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.
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.
Even when, in the culture of a voice, we have advanced so far that none of the inharmonic but only the harmonic over-tones sound with the fundamental tone, we shall always find that every voice has its own peculiar Klangfarbe—i. e., its own characteristic timbre; and it is not possible so to form the tones of a voice that the over-tones sounding with them shall diminish proportionally according to their height. Every voice has one, mostly two, over-tones, which always predominate in every tone, every register, and give the voice its peculiar quality. When, with the first octave, the fifth above it sounds, the voice is full and mellow. A clear, sympathetic, silvery ring is produced by the sounding of the seventh with the octave immediately above it. One of the most beautiful timbres is a result of the prominence of the third with the seventh, etc. This peculiarity appears to be connected with the particular form and structure of the cavity of the mouth. That parts of the cavity of the mouth serve as a sounding-board in the formation of sound, has already been mentioned.[ 11 ]
The perfection of a tone at a certain pitch depends, in the resonance of the cavity of the mouth, upon the utterance of some vowel, to which the parts of the mouth are adjusted; and this perfection is considerably affected by even a slight variation in the timbre of the vowel, as it occurs in different dialects of the same language. On the other hand, the peculiar tones of the cavity of the mouth are almost wholly independent of age and sex. The peculiar pitch of the resonance apparatus has also an influence upon the tone. Every one who knows how to play on any instrument knows that some of its tones sound sweeter and are more easily given than others; these are the tones in which the peculiar tone of the instrument and its over-tones sound together. To describe more particularly the natural laws upon which these facts rest would lead us too far away from our present purpose.
THE VOWELS
Every tone in singing usually takes the sound of some vowel. By the greater or less distinctness of one or another of the over-tones, sounding with the fundamental tone, various timbres of the vowel are produced. But certain vowels in certain parts of the scale can be sung far more easily and sweetly than others. The investigation of this fact has taught us that a tone gains in richness when the tone corresponding to the vowel belongs to the over-tones of the fundamental tone. In the human voice, however, the tones favorable to the several vowels do not admit of being precisely determined.
In different languages and dialects the vowels have different shades, and a scarcely perceptible variation, especially in the clearer vowels, is sufficient to cause the over-tones to be heard more or less distinctly. After I had learned, with the kind assistance of Professor Helmholtz, by means of his artificial apparatus for the sharpening of the ear, to find out over-tones and to know their peculiarities, I was soon able, without any artificial help, to discover the vowels favorable to them by the fuller sound of certain tones. In the female voice all tones below the c1