Harmonicity

A sound is harmonic if the frequencies that compose it are all multiples of a single fundamental frequency (F0). Harmonicity plays an important role in music because many musical instruments produce harmonic sounds, as do voices. Sounds with harmonic frequencies are periodic in time and are typically perceived as having a single coherent pitch. Harmonic frequency relations are thought to help listeners segregate sound sources from a mixture of concurrent sounds. Harmonicity is also believed to underlie consonance in Western music, in that the aggregate spectrum of most consonant chords resembles that of a single harmonic sound despite being generated by multiple tones.

Figure 1 shows the waveform and spectra of a note played on an oboe. It is visually apparent that the waveform consists of a pattern that repeats in time, in this case every 2.27 milliseconds (ms). It is also apparent that the spectrum contains regularly spaced peaks, in this case occurring at integer multiples of 440 hertz (Hz). These frequencies are harmonics, and 440 Hz is their fundamental frequency (F0). It is visually apparent that the waveform consists of a pattern that repeats in time, in this case every 2.27 ms. The F0 is the frequency of the waveform's repetition (440 cycles per second, i.e., the reciprocal of the period). The amplitudes and phases of the harmonics determine the shape of the repeating pattern in the waveform, but the period is determined by the F0. The F0 need not be physically present, however. The waveform of a sound is [Page 528]periodic, with a period corresponding to an F0, so long as whatever frequencies are present are multiples of that F0. Some audio playback devices cannot produce low frequencies, such that the F0 of music and speech sounds is often physically absent from the sound received by the ear.

Figure 1Waveform (a) and spectrum (b) of a note played on an oboe. The note is the A above middle C, with an F0 of 440 Hz. The waveform repeats every 2.27 ms, which is the period. The spectrum contains peaks at integer multiples of the F0. This is harmonicity, the frequency-domain signature of periodic sounds.

Harmonicity is present in all sounds generated by periodic processes. These include many sounds in speech and music. Mammalian vocal cords create periodic/harmonic sounds by opening and closing at regular time intervals. Musical instruments use a variety of physical means to create harmonic sounds, ranging from plucked or bowed strings, the length of which determines the F0 of the vibration, to tubes whose resonances are harmonic. Harmonic sounds are also sometimes made by machines, in which the rotation of mechanical parts (e.g., in an engine) causes a rapidly repeating sound pattern.

Sounds that are aperiodic have spectra that are inharmonic. Two types of inharmonic sounds commonly occur in music. The first are those that are noise-like, containing many densely spaced frequency components. This class includes many percussive sounds. The second are those that contain a smaller number of relatively discrete frequency components that are not harmonically related. Gongs and bells often fall in this latter category.

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