A Dictionary of Music and Musicians/Variations

by Hubert Parry

VARIATIONS. In the days when modern music was struggling in the earliest stages of its development, when most of the forms of art which are familiar in the present day were either unknown or in their crudest state of infancy, composers who aimed at making works of any size laboured under great disadvantages. They were as fully conscious as composers are now of the necessity of some system of structure or principle of art to unify the whole of each work, and to carry on the interest from moment to moment; but as they had not discovered any form which could extend for more than a few phrases or periods, their only means of making the music last any length of time was to repeat, and to disguise the repetition and give it fresh interest by artistic devices.

In choral music they took some old familiar piece of plainsong, or a good secular tune, put it into very long notes, and gave it to one of the voices to sing; and then made something ostensibly new upon this basis by winding round it ingenious and elaborate counterpoint for all the other voices. The movement lasted as long as the tune served, and for other movements if the work happened to be a mass, or work necessarily divided into separate pieces they either took a new tune and treated it in the same way, or repeated the former one, and sometimes sang it backwards for variety, with new turns of counterpoint each time.

Similarly, in instrumental music, as soon as their art was enough advanced to produce good, clear, and complete dance-tunes and songs, they extended the musical performance by repeating the tunes, with such other touches of fresh interest as could be obtained by grace-notes and ornamental passages, and runs inserted in the bass or other parts. In this way the attention of composers came to be very much drawn to the art of varying a given theme, and presenting it in new lights; and they carried it to a remarkably advanced stage when scarcely any of the other modern forms of art had passed the period of incubation.

In choral music the art was limited to the practice of using a given tune as the central thread to hold the whole work together; and it almost died out when maturer principles of structure were discovered; but in instrumental music it has held its own ever since, and not only plays a part of great importance in the most modern sonatas and symphonies, but has given rise to a special form which has been a great favourite with all the greatest masters, and is known by the name of Variations.

The early masters had different ways of applying the device. One which appears to have been a favourite, was to write only one variation at a time, and to extend the piece by joining a fresh theme to the end of each variation, so that a series of themes and single variations alternated throughout. In order to make the members of the series hang together, the variations to the different themes were often made in similar style; while the successive themes supplied some little contrast by bringing different successions of harmony into prominence. There are several pieces constructed in this fashion by Byrd and Bull and Orlando Gibbons, who were among the earliest composers of instrumental music in modern Europe; and they consist chiefly of sets of Pavans, or Galiards, or neat little tunes like Bull's 'Jewel.' Many are interesting for ingenuity and originality of character, but the form in this shape never rose to any high pitch of artistic excellence. Another form, which will be noticed more fully later on, was to repeat incessantly a short clause of bass progression, with new figures and new turns of counterpoint over it each time; and another, more closely allied to the modern order of Variations, was a piece constructed upon a theme like Sellenger's Round, which did not come to a complete end, but stopped on the Dominant harmony and so returned upon itself; by which means a continuous flow of successive versions of the theme was obtained, ending with a Coda.

These early masters also produced examples of a far more mature form of regular theme and variations, not unlike thoroughly modern works of the kind; in which they showed at once a very wide comprehension of the various principles upon which variations can be constructed, and an excellent perception of the more difficult art of varying the styles of the respective members of the series so as to make them set off one another, as well as serve towards the balance and proportion of the whole set.

Two of the works which illustrate best the different sides of the question at this early date are Byrd's variations to the secular tune known as 'The Carman's Whistle' and Bull's set called 'Les Buffons.' These two represent respectively two of the most important principles upon which variations are made, since the first series is almost entirely melodic, and the second structural; that is, each variation in the first series is connected with the theme mainly through the melody, whereas in the second the succession of the harmonies is the chief bond of connection; both themes are well adapted to illustrate these principles, the tune of the first having plenty of definite character, and the harmonies of the second being planned on such broad and simple lines as are most likely to remain in the memory. Byrd's series consists of eight variations, in all of which, except the last, the melody is brought very prominently forward; a different character being given to each variation by the figures introduced to accompany it. The way in which the various styles succeed one another is very happy. The first is smooth and full, and the second rugged and forcible; the third quiet and plaintive, and the fourth lively and rhythmic; and so on in similar alternation to the last, which is appropriately made massive and full, and is the only one which is based exclusively on the harmonies, and ignores the tune. The two following examples give the opening bars of the fourth and sixth variations, and illustrate the style and way of applying the characteristic figures very happily. The upper part is the tune of the theme.

Byrd's variations are remarkable not only for their intrinsic qualities, but also as rare examples of melodic treatment in those early days, when composers were more inclined to notice the bass than the tune. Bull was by no means so great a genius as Byrd, but he had a vein of melody, a good deal of vivacity, and a considerable sense of effect. In 'Les Buffons' the former gift is scarcely brought into play, but the two latter are very serviceable. The theme is the simplest possible succession of chords, as follows:—

Upon this fourteen variations are constructed, which are varied and contrasted with one another throughout, upon the same general principles of succession as in Byrd's series. Many of them are merely made of scale passages, or rather commonplace figures; but some are well devised, and the two following are interesting as examples of the freedom with which composers had learnt to treat structural variations even in such early days. Ex. 4 is the beginning of the second variation, and Ex. 5 is the thirteenth, which flows out of the one preceding it.

