--------------------------+---+---+---+---+---+---+---+---+---+---
INSTRUMENTS. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
--------------------------+---+---+---+---+---+---+---+---+---+---
/ Wide stopped | / | | | | | | | | |
| +---+---+---+---+---+---+---+---+---+---
| Narrow " | / | | / | | / | | / | | / |
| +---+---+---+---+---+---+---+---+---+---
| Narrow cylinder | / | / | / | / | / | / | | | |
ORGAN < +---+---+---+---+---+---+---+---+---+---
PIPES. | Principal }| / | / | / | | | | | | |
| (Wood) }| | | | | | | | | |
| +---+---+---+---+---+---+---+---+---+---
| Conically }| / | | | | / | / | / | | |
\ narrow at top. }| | | | | | | | | |
+---+---+---+---+---+---+---+---+---+---
Flute | / | / | / | / | | | | | |
+---+---+---+---+---+---+---+---+---+---
Violin | / | / | / | / | / | / | / | / | / | /
+---+---+---+---+---+---+---+---+---+---
Piano | / | / | / | / | / | / | / | / | |
+---+---+---+---+---+---+---+---+---+---
Bell | / | / | / | / | / | / | / | | |
+---+---+---+---+---+---+---+---+---+---
Clarionet | / | | / | | / | | / | | / |
+---+---+---+---+---+---+---+---+---+---
Bassoon | / | / | / | / | / | / | / | | |
+---+---+---+---+---+---+---+---+---+---
Oboe | / | / | / | / | / | / | / | | |
--------------------------+---+---+---+---+---+---+---+---+---+---
It must not be inferred that all of the overtones are of equal strength:
they are very far from that; but these differ in different
instruments, and it is this that constitutes the difference between a
good instrument and a poor one of the same name.
In a few of the spaces very light lines are made for the purpose of
indicating that such overtones are quite weak. For instance: the piano
has the sixth, seventh, and eighth thus marked; these tones being
suppressed by the mechanism, as described on a former page.
Only a few of the many forms of organ-pipes are given; but these are
sufficient to show what a physical difference there is between the
musical tones in such pipes.
As for the human voice, it is very rich in overtones; but no two voices
are alike, therefore it would be impossible to tabulate the components
of it in the manner they are tabulated for musical instruments.
In Helmholtz's experiments in the analysis of sounds, use was made of
the principle of resonance of a body of air enclosed in a vessel. In the
experiment with the tuning-fork to determine the wave-length, p. 78, it
is remarked that no response came until the volume of the air in the
tube was reduced to a certain length, which depended upon the vibration
number of the fork. If instead of a test-tube a bottle had been taken,
the result would have been the same. Every kind of a vessel can respond
to some tone of a definite wave-length, and a sphere has been found to
give the best results. These are made with a hole on one side for the
sound-wave to enter, and a projection on the opposite side, through
which a hole about the one-eighth of an inch is made, this to be placed
in the ear. Any sound that is made in front of the large orifice will
not meet any response, unless it be that particular one which the globe
can naturally re-enforce, when it will be plainly heard. Suppose, then,
one has a series of twenty or more of these, graduated to the proper
size for re-enforcing sounds in the ratio of one, two, three, four, and
so on. Take any instrument, say a flute: have one to blow it upon the
proper pitch to respond to the largest sphere, then take each of the
spheres in their order, applying them to the ear while the flute is
being sounded. When the overtones are present they will be heard
plainly and distinct from the fundamental sound. In like manner any or
all other sounds may be studied.
But Helmholtz did not stop after analyzing sounds of so many kinds: he
invented a method of synthesis, by which the sounds of any kind of an
instrument could be imitated. A tuning-fork, when made to vibrate by an
electric current, gives out a tone without harmonics or overtones. So if
a series of forks with vibration periods equal to the numbers of the
series of overtones given on p. 86 be so arranged that any of them may
be made to vibrate at will, it is evident that the resulting compound
tone would be comparable with that from an instrument having such
overtones. Thus, if with a tuning-fork giving a fundamental C, other
forks giving two, three, and four times the number of the fundamental
were associated, each one giving a simple tone, we should have for a
resultant the tone of a flute, as shown on p. 91. If one, three, five,
seven, and nine, were all sounded, the resulting tone would be that of
the clarionet, and so on. This he actually accomplished, and now makers
of physical apparatus advertise just such instruments.
Helmholtz also contrived a set of tuning-forks, which, when bowed, will
give out the vowel sounds like the voice.
It was remarked upon p. 89 that it has generally been considered that
age has a mellowing effect upon the sound of a violin. Once in
possession of the facts concerning sound that have been alluded to on
the preceding pages, it is easy to see how such an opinion should arise,
and also the fallacy of it. It is proved conclusively that the ability
to hear high sounds decreases as one grows older. As the violin gives a
very great number of overtones, even up to the limits of audibility, it
is plain that if such an instrument should not change in its quality of
tone in the least degree, yet to a man who played upon it for a number
of years it would seem to change by subtracting some of the higher
overtones from the sound; that is, it would seem to become mellower.
There is no evidence that such a physical change takes place in the
instrument. It is not here affirmed that no change does take place. It
may be probable; but all the evidence we have is the opinions of
individuals whose hearing we know does change; and this change is
competent to modify the judgment as to the quality of the sound in the
same direction. Before it can be affirmed that such a physical change
does take place in the violin as to make a perceptible difference in the
quality of its tone, it will be needful to determine accurately the
number and intensity of the overtones at intervals during many years,
and then to compare them. This has not yet been done.