Our outline of the way modern and Baroque trumpets generate their tones through various cooperation between air column resonance peaks gives us a solid basis from which we can begin an inquiry into the acoustical and musical nature of these generated tones. Let us consider how tone color is influenced by the air column of the trumpet. We must first of all distinguish clearly between the internal tone color that could be perceived with the help of a probe microphone inserted into the mouthpiece cup and the tone color of the sound that issues from the bell in the normal manner. Our discussion so far has been concerned with the interaction of the internal sound waves with the lips, so we will begin with the tone color within the mouthpiece, and then consider how this is modified as it leaves the bell of the instrument and enters the concert hall.

Among the successes of Walter Worman's research into tone production by wind instruments was a clear-cut description of how the internal tone color (i.e., the strengths of the various partial components that make up the internal tone) depends on the playing level and on the nature of the air column. In instruments having a pressure-controlled air valve (whether lip, or reed), the strengths of the various harmonics generated in a regime of oscillation have a particularly simple relation. Leaving out the quantitative details, we find that theory and laboratory experiment agree on the following description of this internal sound. When one plays pianissimo on any note whatever, the internal sound has an almost purely sinusoidal waveform and sounds very much like a tuning fork if we listen in with the aid of a probe microphone. That is, the sound is made up of a fundamental component at the playing frequency, with almost nothing to be found at the frequencies of the harmonically related higher partials. As one plays louder the tone spectrum develops, harmonic by harmonic, the lower ones growing first. The tones that are generated by an oscillatory regime involving several resonance peaks develop their higher partials rather quickly and the internal sound becomes full and rich at a lower dynamic level than is the case for notes that rely upon only one or two air column resonances. We also find that the strength of any particular generated partial is large if the resonance peak associated with it in the regime is tall, and it is weaker if the peak is less tall.

Let us turn our attention to the practical implications of this for a modern trumpet. In 1970 a series of measurements was made with the help of Charles Schlueter, who plays principal trumpet in the Minneapolis Symphony (in 1970 he was a member of the Cleveland Orchestra). Schlueter played diminuendos and crescendos on one of my instruments, a Bb trumpet, Selmer Paris, serial no. 4866. This was equipped with both an internal and an external microphone, which were fed to a tape recorder so that the results could be studied at leisure in various ways. The trumpet is the same one from which the resonance curves shown in Figs. 7, 8, and 9 were obtained.

Figure 13a shows the relative strength of the internal partials belonging to the written C₄ (see Fig. 7 for the air column resonances that participate in the generation of this tone).

Figure 13a: Internal partials of the written C₄ (concert Bb₃) on a modern trumpet

The uppermost of the Fig. 13a curves connects black dots that indicate the strengths of the first eleven partials produced when the trumpet is played fortissimo. The lower families of curves indicate similarly the strength of the partials at lower dynamic levels. We can see clearly here that as one plays more softly, the higher-frequency partials become weak more quickly than do the lower ones. At the weakest pianissimo that can be sustained by the player, the internal tone contains almost nothing beyond its fundamental component. I should like to emphasize that data of this sort are extremely stable. Measurements made on many separate tones, some starting mp and swelling to fff and some diminishing from mf to ppp, join smoothly when the curves are analyzed and the spectra plotted on a graph. The open-circled data points in our graph for C₄ can be used to show in addition that the behavior described here is determined chiefly by the trumpet and its mouthpiece, and only secondarily by the player. This particular curve shows the spectrum of a tone played at a loudness lying between mp and p. It is based on the analysis of a tone that I myself played and recorded in the course of setting up, testing, and calibrating my equipment, several days before Charles Schlueter came in for the more formal experiments.

Figure 13b: Internal partials of the written C₅

Figure 13b shows the measured internal spectra belonging to various playing levels of the written note C₅. We notice that the spectrum lacks appreciable strength in the harmonics beyond the fifth partial, even when the note is played very loudly. The tone does not become as pure at the pianissimo level, however.

Figure 14a: Internal partials of the written G₅

Figure 14b: Internal partials of the written E₆

Figures 14a and 14b show similar spectra for the staff-top G₅ and the high E₆. The spectra of these higher notes show the progressive impoverishment of the tone color as one goes higher in the scale. It is possible to show by auxiliary experiments, especially with cylindrical pipes and with French horns, that these phenomena are not so much due to the limitations of the player's lips as they are to the diminishing number and strengths of the resonances that take part in the oscillations as one goes up the scale (see Figure 7 and Figure 8 for the regimes of oscillation that determine these tones).

I must emphasize at this point that the spectra described here have been plotted to include only the first few harmonic components of the tone. There are components at higher frequencies which have a noticeable effect on the overall tone color; however, they play a much subtler role than do the ones shown. One finds that the basic character of most wind instrument tones is established by the first half dozen components, to the extent of identifying the instrument's style of construction, its player, and often even its maker. I should also remind the reader at this point that the internal spectra discussed so far are not the ones that are supplied to our ears in the concert hall.

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