e larger the
number of swings made by the more quickly moving pendulum relatively to
that of the slower pendulum in a given time, the higher or sharper is the
harmony said to be. Thus, 1:3 is a higher harmony than 1:2, and 2:3 is
lower or flatter than 3:8.

The tuning of a harmonograph with independent pendulums is a simple matter.
It is merely necessary to move weights up or down until the respective
numbers of swings per minute bear to one another the ratio required. This
type of harmonograph, if made of convenient size, has its limitations, as
it is difficult to get as high a harmonic as 1:2, or the octave with it,
owing to the fact that one pendulum must in this case be very much shorter
than the other, and therefore is very sensitive to the effects of friction.

[Illustration: FIG. 176a.--Hamonograms illustrating the ratio 1:3. The
two on the left are made by the pendulums of a twin elliptical harmonograph
when working concurrently; the three on the right by the pendulums when
working antagonistically.]

[Illustration: FIG. 177a.--Harmonograms of 3:4 ratio (antagonistically).
(Reproduced with kind permission of Mr. C. E. Benham.)]

The action of the Twin Elliptic Pendulum is more complicated than that of
the Rectilinear, as the harmony ratio is not between the swings of
deflector and upper pendulum, but rather between the swings of the
deflector and that of the system as a whole. Consequently "tuning" is a
matter, not of timing, but of experiment.

Assuming that the length of the deflector is kept constant--and in practice
this is found to be convenient--the ratios can be altered by altering the
weights of one or both pendulums and by adjustment of the upper weight.

For the upper harmonies, 1:4 down to 3:8, the two pendulums may be almost
equally weighted, the top one somewhat more heavily than the other. The
upper weight is brought down the rod as the ratio is lowered.

To continue the harmonies beyond, say, 2:5, it is necessary to load the
upper pendulum more heavily, and to lighten the lower one so that the
proportionate weights are 5 or 6:1. Starting again with the upper weight
high on the rod, several more harmonies may be established, perhaps down to
4:7. Then a third alteration of the weights is needed, the lower being
reduced to about one-twentieth of the upper, and the upper weight is once
more gradually brought down the rod.

Exact figures are not given, as much depends on the proportions of the