Keys vs. Slides
Saxophones change the effective length of tubing with tone holes, more commonly known as keys. When all the keys are closed, the full length of the instrument produces sound. When all but the last key are closed, the instrument is effectively open to the atmosphere at that point; therefore, reflection occurs there instead of in the bell. This makes the fundamental wavelength slightly shorter, and the pitch higher by one half-step (the smallest musical increment in pitch). This pattern continues, key by key, to raise the fundamental. To get into the second half of the saxophone’s normal range, the octave or register key is pressed. This opens a small hole near the top of the instrument that disturbs the fundamental harmonic and prompts the second harmonic to speak instead. The wavelengths of f2 are half that of f1 for each key, raising the pitch produced by an octave. This continues until all keys are open and the top of the range reached.
Trombones change the effective length of tubing with a slide. The slide is what sets the trombone apart from other instruments. It is simply a loop of pipe that fits inside another and slides in and out of a fixed loop. As the slide moves out, the overall tube elongates. When it moves in, the overall tube shortens. The fundamental tone on the trombone is very weak and typically ignored. Instead, musicians focus on the second harmonic (f2). When the slide is all the way in and the second harmonic is played, a B flat is produced. The slide can then be moved into six more positions (seven total) to reach a tone of E. In order to play higher than the B flat, trombonists use the third harmonic (f3) to produce an F. Played in reverse order, the seven positions come back down to B, right above B flat. Each set of tones possible with a specific harmonic and the seven positions is called a shelf. In order to play higher, musicians continue the previous pattern on a higher shelf and use the positions to bridge the gap. View this video for a demonstration of this process as a chromatic scale. Note that after the slide moves into first position, it must be moved outwards to get the next highest note because the next shelf is higher than just a half step.