In the time which followed Byrd and Bull the best energies of composers were chiefly directed to the development of such instrumental forms as the Suite and the Canzona, and the earlier kinds of Sonata; and Sets of Variations were not so common. There are a few examples among Frescobaldi's compositions; as the 'Aria detta Balletto' in the second book of Toccatas, Canzonas, etc., which is curious on account of the way the variations are put into different times; but his works of the kind are on the whole neither so interesting nor so satisfactory as Byrd's. It is also common to meet with an occasional variation on one or more of the regular dance-movements in the Suites; and in that position they were commonly called Doubles. There is a curious and unusual experiment in a Suite of Kuhnau's in E minor, in which the Courante in 6-4 time is a complete variation of the Allemande in common time that precedes it. But the art of varying a theme of some sort was cultivated to a greater extent about this time under other guises. In Germany composers were fond of harmonising their Chorales in all sorts of ingenious ways, such as are found later in perfection in Bach's Cantatas and Passions; they also used the Chorales as a kind of Canto fermo upon which they based elaborate movements for the organ, full of ingenious and effective figures and various devices of counterpoint; and not a little of the great development of organ-playing, which culminated in J. S. Bach, was carried on by the cultivation of this form of art. Another form which was more obviously allied to the sets of variations, and indeed can in some cases hardly be distinguished from them, was the ground-bass or basso ostinato, which was a very favourite form of art all over Europe during the greater part of the 17th century. The principle of following the bass of the theme is indeed constantly made use of in variations, and in theory the only difference between the two forms is that in a ground-bass the bass passage, which is repeated over and over again, is the whole bond of connection which joins the series together; while in variations the bass may change entirely so long as the theme is recognisable either by means of the melody or the succession of the harmonies. But in practice, though there are many examples in which a good clear bass figure is made to persist with obstinate regularity in this form, it often gave place to the succession of the harmonies, or was itself so varied as to become scarcely recognisable. For instance, a so-called Ground by Blow in E minor, with twenty-eight divisions, begins with a section that is much more like a theme for variations; and though the bass moves in good steps, it has no very decided figure whatever. A comparison of the first half of the so-called ground with the corresponding part of the bass of the twentieth division will show that the view musicians then took of the repetitions was at least a liberal one:—

In this case the outline of the bass as defined by the successive steps downwards is pretty well maintained, but in a few other divisions which are more elaborately constructed, not only is the bass altered, but even harmonies which do not strictly correspond to the originals are introduced. Such treatment clearly destroys the individuality of the form of art, and makes the work to all intents a theme with variations, under limitations. The real type of movement constructed on a ground-bass has a decided character of its own, as the obstinate reiteration of a good figure is necessarily a striking bond of connection throughout the piece; and if the figures built upon it are well varied it can be made very amusing. In Purcell's use of this form, which he was evidently fond of, the type is kept much purer, and the divisions on the ground are really what they pretend to be. A quotation of the bass of a ground in one of his Suites will illustrate better than any description the difference between the real thing and a hybrid like Blow's:—

But even so genuine a specimen as Purcell's is closely allied to a theme with variations; and at a time when the form was so popular that it was not only a favourite with composers, but the constant resource of performers with any talent for extemporising to show off their skill in two directions at once, it seems very likely that the more elastic but less pure form adopted by Blow and others should have been easily allowed to pass in the crowd of experiments; and thus composers were constantly developing the form of 'Theme and Variations' under another name.

A celebrated example which bears upon this question is the twelfth and last Sonata of Corelli's Opera Quinta, which is called 'La Follia.' This is sometimes described as a Theme and twenty-two variations, and sometimes as Divisions on a ground. The bass of the theme was well known in those days as Farinelli's Ground, from the inventor, and was commonly used by musicians and composers, as for instance by Vivaldi. Hawkins speaks of it as 'the favourite air known in England as Farinelli's Ground,' showing a confusion in his mind even as to the difference between a 'ground' and a tune. In Corelli's work the bass is not repeated at all regularly, so it is to all intents and purposes a series of free variations. These are most of them very simple, being different forms of arpeggios on the harmonies of the theme, but they are well devised so as to contrast and set off one another, and are effective in their way for the violin. The tempos vary from Adagio and Andante to Allegro and Vivace, and the time-signatures also, as 3-4, 4-4, and 3-8. Corelli evidently took an easy view of variations, for both in this set and in the Chaconne in the twelfth Sonata of op. 2, the harmonies are not at all strictly followed, and occasionally have next to nothing to do with the theme for several bars together; and this appears to have been rather a characteristic of the Italian style of writing such things. The treatment of the form in this instance, and in many others of nearly the same period (as those by Blow, and many by Locatelli and others a little later), together with the lax way in which Hawkins speaks of the subject, tend to the conclusion that this popular form of Ground-bass movement was gradually becoming mixed up with the form of Theme-and-Variations, and trenching on its province. Even the length of the bass in the Follia and other examples is in favour of this view, because the effect of the ground-bass is lost when it extends beyond very moderate limits. The best examples are after such a concise fashion as the bass quoted from Purcell, and such superb specimens as the 'Crucifixus' in Bach's Mass, his Passacaglia in C minor, and similar works by Buxtehude for the organ. If the ground-bass has several clauses, as in Corelli's Follia or Blow's piece (Ex. 6), it loses its effect and has to be treated after the manner of a theme; and the adoption of long periods led composers to that treatment, at the same time that the habit of looking at their subject in the direction of the bass rather than the upper part, influenced their manner of dealing with variations.

This condition of things throws an interesting light upon J. S. Bach's thirty Variations on an Aria in G major for a harpsichord with two rows of keys, which is the first very important work of its kind, and still among the most remarkable in existence, though it is never played in public in consequence of the difficulty of giving due effect on one row of keys to the rapid crossing passages which are written for two. The Aria which serves for theme is not after the manner of a modern aria, but is a dance movement like those in the Suites. It is in fact a Sarabande of the expressive and elaborate kind familiar among Bach's works; it has plenty of fine melody but no catching tune, and nothing to invite melodic variations of the modern kind. On the other hand, it is constructed of very broad and simple successions of harmony, with the bass moving a step of some sort in almost every bar; and upon this motion of bass or harmonies the whole series of variations is really constructed. It is therefore actually almost as much of a ground-bass movement as Corelli's Follia, or Blow's example. The actual bass figure is not repeated, but either the steps by which it moves or the regular changes of the harmony are always represented in some way under the elaborate texture of the figures. In fact, what Bach does is to take out the harmonic framework upon which the Aria is built, and use it to build thirty other little movements upon. The way in which these are developed from the original will be best understood by a comparison of the opening bars of some of the variations with the corresponding portion of the bass of the theme.

