The ordinary phenomena of beats produced by two notes nearly in unison are well known. In fact, if the number of vibrations executed per second, or “the frequency” of that note be represented by n, and that of the upper note by n + m, then the number of beats per second will be equal to the difference of these numbers, viz., it will be equal to m. The phenomenon depends upon the fact that the more rapid motions of the higher note gradually gain upon those of the lower; and if at one moment the motions are coincident so as to augment the sound, then at the next moment the coincidence begins to fail. This failure of coincidence continues to increase as time goes on; and at last the movements pass into a phase of complete opposition, so that if the two notes are originally of the same intensity, they completely neutralise one another.