ctave as true before its pitch has been
sufficiently raised. Especially is this true in the upper octaves.
After tuning a string in the treble by its octave in the temperament,
test it as a fifth. For instance, after tuning your first string
beyond the temperament, 3C[#], test it as a fifth to 2F[#]. If you are
yet uncertain, try it as a major third in the chord of A. The beats
will serve you as a guide in testing by fifths, up to about an octave
and a half above the highest tone of the temperament; but beyond this
point they become so rapid as to be only discernible as degrees of
roughness. The beats will serve as a guide in tuning _octaves_ higher
in the treble than the point at which the beats of the _fifth_ become
unavailable; and in tuning _unisons_, the beats are discernible almost
to the last tone.

The best method to follow in tuning the treble may be summed up as
follows: Tune the first octave with the beats as guides both in the
octave and in testing it by the fifth. If yet uncertain, test by
chords. Above this octave, rely somewhat upon the beats in the octave,
still use the fifth for testing, but listen for the pitch in the
extreme upper tones and not so much for the beats except in bringing
up unisons, in which the beats are more prominent.

In the extreme upper tones, the musical ear of the tuner is tried to
the utmost. Here, his judgment of correct harmonic relation is the
principal or only guide, while in the middle octaves the beats serve
him so faithfully, his musical qualifications being brought into
requisition only as a rough guide in determining pitch of the various
intervals. To tune by the beats requires a sharp ear and mental
discernment; to tune by pitch requires a fine musical ear and
knowledge of the simpler laws of harmony.

As stated above, the tuner will fail in many cases to tune his high
octaves sharp enough. Rarely, if ever, will a tuner with a good ear
leave the upper tones too sharp. Now, there is one more fact which is
of the utmost importance in tuning the treble: it is the fact that the
extreme upper octave and a half must be tuned slightly sharper than
perfect; if the octaves are tuned perfect, the upper tones of the
instrument will sound flat when used in scale and arpeggio passages
covering a large portion of the key-board. Begin to sharpen your
octaves slightly from about the seventeenth key from the last;
counting both black and white. In other words, begin to sharpen from