The different timbre of tones thus depends upon the different forms of the vibrations, whence arise various relations of the fundamental tone to the over-tones as they vary in strength. The most thorough inquiries have led to the following results, of the first importance in every formation of tone: _that the appropriate form of the vibratory waves which is the most agreeable to the ear, as well as the fullest, softest and most beautiful timbre which corresponds to that form, is produced when the fundamental tone, and the over-tones following it, so sound that the fundamental tone and the over-tones sound together, the former most strongly, while the latter are heard fainter and fainter in the intervals of the major chord with the minor seventh, so that, with the fundamental tone, still further sound seven over-tones_. If the higher harmonic over-tones grow stronger, and even overpower the fundamental tone, the sound grows shriller, but when the discordant over-tones lying close together, higher than the tones just named, overpower the fundamental tone, the timbre becomes sharp and disagreeable. But these over-tones are not to be confounded with the earlier known combination-tones (_Combinationstöne_), which arise from the sounding together of two consonant intervals, and likewise have their own over-tones. Prof. Helmholtz has by means of his Resonance and Electrical apparatus invented aids by which the forms of the vibrations can be perceived as well as the over-tones, and the different degrees of strength of the latter in relation to one another and to the fundamental tone can be exactly measured. In attempting by means of the above-mentioned apparatus to cause the several over-tones to sound more or less strongly with the fundamental tone, and again entirely to veil others, it became possible to Prof. Helmholtz to produce artificially most opposite timbres, as well as all the vowels of speech.