The ways in which singers reinforce harmonics and the acoustical properties of these sounds were little documented until a decade ago, when Tuvan and Mongolian music began to reach a worldwide audience. Explaining the process is best done with the aid of a widely used model of the voice, the source-filter model. The source--the vocal folds--provides the raw sonic energy, which the filter--the vocal tract--shapes into vowels, consonants and musical notes.

Hooked on Harmonics

At its most basic, sound is a wave whose propagation changes pressure and related variables--such as the position of molecules in a solid or fluid medium--from moment to moment. In speech and song the wave is set in motion when the vocal folds in the larynx disturb the smoothly flowing airstream out from (or into) the lungs. The folds open and close periodically, causing the air pressure to oscillate at a fundamental frequency, or pitch. Because this vibration is not sinusoidal, it also generates a mixture of pure tones, or harmonics, above the fundamental pitch. Harmonics occur at whole number multiples of the fundamental frequency. The lowest fundamental in operatic repertoire, for example, is a low C note whose conventional frequency is 65.4 hertz; its harmonics are 130.8 hertz, 196.2 hertz and so on. The strength of the harmonics diminishes as their frequencies rise, such that the loudness falls by 12 decibels (a factor of roughly 16 in sonic energy) with each higher octave (a factor of two in pitch.

The second component of the source-filter model, the vocal tract, is basically a tube through which the sound travels. Yet the air within the tract is not a passive medium that simply conveys sound to the outside air. It has its own acoustical properties--in particular, a natural tendency to resonate at certain frequencies. Like the whistling sound made by blowing across the top of a glass, these resonances, known as formants, are set in motion by the buzz from the vocal folds. Their effect is to amplify or dampen sound from the folds at distinctive pitches, transforming the rather boring buzz into a meaningful clutch of tones.

The sculpting of sound does not end once it escapes from the mouth. As the wave wafts outward, it loses energy as it spreads over a larger area and sets the freestanding air in motion. This external filtering, known as the radiation characteristic, dampens lower frequencies to a greater extent than it does higher frequencies. When combined, the source, filter and radiation characteristic produce sound whose harmonics decrease in power at the rate of six decibels (dB) per octave--except for peaks around certain frequencies, the formants [see "The Acoustics of the Singing Voice," by Johan Sundberg; Scientific American, March 1977; and "The Human Voice," by Robert T. Sataloff; Scientific American, December 1992].

In normal speech and song, most of the energy is concentrated at the fundamental frequency, and harmonics are perceived as elements of timbre--the same quality that distinguishes the rich sound of a violin from the purer tones of a flute--rather than as different pitches. In throat-singing, however, a single harmonic gains such strength that it is heard as a distinct, whistlelike pitch. Such harmonics often sound disembodied. Are they resonating in the vocal tract of the singer, in the surrounding physical space or merely in the mind of the listener? Recent research by us and by others has made it clear that the vocally reinforced harmonics are not an artifact of perception but in fact have a physical origin.