Physics of music
- Sigalia Dostrovsky,
- Murray Campbell,
- James F. Bell
- and C. Truesdell
This article is concerned with the history of vibration theory as it relates to music. For further information see Acoustics and Sound.
Sigalia Dostrovsky, revised by Murray Campbell
The basic ideas of the physics of music were first obtained in the 17th century. Acoustic science then consisted mainly in the study of musical sounds; in fact, music provided both questions and techniques for the study of vibration. Music gave experience in comparing the pitch and timbre of tones, and so the means for careful experiment on sound; musical instruments offered empirical information on the nature of vibration; and, rather remarkably, the Pythagorean ratios of traditional music theory provided frequency ratios.
Early in the 17th century it was realized that the sensation of pitch is appropriately quantified by vibrational frequency – that is, pitch ‘corresponds’ to frequency. This realization came as part of a preliminary understanding of consonance and dissonance. Once the correspondence had been made, it was possible to determine the relative vibrational frequencies of tones from the musical intervals they produced. When relative frequencies were known, there was the challenge of determining frequencies absolutely; and the first measurements were made during the century. The idea that pitch corresponds to frequency motivated efforts to understand overtones, since, during most of the 17th century, it seemed paradoxical that a single object could vibrate simultaneously at different frequencies. This paradox was resolved by the end of the century through an initial understanding of the ‘principle of superposition’. Also by this time the connection between overtones and timbre was noticed, and beats were explained quantitatively. During most of the century, sound was described as a succession of pulses, its wave nature being understood qualitatively. But late in the century the first mathematical analysis of the propagation of sound waves was made....