The following is the bass of the first eight bars of the Aria, with figures to represent the principal harmonies:—

In a good many variations, such as the 1st, 2nd, 4th, 12th, and 22nd, these steps are very clearly maintained. The bass figure of the 2nd variation will serve to illustrate this:—

It is very rare however that the same positions of the chords are rigidly adhered to throughout. All positions are held to be interchangeable. This would be less possible in dealing with a modern theme with weak or irregular motions of harmony; but where the changes are so strict and clear, the successions are traceable even through a looser treatment of the original. An example which will illustrate Bach's method of interchanging positions of the same chords, and the ingenuity with which he builds one form upon another, is the opening of the tenth variation, which is a complete little four-part Fughetta:—

In bar (b) the first position of the chord of the Dominant is implied instead of its first inversion; in bar (c) there is a similar interchange, and in bars (d) and (g) the principal emphasis of the bar falls upon a first inversion instead of a first position of the same chord.

In other variations he goes much further still. In the ninth the strict succession of chords is frequently altered, but in such a way that the character and general contour of the harmonic succession is still to be felt in the background. For instance, in the passage corresponding to bars (e) and (f) the harmonies of E minor and G are forced in in the place of those of G and A. Then the harmony of C and A, which really represents bar (f), is driven into the bar corresponding with (g); and in order to make the final chord of the cadence answer in position with the original, all that appears of the chord corresponding to bar (g) is the last quaver. The following example will show the nature of the change, beginning at the half-bar corresponding with (d) where the first half close falls, up to the first close in the principal key in bar (h):—

This appears to be rather an extreme instance, but in reality the change is caused by nothing more than the happy idea of turning the passing note in bar (d) in an opposite direction, and so leading to the intrusion of the chord of E; thus causing the chords of G and C, which follow in their proper order, to come one step too late, and forcing the penultimate chord of the cadence into very close quarters. But the form of the cadence is preserved all the same, and so the change turns out to be more in superficial appearance than reality; while the regularity of the succession is still sufficiently obvious to identify the theme.

The manner in which all the variations are written is contrapuntal, and in many cases they are cast in some one or other of the old contrapuntal forms. Every third variation throughout, except the last, is a Canon of some sort, with a free bass which generally follows the outlines of the bass of the theme. These take all the intervals in regular order—a Canon at the unison in the 3rd variation, a Canon at the second in the 6th, and so on up to a Canon at the ninth in the 27th variation, the Canons at the fourth and fifth being complicated by making them in contrary motion. Variation 10 is a complete Fughetta, and Variation 16 an Overture after the French model, managed by making the part which represents the first half of the theme into the Maestoso movement, and the latter part into the fugal one. The last variation is a 'Quodlibet'; that is, a movement in which several bits of familiar tunes are worked in together. The tunes are 'Volkslieder' of a very bright and happy type. It begins with one to the words 'Ich bin so lang nicht bei dir g'west,' on the top of which another, 'Kraut und Ruben haben mich vertrieben,' is introduced; and the fragments of the two, and probably bits of others which are not identified, are mixed up together in amusing but artistic confusion throughout, always following the harmonic succession of the original aria. After the Quodlibet the theme is directed to be played again, so as to make the cycle complete—a plan followed by Beethoven more than once, most notably in the last movement of his Sonata in E, op. 109. Every variation in the series has a perfectly distinct character of its own, and is knit together closely and compactly by the figures used; which vary from the most pointed vivacity to the noblest dignity and calm; and are so distributed as to keep the action always going, and the interest alive at every step; the result of this many-sided technical workmanship being a perfectly mature art-form. In this respect, as in many others, Bach seems to sum up in his own lifetime the labours of several generations, and to arrive at a point of artistic development which the next generation fell far behind; for a height equal to that of his work was not again reached till Beethoven's time. But the aspect of Bach's work is peculiar to himself and his time. The technical side is brought into extreme prominence. This is shown most obviously in the canons and fugues, but it is also shown in the texture of the other variations. Some few are extremely expressive and beautiful, but it was not with the paramount object of making them all so that Bach attacked his problem, for his variations are rather developments of ideas embodied in vigorous and regular rhythmic figures than romantic or dramatic types. Both the ideas and the way of treating them belong to the old contrapuntal school, and that style of variation-writing which is most richly and comprehensively shown in this series of variations, comes to an end with Bach.

He produced several other sets in the same manner, notably the famous Chaconne in the Suite in D for violin solo; but it is not necessary to analyse that work, since the same principles are observed throughout, even to the repetition of the theme at the end to clench it all together. As in the previous case, the basis of the variation is the harmonic framework of the theme; and the melody hardly ever makes its reappearance till its resumption at the end. The bass steps are just as freely dealt with as in the previous case, from which it may be gathered that Bach considered the harmonic structure the chief thing in a Chaconne (which has the reputation of being a movement on a ground-bass) as much as in a regular Theme and variations. He also produced an example of a different kind, in a little set of eight variations on a very beautiful and melodious theme in A minor. In this the harmonic framework is not nearly so noticeable, and the variations are not made to depend upon it so much as in the other cases. Some few of them are constructed on the same principles as the great set of thirty, but more often the melody of the theme plays an unmistakeable part. This may be seen from a comparison of the melody of the 3rd, 4th, and 5th bars of the theme, with the same portion of the third variation.

The influence of the tune is similarly apparent in several other variations, putting a new complexion upon variation-making, in the direction cultivated by the next generation; but the result is neither so vigorous nor so intrinsically valuable as in other works more after Bach's usual manner, though historically interesting as an experiment in a line which Bach generally thought fit to let alone.

