e 1.29 beats: nearly one and a third per second, and that
the highest fifth of the temperament, F-341.72 to C-512, should be
1.74, or nearly one and three-quarters. By remembering these figures,
and endeavoring to temper as nearly according to them as possible, the
tuner will find that his temperament will come up most beautifully.
This is one of the features that is overlooked or entirely unknown to
many fairly good tuners; their aim being to get all fifths the same.

~Finishing up the Temperament.~--If your last trial, F-C, does not
prove a correct fifth, you must consider how best to rectify. The
following are the causes which result in improper temperament:

1. Fifths too flat.

2. Fifths not flat enough.

3. Some fifths correctly tempered and others not.

4. Some fifths sharper instead of flatter than perfect; a
condition that must be watched with vigilance.

5. Some or all of the strings tuned fall from the pitch at which
they were left.

From a little reflection upon these causes, it is seen that the last
trial may prove a correct fifth and yet the temperament be imperfect.
If this is the case, it will be necessary to go all over the
temperament again. Generally, however, after you have had a little
experience, you will find the trouble in one of the first two causes
above, unless it be a piano wherein, the strings fall as in Cause 5.
This latter cause can be ascertained in cases only where you have
started from a tuning pipe or fork. Sometimes you may find that the
temperament may be corrected by the alteration of but two or three
tones; so it is always well to stop and examine carefully before
attempting the correction. A haphazard attempt might cause much extra
work.

In temperament setting by our system, if the fifths are properly
tempered and the octaves are left perfect, the other intervals will
need no attention, and will be found beautifully correct when used in
testing.

The mistuned or tempered intervals are as follows:--

INTERVALS FLATTENED. INTERVALS SHARPENED.
The Fifth, slightly. The Fourth, slightly.
The Minor Third, The Major Third,
considerably. greatly.
The Minor Sixth, The Major Sixth,
considerably. greatly.

~Tuning the Treble.~--In tuning the treble, which is always tuned by
exact octaves, from their corresponding tones within the temperament,
the ear will often accept an o