THE DERIVATION OF CHOPIN'S FOURTH BALLADE FROM BACH AND BEETHOVEN

Nigel Nettheim

      It has often been remarked that Chopin's fourth Ballade, opus 52 of 1842, shows the fruits of his studies of Bach's music, but the specific debts have apparently not previously been uncovered.¹  Chopin's attitude to Beethoven was in some ways more critical than admiring, but a clear debt exists here too—one that has not often been discussed either in general or in respect of this particular work.²  It is the purpose of the present paper to set out these debts, which, I believe, show Chopin's work in a new light. I will present the derivation in the order in which I arrived at it, so as to make the reasoning clear.

      To begin at the beginning would be usual, but the introduction to the Ballade can be described adequately only in retrospect; I will therefore return to it after its materials have been identified in the piece proper. The main theme is given in bars 8-22 with Chopin's typical accompaniment of pedalled bass-note and treble chords, the essence of the theme being contained in the first four bars of the melody (Ex. 1).

Ex. 1. Chopin: fourth Ballade, bars 9-12

      A possible division of this melody into figures is shown in the example. The antecedent covers bars 8b-10a and contains an "angular" figure (a in the example), which is repeated. (The notation Xa and Xb is used here for the first and second halves of bar X.) The consequent (bars 10b-12a) contains three identifiable components: a "neighbour-note" figure as preparation for a "repeated-note" figure and a concluding "modified step-down" figure (indicated as b, c and d). (These {p. 96} simplified verbal labels for the figures will perhaps be tolerated as they make references more vivid.)

      On the basis of the contrapuntal treatments to follow and of Chopin's known studies of Bach dating from his early lessons with A. Zwyny we should already keep in mind Bach's works. Is a plausible model to be found? That angular start and those repeated notes are not quite typical of Chopin melodies: do they not stand out as if to ask for an explanation? We can perceive a possible relationship between the consequent just described and the theme of the Prelude in B flat minor, No. 22 from the Well-Tempered Clavier Book I (WTC I/22) (Ex. 2).

Ex. 2. (a) Chopin: fourth Ballade, from bars 11-22  (b) Bach: WTC, I/22, Prelude, bars 1-4, 23

It might be surmised that, if Chopin started from the Bach theme, he modified each of its components, repeating the first two notes, adding an extra repetition to the top repeated note and slightly varying the tailpiece.³  He also took over the initial rest, which may at first have seemed insignificant. The manifold reproduction of the motif on different scale degrees in the sequel is another common feature. Further comparison of the themes reveals other similarities; in such cases only the main correspondences will be reported here. As this Prelude is one of the most directly and strongly moving of the entire WTC, its appeal for Chopin would not be surprising, but the search for models can easily produce illusions, so confirmation will be required of this first clue to the origin of the Ballade.

      It is natural now to look for a model in the WTC for Chopin's antecedent, but none is apparent. Only after we have seen Chopin's later contrapuntal treatment of the theme will we be able to answer this tantalizing question. (It is suggested that the reader avoid looking ahead, in order to follow the natural order of the reasoning.)

      The main material is now spun out for the remainder of the theme, in which we notice that the motifs appear in either half of the notated bar (compare bars 8b-9a, 13a-13b, 18b-19a; for instance, bar 12b is an "extra" half-bar). It seems most unlikely that an audible contrast of metrical orientation is intended here: rather, the underlying metre of the main theme might be taken as 3/8, or as a movable 6/8, {p. 97} rather than as the notated fixed 6/8.⁴  After this spinning-out the theme ends in the subdominant (bar 22a)—an explanation for such an unusual choice of key must await later events. From that key a single dominant 7th chord (bar 22b) allows the reproduction of the theme (bars 23-37), with the addition of just a touch of diminution the significance of which will also be suggested later. That is not the only change, for the whole theme has also been shifted by a half-bar; but in view of the foregoing observations it may be assumed that this shift has no real significance.

      A further reproduction of the theme is to follow, but Chopin first inserts a developmental episode (bars 38-57) based upon the main theme's consequent phrase. The first section (bars 38-45) of this episode appears to involve augmentation of the "repeated-note" figure, while the remainder develops all figures of the consequent. The episode departs from the current B flat minor tonality but the latter is recovered as the episode concludes similarly to the end of the theme itself, thus leading smoothly into the next version of the theme.