Handel's way of treating variations was very different from Bach's, and more like the methods of the Italian school, as illustrated by Corelli. In most cases, indeed, he regarded the matter from the same point of view as Bach, since he looked upon the harmonic framework as the principal thing to follow; but he reduced the interest of his representation of that framework in new figures to a minimum. Where Bach used ingenious and rhythmical figures, and worked them with fascinating clearness and consistency, Handel was content to use mere empty arpeggios in different forms. In many of his sets of Variations, and other works of the same kind, he makes the effect depend chiefly upon the way in which the quickness of the notes varies, getting faster and faster up to the brilliant but empty conclusion. The set which has most musical interest is the 'Harmonious Blacksmith' in the Suite in E; and in this the usual characteristic is shown, since the variations begin with semiquavers, go on to triplet semiquavers, and end with scale passages of demisemiquavers. The extraordinary popularity of the work is probably owing chiefly to the beauty of the theme, partly also to the happy way in which the style of the variations hits the mean between the elaborate artistic interest of such works as Bach's and the emptiness of simple arpeggios, and partly to the fact that their very simplicity shows to advantage the principles upon which a succession of variations can be knit together into an effective piece, by giving all the members of the series some relative bearing upon each other. In this set the connection and function of each is so thoroughly obvious that the most ordinary musical intelligence can grasp it, and it is to such grounds of effect that Handel trusted in making all his sets, whether in such an example as the Passacaglia in the G minor Suite or the Chaconne with sixty variations. Only in very few cases does he even appear to attempt to make the separate numbers of the series interesting or musically characteristic, and yet the series as a whole is almost always effective. He is more inclined to allow the tune of his theme to serve as a basis of effect than Bach was. In the variations in the Suite in D it is very prominent, and in the earlier variations of the 'Harmonious Blacksmith' is clearly suggested; and in this way he illustrates the earlier stage of the tendency which came to predominate in the next generation. The following are types of the figures used by Handel in more than one set:—

Another composer showed this tendency to follow the tune even more markedly. This was Rameau, who was born two years before Handel and Bach, but was brought more strongly under the rising influences of the early Sonata period, through his connection with the French operatic school, and the French instrumental school, of which Couperin was the happiest representative. These French composers were almost the first of any ability in Europe to give their attention unreservedly to tunes, and to make tune, and character of a tuneful kind, the object of their ambition. Rameau produced a number of charming tuneful pieces of a harmonic cast, and naturally treated variations also from the point of view of tune, studying to bring the tune forward, and to make it, rather than the harmonic successions, the basis of his variations. When operatic influences came into play and influenced the instrumental music of German composers, and when the traditions of the Protestant school gave place to those of the southern and Catholic Germans, the same result followed.

Other circumstances also affected the form unfavourably. The cause of the falling off in vigour, depth of feeling, and technical resource from the standard of Handel and Bach, is obvious enough in other departments; since men were thrown back as they had been after Palestrina's time, through having to cope with new forms of art. In the case of variations—by this time an old and established form—the cause of such falling off is not easy to see; but in reality variations were just as amenable to unfavourable influences as the rest of instrumental music, since composers began to try to treat them in the same style as their sonata movements. They dropped the contrapuntal methods, with the opportunities afforded by them, and as they had not yet developed the art of expressing effective musical ideas in the modern style apart from the regular sonata form, their works of the kind seem, by the side of Bach's, to be sadly lacking in interest. Moreover, the object of writing them was changing. Bach wrote up to the level of his own ideas of art, without thinking what would please the ordinary public; but the composers of the middle of the 18th century wrote their clavier music chiefly for the use or pleasure of average amateurs, on whom first-rate art would be thrown away; and aimed at nothing more than respectable workmanship and easy agreeable tunefulness. The public were losing their interest in the rich counterpoint and massive nobility of style of the older school, and were setting their affections more and more on tune and simply intelligible form; and composers were easily led in the same direction. The consequences were happy enough in the end, but in the earlier stages of the new style variation-making appears to have suffered; and it only regained its position in rare cases, when composers of exceptional genius returned, in spite of the tendency of their time, to the method of building a fair proportion of their variations on the old principles, and found in the harmonic framework equal opportunities to those afforded by the tunes.

How strongly Haydn and Mozart were drawn in the prevailing direction is shown by the number of cases in which they took simple and popular tunes as themes, and by the preponderance of the melodic element in their variations. This is even more noticeable in Mozart than in Haydn, who took on the whole a more serious and original view of the form. True, he did not write nearly so many sets as his younger contemporary, and several that he did write are of the very slightest and most elementary kind—witness that which forms the last movement of the Clavier Sonata in E♭, that on a tune in 'Tempo di Minuetto' in a sonata in A, and that in a sonata for clavier and violin in C. In these cases he is obviously not exerting himself at all, but merely treating the matter lightly and easily. But when he set about his work seriously, it has far more variety, interest, and many-sided ingenuity than Mozart's. This is the case with several of the sets in the string quartets, and with the remarkable one for clavier alone in F minor, and the beautiful slow movement in the Sonata for Clavier and Violin in F. The things most noticeable in these are the remarkable freedom with which he treats his theme, and the original means adopted to combine the sets into complete and coherent wholes. Probably no one except Beethoven, Schumann, and Brahms took a freer view of the limits of fair variation; the less essential chords and root harmonies of the theme are frequently changed, even without the melody being preserved to make up for the deviation, and in certain cases whole passages appear to be entirely altered, and to have little if any connection with the theme beyond observance of the length of its prominent periods, and the fact that the final cadences come in the right forms and places. This occurs most naturally in a minor variation of a major theme, or vice versa, where a passage in the relative major is made to correspond to a passage in the dominant key, and the succession of chords is necessarily altered to a different course to make the passage flow back to the principal key at the same place, both in variation and theme. There is an extremely interesting example of such changes in the slow movement of the Quartet in E♭, No. 22 Trautwein. The theme is in B♭, and the first variation in B♭ minor. The second half of the theme begins in F, and has a whole period of eight bars, closing in that key, before going back to B♭. The corresponding part of the first variation begins with the same notes transferred from first violin to cello, and has the same kind of motion, and similar free contrapuntal imitation; but it proceeds by a chain of closely interlaced modulations through E♭ minor and A♭, and closes in D♭. And not only that, but the portion which corresponds to the resumption of the principal idea begins in the original key in D♭, and only gets home to the principal key for the last phrase of four bars, in which the subject again appears. So that for eleven bars the variation is only connected with the theme by the fact that the successive progressions are analogous in major and minor modes, and by a slight similarity in the character of the music. This was a very important position to take up in variation-writing, and by such action Haydn fully established a much broader and freer principle of representing the theme than had been done before. The following examples are respectively the first eight bars of the second half of the theme, and the corresponding portion of the 1st variation:—

