preventing excessive wear, the hammer joint should be kept firm and
rigid.

If one of the strings vibrates 100 times in a second, and the other
101, there will be a portion of time during each second when the
vibrations will coincide, and likewise a portion of time when they
will antagonize each other. The periods of coincidence and of
antagonism pass by progressive transition from one to the other, and
the portion of time when exactitude is attained is infinitesimal; so
there will be two opposite effects noticed in every second of time:
the one, a progressive augmentation of strength and volume, the other,
a gradual diminution of the same; the former occurring when the
vibrations are coming into coincidence, the latter, when they are
approaching the point of antagonism. Therefore, when we speak of one
beat per second, we mean that there will be one period of augmentation
and one period of diminution in one second. Young tuners sometimes get
confused and accept one beat as being two, taking the period of
augmentation for one beat and likewise the period of diminution. This
is most likely to occur in the lower fifths of the temperament where
the beats are very slow.

Two strings struck at the same time, one tuned an octave higher than
the other, will vibrate in the ratio of 2 to 1. If these two strings
vary from this ratio to the amount of _one_ vibration, they will
produce _two_ beats. Two strings sounding an interval of the fifth
vibrate in the ratio of 3 to 2. If they vary from this ratio to the
amount of _one_ vibration, there will occur _three_ beats per second.
In the case of the major third, there will occur _four_ beats per
second to a variation of _one_ vibration from the true ratio of 5 to
4. You should bear this in mind in considering the proper number of