, and how much to temper it, as fourths require a different
degree of tempering from the fifths; and he is constantly changing
from an interval upward to one downward; so, this system must be
stamped as tedious and complicated, to say the least. Yet this system
is much followed in factories for rough tuning, and also by many old
professional tuners.

The table on the following page gives the succession of intervals
generally taken by tuners employing this system using the tones within
the F octave mentioned above. Middle C is obtained in the usual way,
from the tuning fork.

SYSTEM A.

By middle C tune F fifth below. Temper sharp.
By F " B[b] (A[#]) fourth above. " "
" C " G fourth below. " flat
" G " D fifth above. " "
" D " A fourth below. " "
" A " E fifth above. " "
" E " B fourth below. " "
" B " F[#] fourth below. " "
" F[#] " C[#] fifth above. " "
" C[#] " G[#] fourth below. " "
" G[#] " D[#] fifth above. " "
Then try D[#] with A[#] previously tuned for "wolves."

We think a little study and trial of this system will produce the
conviction that it is a very difficult and precarious one, and that it
has every disadvantage but one, namely, that it uses the smallest
possible number of tones, which is really of little value, and does
not compensate for the difficulty encountered and the uncertainty of
the results.

Another system which has many advantages over the above, is one which
employs fifths only and covers a compass of an octave and a half. This
system is similar to ours in that it employs fifths in the same
succession as far as G[#], the most of them, however, being an octave
higher. From this G[#] there is a break in the succession, and the
tuner goes back to middle C from which he started and tunes by fifths
downward until he reaches the G[#] at which he left off. This system
employs the tones from F below middle C to C, octave above. Below is
the succession, starting upon 3C, whose pitch is determined as usual.

SYSTEM B.

By 3C tune 2C octave below.
"