The other noticeable feature of Haydn's treatment of the variation-form is illustrated very happily by the 'Andante con Variazioni' in F minor for clavier solo, and by the movement in the F major sonata for clavier and violin; both showing how strongly he regarded the form as one to be unified in some way or other beyond the mere connection based on identity of structure or tune which is common to all the members of the series. The first of these is really a set of variations on two themes; since the principal theme in the minor is followed by a slighter one contrasting with it, in the major. The variations on these two themes alternate throughout, and end with a repetition of the principal theme in its original form, passing into an elaborate coda full of allusions to its principal figures. Thus there is a double alternation of modes and of styles throughout binding the members together; and the free development of the features of the theme in the coda gives all the weight and interest necessary to clench the work at the end. The slow movement for clavier and violin is somewhat different in system, but aims at the same object. After the theme comes an episode, springing out of a figure in the cadence of the theme, and modulating to the dominant and back; then comes the first variation in full, followed by another episode modulating to B♭, with plenty of development of characteristic figures of the theme, coming back (after about the same length as the first episode) to a pause on the dominant chord of the principal key, and followed by another variation with demisemiquaver ornamental passages for the pianoforte. This variation deviates a little at the end, and pauses on the dominant chord again; and then the beautiful and serene theme is given out once more in its original form. This is therefore an ingenious kind of Rondo in the form of variations. The short contrasting episodes are quite in Rondo-form, the only difference being that the two middle repetitions of the theme are made unusually interesting by appearing in a fresh guise. One more point worth noting about Haydn's works of this kind, is that some of his themes are so rich and complex. In a few of the sets in the quartets the theme is not so much a tune as a network of figures combined in a regular harmonic scheme—see Ex. 17; and the same holds true of the 'Andante con Variazioni' mentioned above, which is long, and full of the most various and remarkable figures. It may be said finally that there is no branch of composition in which Haydn was richer and more truly polyphonic than in his best sets of variations.

Mozart, on the other hand, represents the extreme of the melodic form of variations. If in many of Haydn's slighter examples this tendency was perceptible, in Mozart it comes to a head. The variations which he makes purely out of ornamental versions of the tune of the theme, are at least four times as many as his harmonic and more seriously conceived ones. As has been said before, Mozart wrote far more sets than Haydn, and many of them were probably pièces d'occasion—trifles upon which there was neither time nor need to spend much thought. It is scarcely too much to say moreover that variation-writing was not Mozart's best province. Two of his greatest gifts, the power of moulding his form with the most refined and perfect accuracy, and spontaneous melody, have here no full opportunity. The themes which necessarily decide ths form are in many cases not his own, and, except in rare instances, it does not seem to have entered into his head to try to make new and beautiful melodies on the foundation of their harmonic framework. He seems rather to have aimed at making variations which would be easily recognisable by moderately-gifted amateurs; and it must be allowed that it takes a good deal of musical intelligence to see the connection between a theme and a variation which is well enough conceived to bear frequent hearing. It is also certain that the finest variations have been produced by scarcely any but composers of a very deep and intellectual organisation, like Beethoven, Bach, and Brahms. Mozart was gifted with the most perfect and refined musical organisation ever known; but he was not naturally a man of deep feeling or intellectuality, and the result is that his variation-building is neither impressive nor genuinely interesting. Its chief merits are delicate manipulation, illustrating the last phase of harpsichord-playing as applied to the Viennese type of pianoforte with shallow keys, and he obtains the good balance in each set as a whole without any of Haydn's interesting devices. A certain similarity in the general plan of several of the independent sets suggests that he had a regular scheme for laying out the succession of variations. The earlier ones generally have the tune of the theme very prominent; then come one or two based rather more upon the harmonic framework, so as to prevent the recurrence becoming wearisome; about two-thirds of the way through, if the theme be in the major, there will be a minor variation, and vice versâ; then, in order to give weight to the conclusion and throw it into relief, the last variation but one has a codetta of some sort or an unbarred cadenza, or else there is an unbarred cadenza dividing the last variation from the final coda, which usually takes up clearly the features of the theme. These unbarred cadenzas are a characteristic feature of Mozart's sets of variations, and indicate that he regarded them as show pieces for concerts and such occasions, since they are nothing but pure finger-flourishes to show off the dexterity and neatness of the performer. There are two—one of them a very long one—in the set on Paisiello's 'Salve tu Domine,' another long one in that on Sarti's 'Come un agnello,' a long one in that on 'Lison donnait,' and others of more moderate dimensions in the sets on Gluck's ' Unser dummer Pöbel meint,' Mr. Duport's minuet, 'Je suis Lindor,' and others. In his treatment of the harmonic framework, Mozart is generally more strict than Haydn, but he is by no means tied by any sense of obligation in that respect, and even makes excellent point out of harmonic digression. A most effective example, which contains a principle in a nutshell, is his treatment of the most characteristic phrase of 'Unser dummer Pöbel' in the fourth variation. The phrase is as follows:—

To this he gives a most amusing turn by, as it were, missing the mark by a semitone:—

then he goes on to the end of the half of the variation which contains the passage, and begins it again as if for repeat; and then again overshoots the mark by a semitone:—

There is probably no simpler example of an harmonic inconsistency serving a definite purpose in variations. In a less obvious way there are some in which very happy effect is obtained by going an unexpected way round between one essential point of harmony and another, and in such refinements Mozart is most successful.

