CONTRAPUNTAL FORMS, in Music. The forms of music may be considered in two aspects, the texture of the music from moment to moment, and the shape of the musical design as a whole. Historically the texture of music became definitely organized long before the shape could be determined by any but external or mechanical conceptions. The laws of musical texture were known as the laws of "counterpoint" (see Counterpoint and Harmony). The "contrapuntal" forms, then, are historically the earliest and aesthetically the simplest in music; the simplest, that is to say, in principle, but not necessarily the easiest to appreciate or to execute. Their simplicity is like that of mathematics, the simplicity of the elements involved; but the intricacy of their details and the subtlety of their expression may easily pass the limits of popularity, while art of a much more complex nature may masquerade in popular guise; just as mathematical science is seldom popularized, while biology masquerades in infant schools as "natural history." Here, however, the resemblance between counterpoint and mathematics ends, for the simplicity of genuine contrapuntal style is a simplicity of emotion as well as of principle; and if the style has a popular reputation of being severe and abstruse, this is largely because the popular conception of emotion is conventional and dependent upon an excessive amount of external nervous stimulus.
1. Canonic Forms and Devices.
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 1st 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.  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.
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 naturally took up a new theme without troubling to design it for contrapuntal combination with the opening; and the form resulting from this treatment of words was faithfully reproduced in the instrumental ricercari of the time. Occasionally, however, breadth of treatment and terseness of design combined to produce a short movement on one idea indistinguishable in form from a fughetta of Bach; as in the Kyrie of Palestrina's Mass, Salve Regina.
But in Bach's art the preservation of a main theme is more necessary the longer the composition; and Bach has an incalculable number of methods of giving his fugues a symmetry of form and balance of climax so subtle and perfect that we are apt to forget that the only technical rules of a fugue are those which refer to its texture. In the Kunst der Fuge Bach has shown with the utmost clearness how in his opinion the various types of fugue may be classified. That extraordinary work is a series of fugues, all on the same subject. The earlier fugues show how an artistic design may be made by simply passing the subject from one voice to another in orderly succession (in the first example without any change of key except from tonic to dominant). The next stage of organization is that in which the subject is combined with inversions, augmentations and diminutions of itself. Fugues of this kind can be conveniently called stretto-fugues.  The third and highest stage is that in which the fugue combines its subject with contrasted counter-subjects, and thus depends upon the resources of double, triple and quadruple counterpoint. But of the art by which the episodes are contrasted, connected climaxes attained, and keys and subtle rhythmic proportions so balanced as to give the true fugue-forms a beauty and stability second only to those of the true sonata forms, Bach's classification gives us no direct hint. A comparison of the fugues in the Kunst der Fuge with those elsewhere in his works reveals a necessary relation between the nature of the fugue-subject and the type of fugue. In Kunst der Fuge Bach has obvious didactic reasons for taking the same subject throughout; and, as he wishes to show the extremes of technical possibility, that subject must necessarily be plastic rather than characteristic. Elsewhere Bach prefers very lively or highly characteristic themes as subjects for the simplest kind of instrumental fugue. On the other hand, there comes a point when the mechanical strictness of treatment crowds out the proper development of musical ideas; and the 7th fugue (which is one solid mass of stretto in augmentation, diminution and inversion) and the 12th and 13th (which are invertible bodily) are academic exercises outside the range of free artistic work. On the other hand, the less complicated stretto-fugues and the fugues in double and triple counterpoint are perfect works of art and as beautiful as any that Bach wrote without didactic purpose.
Fugue is still, as in the 16th century, a texture rather than a form; and the rules given in most technical treatises for its general shape are based, not on the practice of the great composers, but on the necessities of beginners, whom it would be as absurd to ask to write a fugue without giving them a form as to ask a schoolboy to write so many pages of Latin verses without a subject. But this standard form, whatever its merits may be in combining progressive technique with musical sense, has no connexion with the true classical types of fugue, though it played an interesting part in the renaissance of polyphony during the growth of the sonata style, and even gave rise to valuable works of art (e.g. the fugues in Haydn's quartets, op. 20). One of its rules was that every fugue should have a stretto. This rule, like most of the others, is absolutely without classical warrant; for in Bach the ideas of stretto and of counter-subject almost exclude one another except in the very largest fugues, such as the 22nd in the second book of the Forty-eight; while Handel's fugue-writing is a masterly method, adopted as occasion requires, and with a lordly disdain for recognized devices. But the pedagogic rule proved to be not without artistic point in more modern music; for fugue became, since the rise of the sonata-form, for some generations a contrast with the normal means of expression instead of being itself normal. And while this was so, there was considerable point in using every possible means to enhance the rhetorical force of its peculiar devices, as is shown by the astonishing modern fugues in Beethoven's last works. Nowadays, however, polyphony is universally recognized as a permanent type of musical texture, and there is no longer any reason why if it crystallizes into the fugue-form at all it should not adopt the classical rather than the pedagogic type.
It is still an unsatisfied wish of accurate musicians that the term fugue should be used to imply rather a certain type of polyphonic texture than the whole form of a composition. At present one runs the risk of grotesque misconceptions when one quite rightly describes as "written in fugue" such passages as the first subjects in Mozart's Zauberflöte overture, the andantes of Beethoven's first symphony and C minor quartet, or the first and second subjects of the finale of Mozart's G major quartet, the second subject of the finale of his D major quintet, and the exposition of quintuple counterpoint in the coda of the finale of the Jupiter Symphony, and countless other passages in the developments and main subjects of classical and modern works in sonata form. The ordinary use of the term implies an adherence to a definite set of rules quite incompatible with the sonata style, and therefore inapplicable to these passages, and at the same time equally devoid of real connexion with the idea of fugue as understood by the great masters of the 16th century who matured it. In the musical articles in this Encyclopaedia we shall therefore speak of writing "in fugue" as we would speak of a poet writing in verse, rather than weaken our descriptions by the orthodox epithet of "loose fugato."
