e that thirds are tuned
sharp, there is a limit beyond which we cannot go, and this excessive
sharpness of the third is the thing that tuners always listen for.

[E] In making these suggestions, no calculation is made for the
liability of the tones tuned to fall. This often happens, in which
case your first test will display a sharp third. In cases like this
it is best to go on through, taking pains to temper carefully, and
go all over the temperament again, giving all the strings an equal
chance to fall. If the piano is very bad, you may have to bring up
the unisons roughly, inuring this portion of the instrument to the
increased tension, when you may again place your continuous mute and
set your temperament with more certainty.

The fundamental sounds better to the ear when too sharp. The reason
for this is the same as has already been explained above; namely, if
the fundamental is too sharp the third will be less sharp to it, and,
therefore, nearer perfect.

After you have gone all over your temperament, test every member of
the chromatic scale as a fundamental of a chord, as a third, and as a
fifth. For instance: try middle C as fundamental in the chord of C
(G-C-E or E-G-C or C-E-G). Then try it as third in the chord A flat (E
flat-A flat-C or C-E flat-A flat or A flat-C-E flat). Then try it as
fifth in the chord of F (C-F-A or A-C-F or F-A-C). Take G likewise and
try it as fundamental in the chord of G in its three positions, then
try it as a third in the chord of E flat, then as fifth in the chord
of C. In like manner try every tone in this way, and if there is a
falsely tempered interval in the scale you will be sure to find it.

You now understand that the correctness of your temperament depends
entirely upon your ability to judge the degree of flatness of your
fifths; provided, of course, that the strings stand as tuned. We have
told you something about this, but you may not be able at once to
judge with sufficient accuracy to insure a good temperament. Now, we
have said, let the fifths beat a little more slowly than once a
second; but the question crops up, How am I to judge of a second of
time? The fact is that a second of time is quickly learned and more
easily estimated, perhaps, than any other interval of time; however,
we describe here a little device which will accustom one to estimate
it very accurately in a short time. The pendulum oscillates by an
invariable la