Wind Instruments: Frequency and pitch

Summary: The frequency and pitch of wind instruments are determined by their shape, length, and other factors.

Wind instruments convert the energy of moving air into sound energy—vibrations that are perciptible to the human ear. Under this definition, wind instruments include the human voice; pipe organs; woodwind instruments, such as the clarinet, oboe, and flute; and brass instruments, like the trumpet. The nature of this vibration and the associated resonator tube are responsible for the unique timbre of each type of wind instrument.

Sources of Vibrations

In the human voice, the flow of air from the lungs causes the vocal cords (also called “vocal folds”) in the larynx to open and close in rapid vibration. This periodic stopping of the air stream creates oscillatory pulses of air pressure, or sound. The frequency of this vibration and the pitch of the resulting sound are determined by the length and tension of the cords. A singer or speaker controls these factors using the musculature of the larynx.

The rapid open-close vibration of the vocal cords is present in many wind instruments. In brass instruments, such as the trumpet, trombone, French horn, and tuba, the lips of the musician form a small aperture that opens and closes in response to air pressure. Brass instruments are sometimes called “lip-reed” or just reed instruments. In single-reed instruments, like the clarinet and saxophone, a thin cane reed vibrates in oscillatory contact with a specially shaped structure (the mouthpiece) to bring about the open-close effect. The oboe and bassoon utilize two cane reeds held closely together with a small space between them that opens and closes in response to flowing air, controlled by the muscles of the lips.

A third important mechanism for converting the energy of moving air into vibration is utilized in the flute and the so-called flue pipes of the pipe organ. In these instruments, vibration occurs when flowing air passes over an object with a distinct edge that splits the airstream. The resulting turbulence gives rise to oscillatory vibration. With the modern flute, the flutist’s lip muscles actively control the interaction between the airstream and the edge. With the recorder and other whistle-type instruments, as well as flue pipes of the organ, the interaction is controlled by the mechanical design of the instrument alone.

Tube Resonators and Overtones

With the exception of the human voice, all wind instruments are constructed with a tube resonator enclosing a column of air that functions in much the same way as the vibrating string. Oscillations in air pressure inside the tube reflect from the ends, resulting in significant feedback with the primary vibrating medium. The relationship between the vibration frequency and length of a string fixed at both ends is explained by the concept of “harmonics.” In idealized settings, changing the string length by small integer factors (for example, 1/2,1/3, or 1/4) results in frequency changes that are recognizable as musical intervals (for example, an octave, an octave plus a fifth, or two octaves). The resonating air column in wind instruments behaves similarly to a vibrating string.

An important performance practice on most wind instruments is overblowing. Not to be confused with simply playing overly loudly, the term “overblowing” refers to the fact that changes in the airflow can cause the resonating air column to vibrate at an overtone above its fundamental frequency. Overblowing allows performers on modern instruments to achieve a large range of pitches (often two octaves or more) from a relatively compact resonating tube. Instruments with cylindrical tubes open at both ends, such as in some flutes, overblow at the octave, as do conical instruments that are closed at one end, such as the oboe and saxophone. On the other hand, cylindrical tubes closed at one end, such as the clarinet, overblow at the twelfth—an octave plus a fifth. The relative weakness of the overtone at the octave and other even-numbered overtones account for the particular timbre of the clarinet.

Altering the Tube Length in Performance

Just as the length of a vibrating string determines the frequency or pitch of the vibration, the length of the resonating air column accounts for the pitch of notes played by a wind instrument. In reed instruments, the resonating tube is perforated along its length with holes. By systematically covering some of the holes but not others, the musician effectively changes the length of the resonating column. This change, in turn, causes the vibrating reed assembly to assume the frequency of the air column. Most brass instruments have secondary lengths of tubing that are brought into play by mechanical valves by which the performer alters the length and the fundamental frequency of the vibrating air column. The exception to this is the slide trombone, which features a concentric tube arrangement by which the outer tube can move to lengthen the air column resonator.

Bibliography

da Silva, Andrey Ricardo. Aeroacoustics of Wind Instruments: Investigations and Numerical Methods. Saarbrücken, Germany: VDM Verlag, 2009.

Miller, Dayton Clarence. The Science of Musical Sounds. Charleston, SC: Nabu Press, 2010.

Sundberg, Johan. The Science of Musical Sounds: (Cognition and Perception). San Diego, CA: Academic Press, 1991.

Wood, Alexander. The Physics of Music. 7th ed. London: Chapman and Hall, 1975.