3. Counterpoint on a Canto Fermo.
The early practice of building polyphonic designs on a voice-part confined to a given plain-song or popular melody furnishes the origin for every contrapuntal principle that is not canonic, and soon develops into a canonic principle in itself. When the canto fermo is in notes of equal length and is sung without intermission, it is of course as rigid a mechanical device as an acrostic. Yet it may have artistic value in furnishing a steady rhythm in contrast to suitable free motion in the other parts. When it is in the bass, as in Orlando di Lasso's six-part Regina Coeli, it is apt to cramp the harmony; but when it is in the tenor (its normal place in 16th-century music), or any other part, it determines little but the length of the composition. It may or may not appeal to the ear; if not, it at least does no harm, for its restricting influence on the harmony is small if its pace is slower than that of its surroundings. If, on the other hand, its melody is characteristic, or can be enforced by repetition, it may become a powerful means of effect, as in the splendid close of Fayrfax's Mass Albanus quoted by Professor Wooldridge on page 320 in the second volume of the Oxford History of Music. Here the tenor part ought to be sung by a body of voices that can be distinctly heard through the glowing superincumbent harmony; and then the effect of its five steps of sequence in a melodious figure of nine semibreves will reveal itself as the principle which gives the passage consistency of drift and finality of climax.
When the rhythm of the canto fermo is not uniform, or when pauses intervene between its phrases, whether these are different figures or repetitions of one figure in different parts of the scale, the device passes into the region of free art, and an early example of its simplest use is described in the article MUSIC as it appears in Josquin's wonderful Miserere. Orlando di Lasso's work is full of instances of it, one of the most dramatic of which is the motet Fremuit spiritu Jesus (Magnum Opus No. 553 ), in which, while the other voices sing the scripture narrative of the death and raising of Lazarus, the tenor is heard singing to an admirably appropriate theme the words, Lazare, veni foras. When the end of the narrative is reached, these words fall into their place and are of course taken up in a magnificent climax by the whole chorus.
The free use of phrases of canto fermo in contrapuntal texture, whether confined to one part or taken up in fugue by all, constitutes the whole fabric of 16th-century music; except where polyphonic device is dispensed with altogether, as in Palestrina's two settings of the Stabat Mater, his Litanies, and all of his later Lamentations except the initials. A 16th-century mass, when it is not derived in this way from those secular melodies to which the council of Trent objected, is so closely connected with Gregorian tones, or at least with the themes of some motet appropriate to the holy day for which it was written, that in a Roman Catholic cathedral service the polyphonic music of the best period co-operates with the Gregorian intonations to produce a consistent musical whole with a thematic coherence almost suggestive of Wagnerian Leitmotif. In later times the Protestant music of Germany attained a similar consistency, under more complicated musical conditions, by the use of chorale-tunes; and in Bach's hands the fugal and other treatment of chorale-melody is one of the most varied and expressive of artistic resources. It seems to be less generally known that the chorale plays a considerable though not systematic part in Handel's English works. The passage "the kingdoms of the world" in the "Hallelujah Chorus" (down to "and He shall live for ever and ever") is a magnificent development of the second part of the chorale Wachet auf ("Christians wake, a voice is calling"); and it would be easy to trace a German or Roman origin for many of the solemn phrases in long notes which in Handel's choruses so often accompany quicker themes.
From the use of an old canto fermo to the invention of an original one is obviously a small step; and as there is no limit to the possibilities of varying the canto fermo, both in the part which most emphatically propounds it and in the imitating or contrasted parts, so there is no line of demarcation between the free development of counterpoint on a canto fermo and the general art of combining melodies which gives harmony its deepest expression and musical texture its liveliest action. Nor is there any such line to separate polyphonic from non-polyphonic methods of accompanying melody; and Bach's Orgelbüchlein and Brahms's posthumous organ-chorales show every conceivable gradation between plain harmony or arpeggio and the most complex canon.
In Wagnerian polyphony canonic devices are rare except in such simple moments of anticipation or of communion with nature as we have before the rise of the curtain in the Rheingold and at the daybreak in the second act of the Götterdämmerung. On the other hand, the art of combining contrasted themes crowds almost every other kind of musical texture (except tremolos and similar simple means of emotional expression) into the background, and is itself so transformed by new harmonic resources, many of which are Wagner's own discovery, that it may almost be said to constitute a new form of art. The influence of this upon instrumental music is as yet helpful only in those new forms which are breaking away from the limits of the sonata style; and it is impossible at present to sift the essential from the unessential in that marvellous compound of canonic device, Wagnerian harmony, original technique and total disregard of every known principle of musical grammar, which renders the work of Richard Strauss the most remarkable musical phenomenon of recent years. All that is certain is that the two elements in which the music of the future will finally place its main organizing principles are not those of instrumentation and external expression, on which popular interest and controversy are at present centred, but rhythmic flow and counterpoint. These have always been the elements which suffered from neglect or anarchy in earlier transition-periods, and they have always been the elements that gave rationality to the new art to which the transitions led.
(D. F. T.)
 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.
 For technical terms see articles Counterpoint and Fugue.
Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)