variable, and with an instrumental accompaniment there is
none. In fugues, multiple counterpoint is one of the normal
resources of music; and few devices are more self-explanatory
to the ear than the process by which the subject and counter-subjects
of a fugue change their positions, revealing fresh melodic
and acoustic aspects of identical harmonic structure at every
turn. This, however, is rendered possible and interesting by
the fact that the passages in such counterpoint are separated
by episodes and are free to appear in different keys. Many
fugues of Bach are written throughout in multiple counterpoint;
but the possibility of this, even to composers such as Bach and
Mozart, to whom difficulties seem unknown, depends upon the
freedom of the musical design which allows the composer to
select the most effective permutations and combinations of his
counterpoint, and also to put them into whatever key he chooses.
An unaccompanied round for unequal voices would bring about
the permutations and combinations in a mechanical order;
and unless the melody were restricted to a compass common to
soprano and alto each alternate revolution would carry it beyond
the bounds of one or the other group of voices. The technical
difficulties of such a problem are destructive to artistic invention.
But they do not appear in the above-mentioned operatic rounds,
though these are for unequal voices, because here the length of
the initial melody is so great that the composition is quite long
enough before the last voice has got farther than the first or
second phrase, and, moreover, the free instrumental accompaniment
is capable of furnishing a bass to a mass of harmony
otherwise incomplete.
The resources of canon, when emancipated from the principles of the round, are considerable when the canonic form is strictly maintained, and are inexhaustible when it is treated freely. A canon need not be in the unison; and when it is in some other interval the imitating voice alters the expression of the melody by transferring it to another part of the scale. Again, the imitating voice may follow the leader at any distance of time; and thus we have obviously a definite means of expression in the difference of closeness with which various canonic parts may enter, as, for instance, in the stretto of a fugue. Again, if the answering part enters on an unaccented beat where the leader began on the accent, there will be artistic value in the resulting difference of rhythmic expression. This is the device known as per arsin et thesin. All these devices are, in skilful hands, quite definite in their effect upon the ear, and their expressive power is undoubtedly due to their special canonic nature. The beauty of the pleading, rising sequences in crossing parts that we find in the canon in the 2nd at the opening of the Recordare in Mozart’s Requiem is attainable by no other technical means. The close canon in the 6th at the distance of one minim in reversed accent in Bach’s eighteenth Goldberg variation owes all its smooth harmonic expression to the fact that the two canonic parts move in sixths which would be simultaneous but for the pause of the minim which reverses the accents of the upper part while it creates that chain of suspended discords which give harmonic variety to the whole.
Two other canonic devices have important artistic value, namely, augmentation and diminution (two different aspects of the same thing) and inversion. In augmentation the imitating part sings twice as slow as the leader, or sometimes still slower. This obviously should impart a new dignity to the melody, and in diminution the expression is generally that of an accession of liveliness.[1] Neither of these devices, however, continues to appeal to the ear if carried on for long. In augmentation the answering part lags so far behind the leader that the ear cannot long follow the connexion, while a diminished answer will obviously soon overtake the leader, and can proceed on the same plan only by itself becoming the leader of a canon in augmentation. Beethoven, in the fugues in his sonatas op. 106 and 110, adapted augmentation and diminution to modern varieties of thematic expression, by employing them in triple time, so that, by doubling the length of the original notes across this triple rhythm, they produce an entirely new rhythmic expression. This does not seem to have been applied by any earlier composer with the same consistency or intention.
The device of inversion consists in the imitating part reversing every interval of the leader, ascending where the leader descends and vice versa. Its expressive power depends upon such subtle matters of the harmonic expression of melody that its artistic use is one of the surest signs of the difference between classical and merely academic music. There are many melodies of which the inversion is as natural as the original form, and does not strikingly alter its character. Such are, for instance, the theme of Bach’s Kunst der Fuge, most of Purcell’s contrapuntal themes, the theme in the fugue of Beethoven’s sonata, op. 110, and the eighth of Brahms’s variations on a theme by Haydn. In such cases inversion sometimes produces harmonic variety as well as a sense of melodic identity in difference. But where a melody has marked features of rise and fall, such as long scale passages or bold skips, the inversion, if productive of good harmonic structure and expression, may be a powerful method of transformation. This is admirably shown in the twelfth of Bach’s Goldberg Variations, in the fifteenth fugue of the first book of his Forty-eight Preludes and Fugues, in the finale of Beethoven’s sonata, op. 106, and in the second subjects of the first and last movements of Brahms’s clarinet trio.
The only remaining canonic device which figures in classical music is that known as cancrizans, in which the imitating part reproduces the leader backwards. It is of extreme rarity in serious music; and, though it sometimes happens by accident that a melody or figure of uniform rhythm will produce something equally natural when read backwards, there is only one example of its use that appeals to the ear as well as the eye. This is to be found in the finale of Beethoven’s sonata, op. 106, where it is applied to a theme with such sharply contrasted rhythmic and melodic features that with long familiarity a listener would probably feel not only the wayward humour of the passage in itself, but also its connexion with the main theme. Nevertheless, the prominence given to the device in technical treatises, and the fact that this is the one illustration which hardly any of them cite, show too clearly the way in which music is treated not only as a dead language but as if it had never been alive.
All these devices are also independent of the canonic idea, since they are so many methods of transforming themes in themselves and need not always be used in contrapuntal combination.
2. Fugue.
As the composers of the 16th century made progress in harmonic and contrapuntal expression through the discipline of strict canonic forms, it became increasingly evident that there was no necessity for the maintenance of strict canon throughout a composition. On the contrary, the very variety of canonic possibilities, apart from the artistic necessity of breaking up the uniform fulness of harmony, suggested the desirability of changing one kind of canon for another, and even of contrasting canonic texture with that of plain masses of non-polyphonic harmony. The result is best known in the polyphonic 16th-century motets. In these the essentials of canonic effect are embodied in the entry of one voice after another with a definite theme stated by each voice in that part of the scale which best suits its compass, thus producing a free canon for as many parts as there are voices, in alternate intervals of the 4th, 5th and octave, and at such distances of time as are conducive to clearness and variety of proportion. It is not necessary for the later voices to imitate more than the opening phrase of the earlier, or, if they do imitate its continuation, to keep to the same interval.
Such a texture differs in no way from that of the fugue of more modern times. But the form is not what is now understood as fugue, inasmuch as 16th-century composers did not normally think of writing long movements on one theme or of making a point of the return of a theme after episodes. With the appearance of new words in the text, the 16th-century composer
- ↑ But see the E. major fugue in the second book of the Wohltemperirtes Klavier, where the entry of the diminished subject (in a new position of the scale) is very tender and solemn.