When he introduces sets of variations into sonatas and such works as his Clarinet Quintet, he seems to have taken more pains with them; there are proportionately more free and harmonic variations among them; and the element of show illustrated by the unbarred cadenza is not so prominent. There are good examples of variety of treatment and success in balancing the various members of the series in the variations in the fine Sonata in F for violin and pianoforte. True, the basis of the variations is for the most part melodic, but the principle is treated with more solid effect than usual. The same remark applies to the last movement of the PF. Sonata in, written in 1777. This contains some extremely happy examples of the exclusive use of the harmonic principle, as in the 9th variation, in which the vigour and individuality of the figure give the variation all the appearance of an independent piece. Similarly in the nth, Adagio cantabile, and in the last, in which the time is changed from 4-4 to 3-4, the melody is new, and not merely the theme in an ornamental dress.

An excellent use to which Mozart frequently puts variations is that of presenting the subjects of sonata-movements in new lights, or adding to their interest by new turns and ornaments when they reappear a second or third time in the course of the movement. One example is the recurrence of the theme in the 'Rondo en Polonaise' which forms the middle movement in the Sonata in D just referred to. Another is the slow movement of the well-known Sonata in C minor, connected with the Fantasia in the same key.

The cases in which Mozart ventured to give a variation a thoroughly independent character are rare. He seems to have thought it better to keep always in sight of his theme, and though he invented some charming and effective devices which have been used by later composers, as a rule the variations wait upon the theme too subserviently, and the figures are often too simple and familiar to be interesting. The following ('Je suis Lindor') is a fair sample of his way of ornamenting a tune:—

Beethoven's work forms an era in the history of variation-making. It was a branch of art eminently congenial to him; for not only did his instinct for close thematic development make him quick to see various ways of treating details, but his mind was always inclined to present the innermost core of his idea in different forms. This is evinced plainly enough in the way in which he perfects his subjects. His sketch-books show how ideas often came to him in the rough; and how, sometimes by slow degrees, he brought them to that refined and effective form which alone satisfied him. The substratum of the idea is the same from first to last, but it has to undergo many alterations of detail before he finds the best way to say it. Even in this his practice differed extremely from Mozart's, but in the treatment of the actual form of 'Theme and variations' it differed still more. In principle Beethoven did not leave the line taken up by the composers of the Sonata period, but he brought the old and new principles more to an equality than before, and was also very much more daring in presenting his model in entirely new lights. The proportion of purely ornamental variations in his works is small; and examples in which the variations follow the theme very closely are more conspicuous in the early part of his life than later; but even among such comparatively early examples as the first movement of the Sonata in A♭ (op. 26), or the still earlier ones in the Sonata in G (op. 14, no. 2), and the set on Righini's air, there is a fertility of resource and imagination, and in the last case a daring independence of style which far outstrips anything previously done in the same line.

In some sets the old structural principle is once more predominant, as in the well-known 32 in C minor (1806), a set which is as much of a Chaconne as any by Corelli, Bach, or Handel. The theme is in chaconne time, and the strong steps of the bass have the old ground-bass character. It is true he uses the melody of the theme in one or two instances—it would be almost impossible to avoid it at a time when melody counted for so much; but in the large majority the variation turns upon the structural system of the harmonies. Among other points this set is remarkable as a model of coherence; almost every variation makes a perfect complement to the one that precedes it, and sets it off in the same way. In several cases the variations are grouped together, externally as well as in spirit, by treating the same figures in different ways; as happens with the 1st, 2nd and 3rd, with the 7th and 8th, and with the 26th and 27th and others. The 12th marks a new departure in the series, being the first in the major, and the four that follow it are closely connected by being variations upon that variation; while at the same time they form the single block in the major mode in the whole series. Every variation hangs together as closely as those in Bach's great set of thirty by the definite character of the figures used, while the whole resembles that set in the vigour of the style.

In most of the other remarkable sets the principles of treatment are more mixed. For instance, in that on the Ballet Air from the 'Men of Prometheus,' some have a technical interest like Bach's, and some have an advanced ornamental character after the fashion of Mozart's. Among ingenious devices which may fairly be taken as types, the sixth variation is worth noting. The tune is given intact at most available points in its original pitch and original form, but the harmonies are in a different key. A marked feature in the series is that it has an introduction consisting merely of the bass of the theme, and three variations on that are given before the real theme makes its appearance; as happens also in the last movement of the Eroica Symphony, which has the same subject, and some of the same variations, but is not a set of variations in the ordinary sense of the word, since it has various episodes, fugal and otherwise, as in the movement from Haydn's violin and pianoforte sonata described on p. 223.

Others of Beethoven's sets have original external traits; such as the set in F (op. 34), in which all the numbers are in different keys except the theme and the two last variations, the others going in successive steps of minor thirds downwards. The variations themselves are for the most part based on the melody, but a most ingenious variety of character is kept up throughout, partly by changing the time in each successively.

The sets so far alluded to belong to the early or middle period of Beethoven's life, but the finest examples of his work of this kind belong to the last period, such as those in the Quartet in E♭, and the variations 'In modo lidico' in the Quartet in A (op. 132), those in the Trio in B♭, in the Sonatas in E (op. 109), and C minor (op. 111), the two in the 9th Symphony, and the thirty-three on the valse by Diabelli. These last five are the finest and most interesting in existence, and illustrate all manner of ways of using the form. In most cases the treatment of the theme is very free, and is sometimes complicated by the structure of the movement. In the slow movement of the 9th Symphony for instance the theme and variations are interspersed with episodes formed on a different subject and by passages of development based on the principal theme itself. In the choral part the variations are simply based upon the idea, each division corresponding to a variation being really a movement made out of a varied version of the theme adapted in style to the sentiment of the words, and developed without regard to the structure of the periods or plan of the tune.

The sets in the two Sonatas are more strict, and the harmonic and structural variations are in about equal proportions. Their coherence is quite as strong as that of the thirty-two in C minor, or even stronger; while there is infinitely more musical interest in them. In fact, there is a romantic element which colours each set and gives it a special unity. The individual character given to each variation is as strong as possible, and such as to give it an interest of its own beyond its connection with the theme; while it is so managed that whenever the freedom of style has a tendency to obliterate the sense of the theme, a variation soon follows in which the theme is brought forward clearly enough to re-establish the sense of its presence as the idea from which the whole series springs. The set in op. 109 is an excellent model of the most artistic way of doing this, without the device being so obvious as it is in the works of the earlier masters. The first variation has such a marked melody of its own that it necessarily leads the mind away from the theme. But the balance is re-established by the next variation, which is a double one, the repeats of the theme being given with different forms of variations, severally like and unlike the original. The next variation is also double, but in a different sense, the repeats being given in full with different treatment of the same figures. Moreover the balance is still kept up, since the first half is chiefly structural, and the second resumes the melody of the theme more clearly. The next two are more obscure, and therefore serve all the better to enhance the effect of the very clear reappearance of the theme in the final variation. This plan of making double variations was a favourite one with Beethoven, and he uses it again in the fourth variation in op. 111, and in the Diabelli set. In op. 111 it is worth noticing that there is an emotional phase also. The first two variations gradually work up to a vehement climax, culminating in the third. After this outburst there comes a wonderful stillness in the fourth (9–16), like the reaction from a crisis of passion, and this stillness is maintained throughout, notwithstanding the two very different manners of the double variation. Then there is a codetta and a passage wandering through mazes of curious short transitions, constantly hinting at figures of the theme; out of which the theme itself emerges at last, sailing with wind and tide in perfect fruition of its freedom; the last variation of all seems to float away into the air as the tune sings through the haze of shakes and rapid light passages that spin round it, and the whole ends in quiet repose. In such a sense Beethoven gave to his variations a dramatic or emotional texture, which may be, by those who understand it, felt to be true of the innermost workings of their emotions, but can hardly be explained in words.

Technically the most remarkable set of all is that of thirty-three on the Diabelli valse. In this appear many traits recalling those in Bach's set of thirty. For instance, there is a fugetta, cast in the structural mould of the theme; there are imitative variations, of thoroughly modern type; and there are also examples of the imitations being treated by inversion in the second half, as was the manner of Bach. But in style there is little to recall the methods of the older master, and it is useless to try and lay down hard and fast technical rules to explain the detailed connection of theme and variation. In all these last sets, and in the Diabelli set especially, Beethoven is making transformations rather than variations. He takes the theme in all its phases—harmonic, melodic, or rhythmic and having the idea well in his mind, reproduces it with unlimited variety in different aspects. At one moment a variation may follow the melody of the theme, at another the harmonic structure, at another it will be enough that some special trait like the persistence of an inner portion of the harmony in thirds or otherwise is reproduced, as in the second phrase of Variation No. 8. At other times he will scarcely do more than indicate clearly the places where the cadences and signs of the periods fall, as in Variation 13, with the long pauses; while at other times he works by nothing more than analogy, as in the relations of the end of the first half and beginning of the second half of Variation 5, and the beginnings of the second halves of Nos. 9, 13, and 22. In other cases there are even more complicated reasons for the connection. An example occurs as early as the first variation. The strong type of figure, moving by diatonic steps, adopted at the beginning, is worked out in longer reaches in the second half, until it forces the harmony away from the lines of the theme into short transitional digressions. These occur in two successive periods, which are brought round again and rendered externally as well as ideally intelligible by the way in which the periods are made to match. In a few other cases nothing but the strong points of the periods are indicated, and the hearer is left in doubt till he hears the strong cadence of the period, and then he feels himself at home again directly, but only to be immediately bewildered by a fresh stroke of genius in a direction where he does not expect it. The happiest example of this is Variation 13, already alluded to, which is principally rhythmic, just indicating by a sort of suggestion here and there a humorous version of the theme, and making all the progressions seem absurdly wrong at first sight, though they come perfectly right in the end. The two following examples are the first halves of the theme and of Variation 13:—

Another most wonderful variation is the twentieth, in which again there is a mere suggestion of the theme woven into mazes of transitions, passing away from the harmony of the theme in the less essential points, but always making the balance even again at the close, melodic and structural principles being mixed up almost inextricably. Example 25 shows the portion of this variation corresponding to the part of the theme given in Ex. 23:—

In almost all the variations except the fugue (no. 32) the periods are kept quite clear, and match the original faithfully; and this is the strongest point in helping the hearer or reader to follow the connection. The free fugue, which comes last but one, is exactly in the very best place to break any sense of monotony in the recurrence of these exact periods, while the last variation sets the balance even again in a very distinct and weighty way, in favour of the plan and melody of the theme.

In connection with the point illustrated by the fugue in this set, it is noticeable that Beethoven from the first seems to have aimed at relieving in some striking and decisive way the monotony which is liable to result from the constant recurrence of short sections, and the persistence of one key. His codas are frequently very long and free, and often contain extra variations mixed up with telling passages of modulation. The early set of variations on a theme by Righini (1790) affords one remarkable illustration of this, and the twelve on the Russian air from 'Das Waldmädchen' (1797), another. In the last movement of op. 111 the same end is gained by the string of transitions in the body of the movement before the last two variations; a similar passage occurs in the slow movement of the 9th Symphony; and in a few instances he gained the same end by putting some of the variations in a different key, as in those of the E♭ Quartet, which also contain a modulating episode near the end.

The history of variations seems to be summed up in the set we have just been considering. In the earlier stages of the art the plan of the bass and the harmonies indicated by it was generally the paramount consideration with composers, and great technical ingenuity was expended. In characteristic sets of the earlier sonata-period the melody became paramount, and technical ingenuity was scarcely attempted. In Beethoven's latest productions structural and melodic elements are brought to a balance, and made to minister in all the ways that artistic experience and musical feeling could suggest to the development of the ideas which lie in the kernel of the theme, and to the presentation of them in new lights.

No composer had ever before attempted to produce variations on such principles as Beethoven did, and the art has hardly progressed in detail or in plan since his time; but several composers have produced isolated examples, which are really musical and interesting. Schubert is particularly happy in the variations on the 'Tod und Mädchen' theme in the D minor Quartet, in which there is great beauty of sound, charm of idea, and contrast of style, without anything strikingly original or ingenious in principle. Weber produced numbers of very effective and characteristic sets for pianoforte. Mendelssohn left one or two artistic works of the kind, of which the 'Variations serieuses' is the best. In this set there are happy instrumental effects, and the whole makes an effective pianoforte piece; but Mendelssohn's view of this branch of art was only at the level of the simple standard of Mozart, and not even so free and spontaneous as Haydn's; and in his application of melodic and structural principles he is extremely strict. Far more interesting is Schumann's treatment of the form in such examples as the Andante and Variations for two pianos, and the well-known 'Etudes Symphoniques.' His view of the art tended to independence as much as Mendelssohn's did to rigidity, and at times he was even superfluously free in his rendering of the structural aspect of the theme. His devices are less noticeable for ingenuity than for the boldness with which he gives a thoroughly warm, free, and romantic version of the theme, or works up some of its characteristic figures into a movement of nearly equal proportions with it.

By far the finest variations since Beethoven are the numerous sets by Brahms, who is akin to Beethoven more especially in those characteristics of intellect and strong emphatic character, which seem to make variations one of the most natural modes of expressing ideas. In the Variations and Fugue on a theme of Handel's (op. 24), the superb set for orchestra on a theme of Haydn (op. 56a), those for four hands on a theme of Schumann's (op. 23), the two Paganini sets, and the fine set on an original theme in D (op. 21, no. 1), he has not only shown complete mastery and perception of all aspects of the form, but a very unusual power of presenting his theme in different lights, and giving a most powerful individuality both of rhythm and figure to the several members of each series. His principles are in the main those of Beethoven, while he applies such devices as condensation of groups of chords, anticipations, inversions, analogues, sophistication by means of chromatic passing notes, etc., with an elaborate but fluent ingenuity which sometimes makes the tracing of the theme in a variation quite a difficult intellectual exercise. But analysis almost always proves the treatment to be logical, and the general impression is sufficiently true to the theme in broad outline for the principle of the form to be intelligible. He uses double variations with the happiest effect, as in those on the theme by Haydn, where the characteristic repetition of halves is sometimes made specially interesting by building one variation upon another, and making the repetition a more elaborate version of the first form of each half of the variation. Where the variations are strongly divided from one another, and form a string of separate little pieces, the contrasts and balances are admirably devised. In some cases again the sets are specially noticeable for their continuity, and for the way in which one variation seems to glide into another; while they are sometimes connected by different treatment of similar figures, so that the whole presents a happy impression of unity and completeness. Brahms is also, like Beethoven, most successful in his codas. Two very large ones are the fugue in the Handel set, and the fine, massive coda on a ground-bass derived from the first phrase of the theme, in the Haydn variations. Another on a large scale, but in different style, is that which concludes the Hungarian set (op. 21, no. 2.)

In the following examples—which show the first four bars of the theme, and the corresponding portion of the third variation in the first Paganini set, the nature of several very characteristic devices, such as anticipation, insertion of new chords between essential points of the harmonic succession, doubling the variation by giving the repetition of each half in full, with new touches of effect, etc.,—is illustrated.

A peculiar adaptation of the Variation-principle to the details of other forms of art remains to be noticed. In this also Beethoven led the way. A very fine example is the conclusion of the Marcia Funebre of the Eroica symphony, where the subject is made to express a terrible depth of grief by the constant breaks of the melody, which seem to represent sobs. A similar device—in that case amounting to a complete variation—is the repetition of the short 'Arioso dolente' in A♭ minor in the middle of the final fugue in the Sonata in A♭ (op. 110). Here again the object is obviously to intensify the sadness of the movement by constant breaks and irregularities of rhythm. Another passage of the same kind is the end of the overture to 'Coriolan.'

With a similar view Berlioz has given varied forms of his 'idée fixe' in the 'Episode de la vie d'un artiste'; adapting it each time to the changed conditions implied by the movement in which it appears. Its original form is as follows:—

In the ball scene it takes a form appropriate to the dance motion:—

Another form occurs in the 'Scéne aux Champs,' and in the final 'Nuit de Sabbat' it is purposely brutalised into the following:—

Wagner, carrying out the same method on a grander scale, has made great use of it in adapting his 'leitmotiven' to the changed circumstances of the individuals or ideas to which they belong. One of the most remarkable instances is the change from one of Siegfried's tunes as given by his own horn in his early days, representing his light-hearted boyish stage of life—

to the tune which represents him as the full-grown hero bidding adieu to Brünnhilde, which is given with the whole force of the orchestra.

Liszt has frequently made characteristic variations of his prominent figures for the same purposes, as in the 'Faust' symphony, and 'Le Preludes.'

Among the devices known as 'æsthetic,' variations again play a most prominent part; movements of symphonies and sonatas, etc., being often linked together by different forms of the same idea. Interesting examples of this are to be met with in Schumann's Symphonies in D minor and C, and again in Brahms's Symphony in D. [See Symphony, pp. 35 and 42.]

In such a manner the principle of variation has pervaded all musical art from its earliest days to its latest, and appears to be one of its most characteristic and interesting features. In its early stages it was chiefly a mechanical device, but as the true position of ideas in music has come more and more to be felt and understood, the more obvious has it become that they can be represented in different phases. Thus the interest of the development of instrumental movements in modern symphonies and sonatas is frequently enhanced by the way in which the subjects are varied when they are reintroduced according to the usual principles of structure; in operas and similar works ever since Mozart's time characteristic features are made all the more appropriate by adapting them to different situations; and it is even possible that after all its long history the Variation still affords one of the most favourable opportunities for the exercise of their genius by composers of the future.

[ C. H. H. P. ]