As now the strength of the tone is determined by the breadth of the vibrations, and the pitch by their number, so the varieties of timbre are ascribed to the different forms of the waves of vibration. For as the surface of the water is stirred differently by the falling into it of a stone, by the blowing over it of the wind, or the passing through it of a ship, &c., so the movements of the air take different shapes from sounding bodies. The movement proceeding from the string of a violin over which the bow is drawn, is different from those movements caused by the hammer of a piano or by a clarionet. OVER-TONES (OBERTÖNE) That timbre is dependent on the form of the vibrations is confirmed by Helmholtz, and acknowledged as so far correct that every different timbre requires a different vibratory form, but different forms sometimes correspond to nearly the same timbre. But how far the different forms of vibration correspond with different timbres, Helmholtz shows by a fact which has hitherto escaped the notice of physicists, although it forms the foundation of all music. We have learned by the stereoscope that we have two different views of every object, and compose a third view from those two. _Just so the ear perceives different musical tones which come to our consciousness only as one tone._ It is in general, and especially in the case of the human voice, very difficult to distinguish these single parts of tone, because we are accustomed to take the impressions of the external world without analyzing them, and only with a view to their use. But when we are once convinced of the existence of partial tones (_Partialtöne_), if we concentrate our attention, we can also distinguish them. The ear hears, then, not only that tone, the pitch of which is determined, as we have shown, by the duration of its vibrations, but a whole series of tones besides, which Helmholtz names “_the harmonic over-tones_” of the tone, in opposition to that first tone (fundamental tone) which is the lowest among them all, generally the strongest also, and according to the pitch of which we decide the pitch of the tone. The series of these over-tones is for each musical tone precisely the same; they are, namely, the tones of the so-called acoustic series, arising, as already described, from the doubling of the vibrations. First, the fundamental tone, then its octave with twice as many vibrations, then the fifth of this octave, &c.