Acoustics

properly distinguish what belonged to each. Namely, all vibrating bodies agree with one another in certain properties mentioned in §. 45—which contains the first fundamental concepts of the entire science of soundoriginal: "Klanglehre"; the study of how sound is produced and perceived.—but both the modes of vibration and the tonal ratios belonging to them, as well as the laws by which the pitch height and depth of the tones is governed according to differences in dimensions, etc., are of a different nature for every type of vibrating body. It is therefore entirely contrary to nature if one wishes to derive the theory of tonal ratios from certain properties that belong only to a string—or rather, only to its fundamental tone—and not to all types of vibrating bodies. Whether one makes more use of a string than of other vibrating bodies is of no consequence here when explaining a physical subject.

Through this exclusive consideration of strings, to the neglect of other vibrating bodies, a deeply rooted prejudice has arisen among many: that with every tone, the higher tones corresponding to the natural numerical sequence 2, 3, 4, 5, etc. These are known as the harmonic series or overtones. always sound simultaneously, and that a musical sound is distinguished from any other noise by this very fact; and further, that the basis for the consonance original: "Conſonirens"; sounding pleasant together. and dissonance original: "Diſſonirens"; sounding harsh or unstable together. of tonal ratios is to be sought in the simultaneous sounding or non-sounding of certain tones. Regarding this, the necessary points have already been stated in the note to §. 5, in the second note to §. 9, and in the 9th section of the second part, which I do not wish to repeat here to avoid prolixity.

Many other prejudices, which have less relation to the whole of acoustics, I shall not mention further here.

A strange misunderstanding arose among many people, through no fault of my own, on the occasion of my investigations into the vibrations of a disc: namely, that every tone produced on a disc yields a certain figure The author refers to "Chladni figures," patterns formed by sand on a vibrating plate.. It can be shown (according to §. 45 and the note...