128 x 1 = 128 = C fundamental.
128 x 2 = 256 = C'.
128 x 3 = 384 = G'.
128 x 4 = 512 = C''.
128 x 5 = 640 = E''.
128 x 6 = 768 = G''.
128 x 7 = 896 = B''[flat].
128 x 8 = 1,024 = C'''.
128 x 9 = 1,152 = D'''.
128 x 10 = 1,280 = E'''.
This series is continued up to the limits of hearing. Now, it appears
that all instruments do not give the complete series: indeed, it is not
possible to obtain them all upon some instruments. Each of them,
however, when present helps in the general effect which we call quality.
Sometimes the overtones are more prominent than the fundamental, as when
a piano-wire is struck with a nail. It has always been noticed that it
does not give out the sound that is wanted when it is struck in this
way. Hence it is the art of an instrument-maker to so construct the
instrument as to develop and re-enforce such tones as are pleasing, and
to suppress the interfering and disagreeable overtones. Piano-makers
learned by trial where was the proper place to strike the stretched wire
in order to develop the most musical sound upon it; but no reason could
be given until it was observed that striking it at a point about
one-seventh or one-ninth its length from either end prevented the
development of the objectionable overtones, the seventh and the ninth.
Hence they can scarcely be heard in a properly constructed instrument.
These overtones are very discordant with the lower sounds.
Organ-pipes have their specific qualities given to them by making them
wide-mouthed, narrow-mouthed, conical, and so on; shapes which
experience has determined give pleasing sounds with different qualities.
The violin is an instrument that seems to puzzle makers more than almost
any other. Some of the old violins made two hundred years ago by the
Amati family at Cremona are worth many times their weight in gold.
Recent makers have tried in vain to equal them; but, when their
ingenuity and skill have failed, they declare that _age_ has much to do
with such instruments, that age mellows the sounding quality of the
violin. But the Cremona violins were just as extraordinary instruments
when they left the hands of the makers as they are now; and the fame of
the Amati family as violin-makers was over all Europe while they were
living.
A good violin when well played gives an exquisite musical effect, and on
account of its range and quality of tones it is the leading orchestral
instrument, always pleasing and satisfying; but in unskilled hands even
the best _Cremona_ will give forth sounds that make one grieve that it
was ever invented. Overtones of all sorts and with all degrees of
prominence may be easily developed upon it: therefore the skilful player
draws the bow at such a place upon the strings as to develop the
overtones he wants, and suppress the ones not wanted. The usual rule is
to draw the bow about an inch below the bridge; but the place for the
bow depends upon where the fingers are that stop the strings, and also
the pressure upon it. It requires an almost incredible amount of
practice to be able to play a violin very well.
In the accompanying table will be found the component parts of tones
upon a few instruments in common use.