The fifth harmonic e is often heard to be surprisingly strong,
when the ear has once isolated it. A person with a trained
musical ear will notice that this fifth harmonic of Cj is a
little flatter than the e of the pianoforte. The notes of
a pianoforte are tuned to equal temperament, which makes all
the major thirds a little sharper than the just intonation, as
will be described later. The difference of pitch between the
two notes is easily detected, if Cj is first sounded strongly, and
then whilst its key is held down, the e of the pianoforte is
sounded gently. Beats will then be heard from the want of
coincidence of pitch between the fifth harmonic of Cj and the
e of the pianoforte.
The detection of the harmonics is made easier if resonance
is used. Depress gently the key corresponding to one of the
harmonics of Cj — say G — so as to raise its damper but not
to sound the note. Now sound Cj loudly and hold down its
key. The third harmonic of Cj will cause resonant vibrations
in the strings of G, and if after a few seconds the finger is
taken off the key Oj, the note G will be heard.
Helmholtz analysed the notes of musical instruments with
the help of the resonators shewn in Fig. 63. He used a set of
resonators tuned to the harmonics of Bt?. Whilst a trombone,
fat instance, was blown to give the note Bl>, he held the
resonators to his ear in turn and recorded his estimate of the
relative strengths of the various harmonics. In the same way
he found what harmonics are present, and with what intensities,
in the notes of other instruments.
