DICTIONARY OF MUSIC - El Atril

HARMONICS HARMONICS 299
ments as separate volumes), and was one of
the best musical periodicals ever published in
England. w. H. H.
HARMONICS, tones of higher pitch which
accompany every perfect musical sound in a
regular series. As they ascend they diminish
in intensity, and ajiproximate in pitch. If
the piano be opened and a bass note be struck
smartly and kept down, on listening atten-
tively a succession of faint sounds will be
heard, apparently rising out of the principal
sound and floating round it. These are the
harmonics. They are really constituents of the
main musical tone, and are produced by the
concurrent vibration of the aliquot 2>arts of the
string. Hence Helmholtz jiroposes to call them
' partial tones ' {Partialtime). This term is no
doubt more appropriate, inasmuch as above the
tentli degree most of these notes form inter\'al3
dissonant from tile jirime note and also from
each other, and thus become perceptibly inharmonic.
On the best musical instruments,
however, these high inharmonic tones are not
reached, the vibratory impulse being exhausted
on the prime note and the lower harmonics,
which are consonant both with the prime note
and among themselves. At the same time the
smaller the aliquot parts become in the ascending
series, the less easily are they set in a state
of separate vibration. Consequently these high
dissonant harmonics are distinctly audible only
on highly resonant metallic instruments, such
as the cymbals, bell, and triangle, and for
practical purposes the old term harmonic
answers as well as the term ' partial.'
A few instruments, such as the tuning-fork
and the wide stopped organ -pipe, practically
yield no harmonics. The human voice, the
harmonium, and all orchestral instruments, are
rich in them—the human voice probably the
richest of all ; but nature has so admirably
compounded them that it is very difficult to
analyse them scientifically. Rameau distinguished
harmonics in the human voice as early
as the beginning of the 18th century.
Harmonics naturally reinforce the fundamental
sound, in which case their extent and
distribution largely influence the intensity and
the quality of the sound. They may, however,
in many instances, be produced singly by
mechanically checking the vibration of the
fundamental note. In this relation they con-
stitute an important practical department in
most orchestral instruments.
Law of Harmiynics.—A sonorous body not
only vibrates as a whole but in each of its
several fractions or aliquot parts, \, -J, \, i, i,
-f, and so on at the same time ; and each of
these parts gives a separate note, the \ yielding
the octave, the i the fifth, the \ the double
octave, the i the third above the double octave,
and so on. The following scheme or diagram,
taken from Momigny, shows the harmonics of
the open string G on
thirteen pflaces :—
the violoncello up to
IMimimilltmiMi^
Here the bottom G is produced by the vibration
of the whole string. The two G's next
above are produced by the vibration of the two
halves. The three D's next above by the vibration
of the three thirds ; and so on. Thus the
diagram represents the whole of the notes produced
by the vibrations of tlie whole string and
its various sections up to its one-fourteenth
part.
In this scheme the first F (counting upwards),
the C a fifth above it, and the topmost notes E
and F, are more or less faulty. In practically
deducing the diatonic scale from this scheme,
these inter\'als have to be corrected by the ear.
By inspection of this scheme we discover the
intervals of the diatonic scale in the following
order :
^*e
From this scale may obviously be deduced the
chords of the third, fifth, seventh, and ninth.
By combining and transposing these notes into
one octave we get the following scale :
-m=r:"^^1 ^r-i~^ which is the scale of C major ascending from
dominant to dominant. As the same thing
happens in other keys, we have thus proved the
law that the intervals of each scale are generated
by its dominant. The dominant, not the tonic,
is therefore the true root of the whole scale.
FiXd'fical eff'Xt of Harmonics heard simul-
taneously ivith the fundamental note.—The harmonics
not only determine the diatonic intervals,
but to some extent the intensity and, as has
been lately proved by Helmholtz, the quality
of musical tones. On applying the ear to the
sound-hole of a violin during a long crescendo
on one note, tlie reinforcement of the tone by
the gradual addition of the higher and more
piercing harmonics is distinctly perceptible.
The principle and the ellect are precisely the
same in a crescendo produced by the addition
of the mixture stops on an organ. The loudest
musical instruments, caeteris jmribus, are those
in whicli the highest harmonics predominate,
e.g. the cymbals, triangle, bell, and gong.
The etlect of harmonics on the quality of
musical sounds is easily tested by carefully comparing
the tones of an old and a new violin.
In the former the strong vibrations of the fundamental
note and the lower harmonics leave but