We can summarize our present understanding of the acoustical aspects of the trumpet by saying that whatever virtues an instrument may have depend ultimately on three things. First of all, it is necessary to adjust the air column shape to locate input impedance peaks at frequencies that cooperate well in forming the various regimes of oscillation. Secondly, the relative heights of the resonance peaks should be suitably arranged for ease of playing. It is here that the role of the mouthpiece and back-bore becomes particularly subtle. Finally, the air column has to be adjusted so that the initially returned echoes from the bell to the mouthpiece come back in good order, to ensure a stable attack.

Looking back over the history of the development of the trumpet, one can see a curious intertwining of the activities of musicians, of instrument makers, and of scientists concerned with musical acoustics. Each has his prime purposes and his particular skills; each ideally should have some appreciation and knowledge of the activities of the others, not only in the direct furtherance of his own profession but also for the stimulation of his own broader thinking. We have repeatedly seen how the significant advances in any one of these three fields have in general come from the labors of individuals who could combine a master's skill in one area, solid competence in another, and at least a strong interest in the third. We must be grateful for the existence of such people, sensitive to hints that come to them from many directions, who have the knowledge and temperament to attempt a synthesis that can further their art.

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