length, being an aliquot division of a lower string. This gave the
instrument a certain brightness or life throughout, an advantage which
has secured its universal adoption. The expedients of an untouched
octave string and of utilizing those lengths of wire that lie beyond the
bridges have been brought into notice of late years, but the latter was
early in the century essayed by W. F. Collard.

From difficulties of tuning, owing to friction and other causes, the
real gain of these expedients is small, and when we compare them with
the natural resources we have always at command in the normal scale
of the instrument, is not worth the cost. The inventor of the damper
register opened a floodgate to such aliquot re-enforcement as can be got
in no other way. Each lower note struck of the undamped instrument,
by excitement from the sound-board carried through the bridge, sets
vibrating higher strings, which, by measurement, are primes to its
partials; and each higher string struck calls out equivalent partials
in the lower strings. Even partials above the primes will excite
their equivalents up to the twelfth and double octave. What a glow of
tone-color there is in all this harmonic re-enforcement, and who would
now say that the pedals should never be used? By their proper use,
the student's ear is educated to a refined sense of distinction of
consonance and dissonance, and the intention and beauty of Chopin's
pedal work becomes revealed.

The next decade, 1790-1800, brings us to French grand pianoforte-making,
which was then taken up by Sebastian Erard. This ingenious mechanic and
inventor traveled the long and dreary road along which nearly all who
have tried to improve the pianoforte have had to journey. He appears, at
first, to have adopted the existing model of the English instrument in
resonance, tension, and action, and to have subsequently turned his