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.
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.