not
following the fugue form strictly, approximate it very nearly. The
first invention and the eighth are perhaps the best for this purpose.
After these, an easy fugue in the "Well-tempered Clavier," such as the
one in D major or that in C minor; more difficult examples are those in
C-sharp major and in G major. In the development of fugues the old
masters made use of a great variety of artifices, including all the
devices of double counterpoint at the tenth and twelfth, canon and
inversion, the latter applied not alone to the relation of the voices
but also to the melodic material constituting a voice. "The fugue,"
Cherubini says, "contains everything which a good composer ought to
know," and it is, in fact, the underlying element in all serious
moments of modern music except those which are purely lyric. The fugue
underlies the elaboration in the middle of a sonata-piece, and, in
fact, is the original source, as said before, of nearly all the serious
moments in the higher departments of art.

The second serious unitary form is the theme and variation. In this
case the theme is itself a complete song form of perhaps two or three
periods, and each variation is precisely of the same number of
measures, and follows the same harmonic structure in many cases.

There are, however, in modern use, two types of the variation form.
One of these, called formal variations, leaves the harmony entirely the
same in all the variations, except, perhaps, to change the melody from
major to minor of the same key and back again. In the best examples
the harmony remains entirely unchanged, but the melody is diversified
rhythmically in various ways. Good examples of this type of variations
are to be found in the works of Mozart and in the second movement of
Beethoven's Sonata in G major, opus 14, and in the second movement of
the "Sonata Appassionata" of Beethoven.

The character variation pursues a different course. At times the key
is changed and the harmony changes very much. In order to see how this
can be accomplished without destroying the identity of the musical
idea, it should be remembered that a musical idea consists essentially
of three elements: it has a rhythm, a melodic figure, and a harmonic
foundation. If the melodic figure is retained, and the harmonic
figure, the rhythm can be diversified indefinitely, and, in fact, if
any two of these elements are retained the third can be modified very
much. In the latest p