fundamental. If a certain F vibrates 100, the C, a fifth above, will
vibrate 150, if tuned so that no waves are heard; but for reasons
which will be fully explained later, the fifth cannot be tuned with
mathematical precision. On account of certain peculiarities in our
tempered scale, the fifth must always be left somewhat flatter than
perfect. This fact is always learned with some astonishment by
beginners.

In your practice on tuning the fifth, first tune it perfectly, so that
no waves are perceptible; then flat it so that there are very slow
waves; less than one per second. Some authorities say there should be
three beats in five seconds; but the tuner must learn to determine
this by his own judgment. The tempering of the fifth will be treated
exhaustively in subsequent lessons.

We advise that you confine your practice to the unison until you are
sure you have a clear conception of its peculiarities in all portions
of the key-board, except the extreme lower and upper octaves; do not
try these yet. Do not begin to practice on the octave until you are
very familiar with the beats in the unison. By gradual progress you
will avoid confusing the ear, each step being thoroughly mastered
before advancing to the next. Remember, there is nothing that is
extremely difficult in learning to tune if you but understand what has
to be done, go about it systematically, and have plenty of patience.

In this lesson we give you our system of setting the temperament; that
is, the succession in which the different tones of the temperament are
tuned. We advise, however, that you do not attempt to set a
temperament until after studying Lesson IX, which enters into the
theory of temperament, testing, etc.