ridge, where the
tuner sets his mutes. If, for instance, he is tuning an octave and has
his mute set precisely in the middle of the vibrating segment, in
place of muting the string it sounds its own octave, which will
disturb the ear in listening for the tone from the one free string.
Move the mute either way until it is found to mute the string
entirely.

QUESTIONS ON LESSON XIV.

1. Explain the cause of the beats.

2. How many _beats_ per second in a unison of two strings, one
tuned to 100, the other to 101 vibrations per second?

3. How many beats per second in an octave, the lower tone of which
is tuned to 100, the upper to 201 vibrations per second?

4. How many beats per second in a fifth, the fundamental of which
is tuned to 100, the fifth to 151?

5. The fifth, 2F-3C, when properly tempered, should beat 1-3/4
times per second. How often should a fifth, an octave higher,
beat?

LESSON XV.

~MISCELLANEOUS TOPICS PERTAINING TO THE PRACTICAL WORK OF TUNING,
REGULATING, AND REPAIRING.~

~Comparison of the Different Systems.~--Up to this time, we have given
no account of any system of tuning except the one recommended. For the
purpose of making the student more thoroughly informed we detail here
several different systems which have been devised and practiced by
other tuners. It is a matter of history that artisans in this
profession and leaders in musical science have endeavored to devise a
system of temperament having all the desirable qualifications.

The aims of many have been to invent a system which uses the fewest
number of tones; working under the impression that the fewer the tones
used in the temperament, the easier the tuner's work. These have
reduced the compass of the temperament to the twelve semi-tones from
middle C to B above; or from F below, to E above middle C. This
system requires the tuner to make use of both fourths and fifths. Not
only does he have to use these two kinds of intervals in tuning, but
he has to tune by fourths up and fourths down, and, likewise, by
fifths up and fifths down. When tuning a fifth upward, he flattens it;
and when tuning a fifth downward he sharpens the lower tone; when
tuning a fourth upward, he sharpens it; when tuning a fourth downward,
he flattens the lower tone.

It is readily seen that by a system of this kind the tuner's mind is
constantly on a strain to know how to temper the interval he is
tuning