vibration of two tones not in a favorable ratio, may produce the
phenomenon known as "beats, waves, or pulsations." Vibrations may
exist either with or without pulsations.

These pulsations are most perceptible in the unison, the octave and
the fifth. They are more easily perceived in the unison than in the
octave, and more easily in the octave than in the fifth. They are also
perceptible in the perfect fourth, the major and minor third and some
other intervals, but on account of their obscurity, and because these
intervals are unnecessary in tuning they have long since been
abandoned in "temperament making" (with the exception of the perfect
fourth) by most tuners, although a few still make use of it. We do not
say that the fourth is unsafe to tune by, but you will see later on
why it is not best to make use of it.

_The Fischer System_ or method of "setting the temperament" has these
advantages: It uses but two kinds of intervals: the fifth and octave;
by employing two whole octaves in place of one or one and a half,
nearly all of the middle section of strings is brought up in pitch
which insures that the temperament will stand better while the
remaining strings are being tuned; and the alternate tuning of the
fifth and octave makes the system exceedingly easy to learn, enabling
the tuner to work with less mental strain. Also the two-octave system
gives a greater compass for testing, thus insuring greater accuracy.

If you have access to a piano, it will now be well for you to begin
training the ear to perceive the pulsations. If you cannot use a
piano, you can train very well by the use of a mandolin, guitar,
violin, zither, or any stringed instrument. An instrument with metal
strings, however, is better, as the vibrations are more perfect.