Modes, Nodes, and Antinodes

Abstract

Student comprehension of certain facts of acoustics is handicapped by conflicting meanings of words used in the teaching of elementary physics. The words partial, overtone, and harmonic are often treated as synonymous with normal mode of vibration. That normal modes are not always harmonic is illustrated by data given for an actual piano string for which the progressive “inharmonicity” is such that the fifteenth mode (for example) has a frequency more than sixteen times that of the first mode. Measurements reported here for the playing of a cornet illustrate that its steady sound is not necessarily (in the sense of the erstwhile synonyms listed previously) a “note compounded of the fundamental and of the partial tones, or overtones, due to the segments.” Vibration antinodes are not always equally spaced in tubular resonators of varying cross section. Elementary textbooks often devote considerable space to the just scale, even though there is almost no experimental evidence that just scales are employed in actual music. On the basis of equal temperament and the standard A of 440 cps agreed upon internationally for musical performance, the frequency of middle C is 261.6 cps and not 256 cps as often cited. Terminology to clarify matters is recommended.