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Acoustical Preliminaries

Musicians are always concerned not only with the correct tuning, but also with the clarity of tones they produce, and with the security with which they can start their sounds. They are also seriously interested in the flexibility of the dynamics available to them on their chosen instruments. For many years it has been possible to make fairly objective measurements of the intonation behavior of musical instruments, leading at times to an overemphasis on this aspect of musical performance. Tuning is a matter of musical context, so that to stand in front of a frequency-measuring machine is to play in an unfamiliar context to say the least. On the other hand, such observations can, when properly used, be the basis for great clarification of the practical business of obtaining musically correct intonation. For instance, if a player seeks out a way of blowing each particular note to give it the clearest sound and the fullest tone, it will automatically lead him to find the pitch that is most associated with the natural behavior of the instrument. In other words, the variability of the measurement of the player's pitch can be greatly reduced if we ask the instrument itself where it would, so to speak, best like to play. It is important to remember, however, that pitch is only one of the aspects of musical tone production to be considered, along with other subtleties such as clarity over a wide dynamic range and prompt starting behavior. It has not been possible until fairly recently to correlate such varying aspects of musical tone production with the details of instrument design.

At this point I would like to describe in a preliminary way some of the acoustical events that occur in a brass instrument when it plays any single note in its scale, and so to relate the playing properties of the instrument to the nature of its air column. We will find that very stringent requirements must be met by a musical air column if it is to play even one note properly; by a very fortunate circumstance, a design that "sings" well can generally also be made to play a whole gamut of tones in good tune. Thus our present restriction of the discussion to a single tone will not limit us in our eventual understanding of the complete instrument as it lives in an orchestra.

In essence, a wind instrument consists of a pipe or horn of varying cross section, which is coupled to a flow-control mechanism that converts a steady wind supply from the player's lungs into oscillations of the air column contained within the pipe. Figure 1 shows in diagrammatic form the general structure that is characteristic of a brass instrument.

Figure 1
Figure 1: General structure of a brass instrument

The flow of air from the player passes between his lips, which open and close rapidly in response to the acoustical variations within the mouthpiece and so admit a periodically varying flow of air into the mouthpiece. It is this varying flow that maintains the oscillations of the air column. Putting it more concretely, the lips function as a sort of valve, which opens and closes in response to the oscillatory variations of air pressure in the mouthpiece as this pressure rises above and falls below atmospheric pressure. This pressure variation arises because the air within the instrument is swinging up and down its length. The air column, on the other hand, is maintained in its longitudinally swinging vibratory motion by the periodic puffs of air that are supplied to it via the lip-valve. If, for example, a trumpet is sounding the oboist's A (440 Hz), the air column is swinging back and forth along the horn in a complex motion that repeats 440 times a second, causing the lips to admit puffs of air of complex shape into the mouthpiece at this same rate of 440 times per second. It will perhaps help us to visualize what is going on if we turn our attention to a very close analogue of this air column system.

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
Bibliographic Notes