In the canonic forms, the earliest known in music as an independent art, the laws of texture also determine the shape of the whole, so that it is impossible, except in the light of historical knowledge, to say which is prior to the other. The principle of canon being that one voice shall reproduce the material of another note for note, it follows that in a composition where all parts are canonic and where the material of the leading part consists of a pre-determined melody, such as a Gregorian chant or a popular song there remains no room for further consideration of the shape of the work. Hence, quite apart from their expressive power and their value in teaching composers to attain harmonic fluency under difficulties, the canonic forms played the leading part in the music of the 15th and 16th centuries; nor indeed have they since fallen into neglect without grave injury to the art. But strict canon soon proved inadequate, and even dangerous, as the sole regulating principle in music; and its rival and cognate principle, the basing of polyphonic designs upon a given melody to which one part (generally the tenor) was confined, proved scarcely less so. Nor were these two principles, the canon and the canto fermo, likely, by combination in their strictest forms, to produce better artistic results than separately. Both were rigid and mechanical principles; and their development into real artistic devices was due, not to a mere increase in the facility of their use, but to the fact that, just as the researches of alchemists led to the foundations of chemistry, so did the early musical puzzles lead to the discovery of innumerable harmonic and melodic resources which have that variety and freedom of interaction which can be organized into true works of art and can give the ancient mechanical devices themselves a genuine artistic character attainable by no other means.

The earliest canonic form is the rondel or rota as practised in the 12th century. It is, however, canonic by accident rather than in its original intention. It consists of a combination of short melodies in several voices, each melody being sung by each voice in turn. Now it is obvious that if one voice began alone, instead of all together, and if when it went on to the second melody the second voice entered with the first, and so on, the result would be a canon in the unison. Thus the difference between the crude counterpoint of the rondel and a strict canon in the unison is a mere question of the point at which the composition begins, and a 12th century rondel is simply a canon at the unison begun at the point where all the voices have already entered. There is some reason to believe that one kind of rondeau practised by Adam de la Hale was intended to be sung in the true canonic manner of the modern round; and the wonderful English rota, “Sumer is icumen in,” shows in the upper four parts the true canonic method, and in its two-part pes the method in which the parts began together. In these archaic works the canonic form gives the whole a consistency and stability contrasting oddly with the dismal warfare between nascent harmonic principles and ancient anti-harmonic criteria which hopelessly wrecks them as regards euphony. As soon as harmony became established on a true artistic basis, the unaccompanied round took the position of a trivial but refined art-form, with hardly more expressive possibilities than the triolet in poetry, a form to which its brevity and lightness renders it fairly comparable. Orlando di Lasso’s Célébrons sans cesse is a beautiful example of the 16th century round, which was at that time little cultivated by serious musicians. In more modern times the possibilities of the round in its purest form have enormously increased; and with the aid of elaborate instrumental accompaniments it plays an important feature in such portions of classical operatic ensemble as can with dramatic propriety be devoted to expressions of feeling uninterrupted by dramatic action. In the modern round the first voice can execute a long and complete melody before the second voice joins in. Even if this melody be not instrumentally accompanied, it will imply a certain harmony, or at all events arouse curiosity as to what the harmony is to be. And the sequel may shed a new light upon the harmony, and thus by degrees the whole character of the melody may be transformed. The power of the modern round for humorous and subtle, or even profound, expression was first fully revealed by Mozart, whose astounding unaccompanied canons would be better known if he had not unfortunately set many of them to extemporized texts unfit for publication. The round or the catch (which is simply a specially jocose round) is a favourite English art-form, and the English specimens of it are probably more numerous and uniformly successful than those of any other nation. Still they cannot honestly be said to realize the full possibilities of the form. It is so easy to write a good piece of free and fairly contrapuntal harmony in three or more parts, and so arrange it that it remains correct when the parts are brought in one by one, that very few composers seem to have realized that any further artistic device was possible within such limits. Even Cherubini gives hardly more than a valuable hint that the round may be more than a jeu d’esprit; and, unless he be an adequate exception, the unaccompanied rounds of Mozart and Brahms stand alone as works that raise the round to the dignity of a serious art-form. With the addition of an orchestral accompaniment the round obviously becomes a larger thing; and when we consider such specimens as that in the finale of Mozart’s Cosi fan tutte, the quartet in the last act of Cherubim’s Faniska, the wonderfully subtle quartet “Mir ist so wunderbar” in Beethoven’s Fidelio, and the very beautiful numbers in Schubert’s masses where Schubert finds expression for his genuine contrapuntal feeling without incurring the risks resulting from his lack of training in fugue-form, we find that the length of the initial melody, the growing variety of the orchestral accompaniment and the finality and climax of the free coda, combine to give the whole a character closely analogous to that of a set of contrapuntal variations, such as the slow movement of Haydn’s “Emperor” string quartet, or the opening of the finale of Beethoven’s 9th Symphony. Berlioz is fond of beginning his largest movements like a kind of round; e.g. his Dies Irae, and Scène aux Champs.

A moment’s reflection will show that three conditions are necessary to make a canon into a round. First, the voices must imitate each other in the unison; secondly, they must enter at equal intervals of time; and thirdly, the whole melodic material must be as many times longer than the interval of time as the number of voices; otherwise, when the last voice has finished the first phrase, the first voice will not be ready to return to the beginning. Strict canon is, however, possible under innumerable other conditions, and even a round is possible with some of the voices at the interval of an octave, as is of course inevitable in writing for unequal voices. And in a round for unequal voices there is obviously a new means of effect in the fact that, as the melody rotates, its different parts change their pitch in relation to each other. The art by which this is possible without incorrectness is that of double, triple and multiple counterpoint (see [Counterpoint]). Its difficulty is 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.