So far we have explored the acoustical requirements that must be met by a trumpet if it is to play steady tones one by one. I have also implied that in general an instrument that speaks with stability and clarity will also have a good tone, in the musician's sense, and also that it can be built to play accurately in tune. There is one more attribute that is required of a musical instrument if it is to be considered of first quality: it must start its tones cleanly and promptly and be forgiving of small inaccuracies of the player's lip tension as he shifts rapidly from one note to the next.
The acoustical properties of an air column that contribute to a clean attack for every note may be looked at in two parts. To begin with, anything that makes for a 'happy' collaboration during the time a note is sustained will in general contribute to a prompt build-up of an oscillation when the tone is started. It seems almost to be a truism that the placement of resonance peaks at frequencies that favor the maintenance of oscillation should also favor the secure beginning of such an oscillation. For the woodwind player, this is very nearly the complete story. The brass player has, however, one more thing to contend with because of the great length of the instrument with which he produces the same notes as the shorter woodwinds do. Basically he must deal with the fact that in a long instrument it takes a long time for acoustical 'messages' to travel from mouthpiece to bell and back, informing the lips of the collaborative job they must do with the air column.
Let us see what happens to the initial part of the acoustical disturbance set up by the player's lips as he attempts to start a tone. This disturbance travels down the bore with a speed that depends on the rate of flare of the air column, and then in the flaring part of the bell some of this wave is reflected back toward the mouthpiece, with the remaining (generally small) fraction of it being radiated out into the room, where we can hear it. The reflected wave, upon returning to the mouthpiece, 'tells' the lips how and when they must reopen to admit the next puff of air in the sequence of puffs that sustain the tone after everything has settled down. Until the first reflections begin to come back, the lips are on their own. The air column has not yet expressed its preference for one or another of the frequencies with which it is able to collaborate. A superb player of the sort who has learned to buzz his lips in perfect pitch even when playing on a brass ring has little problem with a good trumpet. He buzzes the desired note and the air column is very happy to collaborate in its own good time. The collaboration cannot of course even begin until there has been time for at least one complete round trip of the initial sound to go down the air column and back, and it requires two or three more round trips before the regime of oscillation has set itself up completely. In a fast, running passage, there is barely time for one regime of oscillation to be set up before it must give way to the next.
We are now in a position to understand why small irregularities of either the cross section or the taper angle in the air column can be fatal to a clean attack. Even a small step change in cross section in the middle of the air column (produced by a tuning slide, etc.) or an ill-chosen change in the taper will return a premature echo of significant size to the mouthpiece, an echo that is not even a replica of the original disturbance. Such ill-timed, ill-shaped return echoes can upset the best-trained of lips and, having spoiled the steadiness of this initial vibration, will ruin the attack. Such irregularities are of course a complete disaster for the less-skilled player, even if he can maintain a good sound once it is started. Curiously enough, it is possible to build an instrument that gives a strong, clear sustained note, and yet is unwilling to start well at all. Various discontinuities may deliberately be introduced to offset one another, or to counteract other faults of the air column. This can give a well-tuned stable instrument, with good tone, even though it can be extremely treacherous during the attack of its various notes. Every musician has met such instruments, as well as those that attack cleanly but which lack other virtues that are needed for the production of real music.
My description of the starting-up process for trumpet tones so far has left the impression that the longer the air column, the slower or more risky the attack necessarily must be. Anyone acquainted with the long Baroque trumpet is aware, on the other hand, that these instruments are at least the equal if not the better of the modern short design in starting characteristics. The explanation for this can be found in terms of an understanding that 'the speed of sound' is a phrase that actually refers to two different aspects of sound propagation.
The first sort of speed that turns up in relation to acoustical disturbances is what the physicist calls the 'wave velocity' for a sound of precisely defined frequency. The wave velocity in general depends jointly on the frequency of the sound and on the rate of flare of the air column through which it travels. We find that it is this wave velocity for sounds in an air column that determines its resonance frequencies. In the special case of straight-sided air columns (the ordinary pipe, and the simple cone), the wave velocity is independent of frequency, and becomes equal to what we may call the ordinary speed of sound in the open air.
The second kind of speed is known as the 'group velocity.' We may say that this is a measure of the speed with which abrupt disturbances travel down an air column. The group velocity depends on the frequency component that predominates in the disturbance and, once again, it depends on the rate of flare of the horn. As above, the group velocity for sounds in a straight-sided air column is independent of frequency and is equal to the open-air speed of sound.
The actual values of the group velocity and the wave velocity most closely related to it are not at all the same in most horn-like air columns. The round-trip time for the initiating disturbance of a trumpet tone is calculated from the group velocity and not from the wave velocity. In other words, the trumpet maker has the very interesting technical problem of getting a whole set of wave velocities to come out right if he wants good steady sounds, and he must at the same time achieve a correct set of group velocities if he wants these tones to start cleanly!
Now we can understand why the modern short trumpet does not necessarily have an advantage over its longer ancestor. Its shortness does give it an initial advantage, but even in its valve-less form we find it more difficult to find a bore shape that simultaneously reconciles the group and wave velocity requirements over its playing range than is the case for the long instrument playing the same notes. The chief reason is that it becomes easier to reconcile our twin requirements for the higher members in the series of natural frequencies belonging to a given trumpet. It is here the longer trumpet gets the advantage for notes in the treble clef and above. Furthermore the presence of sharp jogs in the valves and sharp reversals of the bore (even when the cross section is maintained) produces troublesome early echoes in the modern valve trumpet to the extent that individual members of the tribe may or may not surpass individual members of the older group.
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