different
tones could be produced. A stag-horn that was blown like a flageolet,
and having three finger-holes, has also been found; while on the old
monuments of Egypt are pictured harps, pipes with seven finger-holes, a
kind of flute, drums, tambourines, cymbals, and trumpets. In later times
these primeval forms have been modified into the various instruments in
use in the modern orchestra. It seems as if no musician had ever been
interested in the question as to why one instrument should give out a
sound so different from another one, even though it was sounding upon
the same pitch. No one can ever mistake the sound of a violin, or a
horn, or a piano, for any other instrument; and no two persons have
voices alike. This difference in tone, which enables us to identify an
instrument by its sound or a friend by his voice, is called quality of
tone, or _timbre_.

About twenty years ago, that great German physicist Helmholtz undertook
the investigation of this subject, and succeeded in unravelling the
whole mystery of the qualities of sound.

He discovered first, that a musical sound is very rarely a simple tone,
but is made up of several tones, sometimes as many as ten or fifteen,
having different degrees of intensity and pitch. The lowest sound, which
is also the strongest, is called the _fundamental_; and it is this tone
we mean when we speak of the pitch of a sound, as the pitch of middle C
upon a piano, or the pitch of the _A_ string on a violin. The higher
sounds that accompany the fundamental are called sometimes harmonics,
sometimes upper partial tones, but generally _overtones_. The character
or quality of a sound depends altogether upon the number and intensity
of these overtones associated with the fundamental. If a sound can be
made upon a pipe and a violin, that consists wholly of the fundamental
with no overtones, the two instruments sound absolutely alike. It is
exceedingly difficult to do this; and such sound when produced is
smooth, but without character, and unpleasing.

Second, Helmholtz discovered that the overtones always stand in the
simplest mathematical relation to the fundamental tone,--in fact, are
simple multiples of that tone, being two, three, four, and so on, times
the number of vibrations of it.

This will be readily understood by considering the position of such
related sounds when they are written upon the staff.

[Illustration]

If we start with C in the bass as indicated in the st