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Brass Musical Instruments
two semitones (Audio 3, http://acousticstoday.org/ws/); and depressing the third valve lowers the frequency by ap- proximately four semitones (Audio 4, http://acousticstoday. org/2-steps/). The idea is that by depressing different combi- nations of these valves, a player can sound any note on the Western scale.
The problem with using valves becomes obvious when you begin to calculate the necessary lengths that each valve must insert into the air column. To lower the pitch by one semi- tone, you must change the length by 5.95%. A typical trum- pet is about 140 cm long, so adding 8.3 cm to the length will lower the pitch precisely where it should be. To lower it two semitones, you need to increase the length by 12.25%, or about 17.2 cm, for the modern trumpet. If you wish to lower the pitch three semitones, it seems logical that you press the second valve to lower the pitch by one semitone and then press the first valve to lower it by two. Unfortunately, press- ing the first valve adds about 6% to the length of the trumpet and you need to add 12.25% of the total length to then lower the pitch 2 more semitones. So the necessary length to lower the pitch by one or two semitones will be different depend- ing on what other valves are depressed. In the case of the trumpet, the necessary added length when depressing both the first and second valve together is 26.5 cm rather than the combined value of 25.5 cm. This presents a challenge to both the instrument maker and the musician.
To solve this problem, most brass instruments are designed so that the tubing inserted by depressing either of the first two valves is slightly longer than it should be if it were the only valve being depressed. In this way, the length is slightly longer than it should be when the valves are used indepen- dently and slightly shorter than it should be when the valves are used in combination. It is incumbent on the player to play the instrument slightly off the resonance to achieve the correct pitch. As noted above, this is not easy because the feedback to the lips forces them to oscillate at the resonance frequency defined by the air column.
It takes skill, but when using the first two valves, a good play- er learns to bend notes and playing the correct pitch is not an unreasonable expectation. Unfortunately, when you add the third valve to the mix, it becomes unreasonable to expect even the best trumpet player to bend the notes enough to play in tune. Therefore, the length of tubing added by de- pressing the third valve is chosen to be approximately what is required to lower the open-valve configuration three
Figure 7. A six-valve trombone made by Adolphe Sax ca. 1863. The instrument does not suffer from the intonation problems of other valved instruments because the valves are never used in combina- tion. From the Metropolitan Museum of Art.
semitones (Audio 5, http://acousticstoday.org/three/) and a slide capable of rapid movement is added to the tubing as- sociated with this valve. On the trumpet, the slide is moved with the ring finger, but on larger instruments like the tuba, the player usually just grasps the slide with his/her free hand and moves it as required. Many trumpets, such as the one shown in Figure 1, also include a slide for the first valve, which is operated with the thumb.
Over the years, there have been several attempts to deal with the problem of mistuned valves, with only limited success. Adolphe Sax invented a brass instrument with six valves that does not merely add tubing to the instrument but rather re- places almost the entire length when the valve is depressed. This arrangement, shown in Figure 7, is like having seven different instruments available to the player and therefore eliminates the problem of mistuning by never having more than one valve depressed at a time. For better or worse, the idea never caught on.
Some Closing Thoughts
The acoustics of brasswind instruments has been studied for almost two centuries, and many of the interesting details have not been discussed here. They are truly fascinating in- struments. But while much of the physics of brass instru- ments is well understood, it would be misleading to leave the
36 | Acoustics Today | Winter 2016