore
Changing the bore diameter from 3mm to 5.4mm displaced resonances far less than altering the cup form. The mouthpiece resonance varied up to 80 cent, the trumpet resonance up to 10 cent. It is remarkable that in the example shown, expansion of the bore decreased the first four trumpet resonances and raised the rest (and vice versa).
The following illustrations show mouthpieces with different backbores.
Fig.9: Standard mouthpiece, x axis length [m], y axis radius [m]
Fig.10: mouthpiece with conical backbore , x axis length [m], y axis radius [m]
Fig.11: Mouthpiece with somewhat bulgy backbore, x axis length [m], y axis radius [m]
Figures 12 & 13 show the displacement of mouthpiece and trumpet resonance relative to the resonance frequency of the standard mouthpiece.
Fig.12: Displacement of mouthpiece resonances by varying the backbore
Fig.13: Displacement of trumpet resonances by varying the backbore
Based on this data, it is possible to make specific improvements intonation of the mouthpiece.
Since a specific type of mouthpiece is used in Vienna, there is not only a unified sound characteristic among trumpets, but there is also a more or less homogeneous trend in intonation.