ngs," others say "setting
the temperament." The former is more commonplace, as it merely
suggests the idea of laying a number of patterns by which all others
are to be measured. The latter term is extremely comprehensive. A
lucid definition of the word "temperament," in the sense in which it
is used here, would require a discourse of considerable length. The
following statements will elicit the full meaning of the term:

The untutored would, perhaps, not think of setting a temperament to
tune by. He would likely begin at some unfavorable point, and tune by
various intervals, relying wholly upon his conception of pitch for the
accuracy of the tones tuned, the same as a violinist in tuning his
four strings. To be sure, pitch has to be reckoned as a rude guide in
setting the tones; but if pitch alone were the guide we would never
attain to any degree of perfection in scale forming. We could never
adjust our tones to that delicate fineness so much appreciated, which
gives to the instrument its surpassing brilliancy.

~Beats, Waves, Pulsations.~--To obtain absolute accuracy the tuner is
guided by beats, waves or pulsations. These three words refer to one
and the same thing, a phenomenon that occurs in certain intervals when
two tones are sounded together that are not in exact tune. These terms
must not be confounded with the term "sound wave" or "vibrations" so
often used in discussions on the theory of sound. However, we think
the student is thoroughly familiar with these terms. The rate of
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: