Real-Time Spectroscopy of Acoustic Waves or Music as Physical Phenomenon

Abstract

The sounds used in music have discrete spectra consisting of a fundamental frequency and of its integer multiples. This is the reason for an affinity of the sounds for which the ratio of the fundamental frequencies is given by a fraction of small integers. Two possible physical mechanisms for this affinity are discussed: (1) an influence of beats between some partial tones and (2) nonlinear interactions between partial tones. Some facts from the music theory are then explained as resulting from the invariance of the most consonant intervals between affine sounds against variations of the timbre and of the register. An analogy is indicated between the classical cadence and the lock-in effect in incommensurate crystals. The lecture is illustrated with extracts from the J.S. Bach Das Wohltemperierte Klavier, the W.A. Mozart sonata for piano KV 570 and a recitative from the Haendel Messiah. PACS numbers: 43.75. + a, 43.66.+y, 43.64.+r