We now turn our attention to an example of the earlier, valve-less form of the trumpet, as we consider a 'Tarr Model' Baroque D trumpet made by Meinl and Lauber. Figure 10 shows the ordinary input impedance curve belonging to this instrument when played with the vent hole closed.

Figure 10: Impedance curve of a Baroque trumpet with its vent hole closed

Comparison with Figure 7 shows that the overall, qualitative shape of the resonance curves for the Baroque D and modern Bb instruments are quite similar. The resonance peaks are, however, more closely spaced along the frequency axis for the D trumpet, simply because of its greater length. For ease in comparing the musical behavior of the two instruments, let us start by considering the regime of oscillation that supports the note concert A₃ of the D trumpet (at 220 Hz in modern tuning). This is only a semitone away from the open tone written as C₄ for the Bb instrument, so that such matters as lip tension and the frequency response of our ears are roughly the same. When one plays loudly on the D trumpet, the tone A₅ is sustained by the cooperation of peaks 3, 6, 9, and 12, with some help from peak 15. All this is shown in the figure. The fact that the successive higher-frequency resonance peaks grow in tallness means that they keep their influence to a somewhat lower dynamic level of playing than is the case for their cousins (peaks 2, 4, 6, and 8) on the modern Bb trumpet. This by itself gives the Baroque instrument a more steady A₃ than is the case for the C₄ of the modern instrument.

The next member of the basic harmonic series of tones available to the Baroque musician is the note D₄, which is sustained by a regime based on resonance peaks 4, 8, and 12, with some help from peak number 16. Once again we have a stable tone involving many cooperating resonances of the air column. The reader by now has enough knowledge of the dynamics of trumpet tone color that he can work out for himself the implications of the resonance curve for other tones in the musical sequence, using Fig. 11 to tell him which resonances collaborate to produce the various tones.

Figure 11: The collaborating resonances for various tones of a Baroque trumpet

We note that above E₅ there is essentially no collaboration. We also note that everywhere in the scale the serial number of the tone is the same as the serial number of the tone in the musician's harmonic sequence. The seventh tone in this sequence, which is not customarily considered part of the named-note sequence, is a fairly well-supported tone based upon peaks 7 and 14. Peak 14 is located at a frequency that is slightly less than twice that of peak 7. When one plays softly (so that peak 7 dominates the regime), the tone comes out most naturally on our instrument as a slightly flat C₅. When, however, the dynamic level is raised progressively, the pitch drops toward a slightly sharp B, as peak 14 asserts its growing influence. In short, we have here a slightly unstable note that can be pulled up or down in pitch by the player to meet at least some of the musical requirements for notes written as B₄ or C₅. The next in the series of tones available to the player is D₅. This is the highest of the tones in the Baroque trumpet's scale for which one has detectable cooperative effects from the higher air column resonances. Peak 8 determines the oscillation in soft playing, and the sound tends to run a little flat during a crescendo because peak 16 again has a frequency slightly lower than twice that of peak 8.

The Tarr Model Baroque D trumpet is supplied with a vent hole located at the junction of the bell with the main cylindrical bore. A considerable increase in the number of playable notes is provided by this hole, employing acoustical means that are not quite the same as those belonging to the unvented trumpet nor yet the same as those associated with note changes on a woodwind. In other words, it is not correct to think of the action of the hole as a simple 'cutting off' of the air column at its position. We are dealing with a tripartite air column--main bore, vent hole, and bell. Tonally we still have a close approximation to the normal trumpet in that most of the sound comes from the bell, and it is therefore radiated in a manner quite similar to that which characterizes the normal notes. Figure 12 shows the measured resonance curve for our trumpet when its vent is left open.

Figure 12: Impedance curve of a Baroque trumpet with its vent hole left open

At first glance the curve appears very similar to that shown in Fig. 10 for the normal instrument. Closer inspection reveals, however, that the resonance peaks are spaced wider apart along the frequency axis, and also that the composite air column gives rise to a rather complex shape for some of the peaks, with small subpeaks and shoulders making their appearance here and there.

Let us look into the acoustical properties of several of the tones that can be played with the vented trumpet, beginning with the tone based on peak 3. This is a wobbly, unclear tone that comes out near C₄ when sounded pianissimo. Louder playing permits one to sound a tone as low as B, because of the influence of peak 5 on the second partial of the tone, and of peak 7 on the third partial. We also find it possible to sound the note as high as C₄#, when peaks 6 and 8 have supplanted peaks 5 and 7 as the influences upon the second and third components of the vibratory recipe.

The next tone in the series is a slightly sharp F₄# based on peak 4 when one plays softly, rising to G₄ when the tone is sounded strongly enough that peaks 8 and 12 begin to exert their influence. Above this we find a clearly defined A₄# based on peak 5. Even though peak 10 is quite sharp relative to twice the frequency of peak 5 it does not try to pull the note sharp on crescendo because of the presence of a small jog on its lower flank. This jog is located at exactly the right place for good cooperation with peak 5, so the note is quite stable.

Peak 6 of the vented series of resonances gives a slightly veiled C₅# that is pitch stable on crescendo but without any cooperative effects from the higher resonance peaks; the second partial of the tone falls at the dip between peaks 11 and 12, so that there is actually a certain amount of anti-cooperation.

The next note in our series is the tone D₅. This is not based on peak 7, but rather is a privileged tone whose frequency lies between those of peaks 6 and 7. The oscillatory energy is produced chiefly through the influence of peak 12 on the second partial component of the played tone, with a little energy input coming from the fundamental component as it works with the jog that is found on the high-frequency flank of peak 6. It will be convenient to label this privileged tone as 6-bis rather than as 7 in the sequence, to emphasize its special status.

We conclude our sketch of the oscillation dynamics of the vented tones with a remark that the seventh of the normal sequence here gives the note F₅, based on peak 7 with the help of peak 14, which pulls it a little sharp on crescendo. Tones 8 and higher run without collaborative influence from higher resonance peaks and need not be discussed further here.

Trumpet Acoustics
Acoustical Preliminaries
The "Water Trumpet"-- An Analog to What Happens inside a Trumpet
The Function of the Player's Lips
The Function of the Pipe and Bell--Inside the Air Column
The Cooperation Needed for Musical Results
The Baroque Trumpet
The 'Internal' Spectrum of the Modern Trumpet
The 'Internal' Spectrum of the Baroque Trumpet
Relation of Internal to External Tone Color Spectrum
The Menke Trumpet
The Problem of Clean Attack
Mahillon in Retrospect
Conclusion
Bibliographic Notes