nor_, at the recapitulation (page 39 of the full score) may be found
a magnificent example of the intensity of effect gained by a canonic
imitation of the main theme--in this instance between the lower and
upper voices. Possibly the finest example of canonic writing in all
literature is the Finale of Cesar Franck's _Sonata in A major_ for
Violin and Pianoforte in which, for several pages, there is an
eloquent dialogue between the two contrasting instruments. The
movement is too long for citation but it should certainly be procured
and studied. In the Trio of the Scherzo in Beethoven's _Seventh Sonata
for Violin and Pianoforte_ there is a free use of canonic imitation
which will repay investigation. Lastly, the _Aria with 30
Variations_--the so-called _Goldberg Variations_ of Bach--is a perfect
storehouse of every conceivable canonic device.

A few standard examples are to be found in the Supplement. These
should be played over and studied until they are thoroughly
familiar--not only for the pleasure to be derived, but for the
indispensable training afforded in polyphonic listening.

Ex. No. 9 Canon by Thomas Tallys (1510-1585).

Ex. No. 10 Canonic Variation by Schumann from the _Etudes
Symphoniques_.

Ex. No. 11 of Bach's _Goldberg Variations_.

Ex. No. 12 Canon in B-flat minor, op. 38, Grieg.

Ex. No. 13 Canon in F-sharp major, op. 35, Jadassohn.

One of the most simple and direct types of polyphonic composition is
the form known as the _Invention_ in which, as the term implies, the
composer--through his _inventive genius_ and by means of the
polyphonic devices of imitation and transposition--develops to a
logical conclusion some short and characteristic motive. We are
fortunate in having from Bach himself, that consummate master of
polyphony, two sets of such Inventions: fifteen for two voices, and
fifteen for three. These flights of fancy--in which art so subtly
conceals art--though originally composed for the clavichord and
harpsichord (the precursors of the pianoforte), are very effective on
our modern instrument and should be in the possession of every
music-student.[36] A brief analysis is now given of the first one in
the set for two voices, and Nos. 4, 8 and 10 in this set are
particularly recommended for study; also Nos. 2, 6 and 14 among those
for three voices. The opening motive

[Music]

is the foundation of the entire composition and is at once imitated,
canonically, in the lower voice. Then th