ose vibrations or waves in the same time bear
some simple ratio to each other, are harmonious; an absolute equality
produces unison; and a group of harmonies is melody both in music and in
color. At this point we cannot but hint at the analogy already
discovered between the elements of music and the elements of form.
Angles harmonize in simple analysis, or intricate synthesis, whose
circular ratios are simple.

Numerical proportions are the roots of that shaft of harmony which,
springing from motion, rises and spreads into the nature around us,
which the senses appreciate, the spirit feels, and the reason
understands. Beauty is order, and the infinity of the law is testified
in the ever-swelling proofs of an unlimited consonance in creation, of
which these analogies are the smallest types. But the idea of numerical
analogy is not new to our age, now that the atomic theory is
established, and people are turned back to the days when the much
bescouted alchemist pored with rheumy eyes over the crucible, about to
be the tomb of elective affinity, and whence a golden angel was to
develop from a leaden saint: when they are reminded of the Pythagorean
numbers, and the arithmetic of the realists of old, they may very well
imagine that the vain world, like an empty fashion, has cycled around to
some primitive phase, and look for the door of that academy 'where none
could enter but those who understood geometry.'

But to return. When the ear accepts a tone, or the eye a single color,
it is noticed that these organs, satiated finally with the sterile
simplicity, echo, as it were, in a soliloquizing manner, to themselves,
other notes or tints, which are the complementary or harmony-completing
ones: so that if nature does not at once present a satisfaction, the
organization of the senses allows them internal resources whereon to
retreat. 'There is a world without, and a world within,' which may be
called complementary worlds. But nature is ever liberal, and her chords
are generally harmonies, or exquisite modifications of concord. The
chord of the tonic, in music, is the primal type of this harmony in
sound; it is perfectly satisfactory to the tympanum; and the ear,
knowing no further elements (for the tonic chord combines them all), can
ask for nothing more.

This chord, constructed on the tonic C, or Do, as a key note, and
consisting of the 1st, 3d, and 5th of the diatonic scale, or Do, Mi,
Sol, is called the fundamental chord.