t on the other side of the trio
of strings. If the piano has been tuned recently by an expert, you may
have to continue your search over several keys before you find an
imperfect unison; but you will rarely find a piano in such perfect
tune that it will not contain some defective unisons. However, if you
do not succeed in finding a defective unison, select a key near the
middle of the key-board, place your mute so that but two strings
sound, and with your tuning hammer loosen one of the strings very
slightly. Now you will notice a throbbing, beating sound, very unlike
the tone produced when the strings were in exact unison. See if you
can count the beats. If you have lowered the tension too much, the
beats will be too rapid to permit counting. Now with a steady and
gradual pull, with the heel of the hand against some stationary part,
bring the string up slowly. You will notice these waves become slower
and slower. When they become quite slow, stop and count, or wave the
hand in time with the pulsations. After practicing this until you are
sure your ear has become accustomed to the beats and will recognize
them again, you may proceed to perfect the unison. Bring the string up
gradually as before, and when the unison is reached you will hear one
single, simple, musical tone, as though it were from a single string.
Never have more than two strings sounding at once. You might go over
the entire key-board now and correct all the unisons if the scale is
yet fairly good. See which string is, in your opinion, the nearest to
correctness with respect to the scale, and tune the other one, or two,
as the case may be, to it. If the scale is badly out of symmetry, you
will not get very good results without setting a temperament; but the
tones will sound better individually. This experiment is more for
practice than for improving the piano.

_The cause_ of the waves in a defective unison is the alternate
recurring of the periods when the condensations and rarefactions
correspond in the two strings and then antagonize. This is known in
physics as "interference of sound-waves."

~The Octave.~--When perfectly tuned, the upper tone of the octave has
exactly double the number of vibrations of the lower. If the lower
tone vibrates 1000 per second, the upper will vibrate 2000. Of course,
the ear cannot ascertain in any way the number of vibrations per
second; we use these figures for scientific demonstration only.
However, there is an inst