the loudness of tone depends upon the _amplitude_ of the
vibrations; the quality of tone depends upon the _form_ of the
vibrations; and the form of the vibrations depends upon the
_resonator_.

The fact that pure white light is a compound of all the tints of the
rainbow into which it may be resolved by the prism is well known, but
the analogous fact that a pure musical tone is a compound of tones of
different rates of vibration, tones of different pitch, is not so much
a matter of common knowledge, and not so obvious.

Analysis shows that a musical tone consists of a fundamental note and
a series of overtones.[5] The ear is quite capable of recognizing many
of these overtones and may be trained to do so. The most obvious can
be readily separated from a fundamental by a simple experiment.

[Footnote 5: For fuller exposition see Tyndall on _Sound_, or the
section devoted to _Acoustics_ in any text-book on Physics.]

The overtones arrange themselves in a definite order, as follows: (1)
the fundamental or prime tone; (2) an overtone one octave above the
fundamental; (3) an overtone a fifth above No. 2; (4) an overtone a
fourth above No. 3 (two octaves above the fundamental); (5) an
overtone a major third above No. 4; (6) an overtone a minor third
above No. 5. There are others in still higher range but those
indicated are easily demonstrated on the piano. For C they would be as
follows:

[Music illustration]

Experiment I

Step to your piano, noiselessly press and hold down the key of No. 2,
then strike the fundamental No. 1, with force and immediately release
it. As a result No. 2 will sound clearly, and if your ears are keen
you will at the same time hear No. 6. In succession hold down the keys
of 3, 4, 5, and 6, while you strike and release the fundamental No. 1.
If your piano is "in tune" you will probably hear No. 6 when holding
the key of any other note of the series.

In a musical tone of rich quality the overtones just indicated are
present in their fulness, while tone that is weak and thin is made so
by the absence or weakness of the overtones. I have stated that the
quality of a tone depends on the _form_ of its vibrations, and that
the form of its vibrations is determined by the character of the
_resonator_. We can now amplify this by saying that while the relative
presence or absence of overtones determines the clang or color of a
tone, their presence or absence is determined by the _character of the