      Chopin's contrapuntal intentions are clearly shown in the third presentation of the main theme, to which a middle voice is added. The contrapuntal line is based upon a "stepping-pairs" figure, and again, in looking in the WTC, we seem to have ended our search when we find that it is virtually the same as the counterpoint in Bach's Fugue in F sharp minor, WTC I/14. This turns out to be a false clue, however, for on looking further we notice the same figure in the latter part of the subject of the Fugue in B flat major, WTC II/21 (Ex. 3). Chopin has followed even more closely the continuation of the B flat major source, suggesting that as the actual model; confirmation must wait for the considerations of tonality to be raised later.

Ex. 3. (a) Chopin: fourth Ballade, bars 58-60  (b) Bach: WTC, II/21, Fugue, bars 1-7

      This third presentation of the main theme concludes the exposition and is dissolved into a link to the subordinate theme. The dissolution (bars 70-71a) is very {p. 98} similar to the corresponding passage in the WTC I/22 Prelude (bar 22), whose relationship to the theme itself has already been seen (Ex. 4). In both pieces the rising 3rds continue upwards to a striking diminished 7th chord while the bass duplicates the move in contrary motion. Chopin has translated Bach's fermata into the "repeated-note" figure at the climax in one of many displays of the combination of logic and effectiveness, for, from one aspect, a repeated note is not unlike a long-held note. It will be noticed that the pitches are almost identical in this comparison—the most intensely expressive passage in the Bach work did not fail to attract Chopin.

Ex. 4. (a) Chopin: fourth Ballade, bars 70-71  (b) Bach: WTC, I/22, Prelude, bar 22

      The following transition (bars 72a-80a), like almost the whole of the piece, is based quite strictly upon the basic materials—in this case, mainly the first three notes of the main theme. The subdominant key reached at the end of the main theme is retained; only its mode is changed to major.

      The subordinate area begins with a four-bar phrase that is seen in retrospect to be not the theme itself but just an introduction to it (bars 80b-84a); it is not entirely easy to convey that introductory status in performance, despite Chopin's dolce marking's being withheld until after those four bars. The following theme (see Ex. 5) is a parallel double-period (bars 84b-99b). A two-note "prepared-downbeat" figure and a "turn" appear in both introduction and theme (x and z in the example, where the note in parentheses appears in the second period only), while a curious "falling sixth-and-step" figure appears only in the introduction (y in the example). A brief echo of the main theme is included at bar 91. Again the orientation of the music to the notated metre might be taken as orthographical rather than aural. The question of a {p. 99} model cannot yet be answered—once more we must wait until we have seen Chopin's attitude to the piece's tonalities.

Ex. 5. Chopin: fourth Ballade, bars 81-88 (upper staff: introduction; lower staff: theme)

      Now begins the development, whose texture is based mostly upon a figuration of 6ths. We will look in some detail at the organization of its five sections.

      The first section (bars 100a-107b) uses all the figures of the main theme including its counterpoint. In detail: it begins with a treatment of the neighbour-note figure, after which the 6ths are broken into a pattern suggesting the angular figure and ending with a modified step-down figure, the whole arranged in a sequence of 4 + 4 bars. The link between the sequence members uses the stepping-pairs figure (bar 103b), while the link to the next section is a brief ritenuto on the repeated-note figure (bar 107b).

      The second section (bars 108a-111b) uses the same materials as the first section (except for the final link) and in the same order. They are now fused even more tightly into a new phrase, the sequence this time being of 2 + 2 bars. This kind of manipulation of thematic elements is a thoroughly Beethovenian procedure.

      The third section (bars 112a-121a) uses the neighbour-note figure and angular figure, arranged as 2 + 2 bars extended into a chain of neighbour-note figures, which now dominate. The trill can be heard as a logical diminution of the neighbour-note figure (bar 120a).

      The furthest point of the development has now been reached, and the fourth section (bars 121a-124b) begins to herald the return of the main theme. The "alto" part of this section, though in the background, plays a significant role in the heralding process, for it is based upon a "rocking-semiquaver" figure previously heard only in the introduction (bars 1-7). The right time has therefore arrived to interrupt our progress through the piece in order to understand its introduction.

      The piece opens with fragments of the thematic materials to follow. The repeated-note figure and its finishing step-down figure are most prominent. Bars 1b-2a contain in the left hand an augmentation of the stepping-pairs figure, and towards the end some neighbour-note figures can be picked out. ⁵  But the ingredient which characterizes the introduction and differentiates it from the exposition proper is its rocking-semiquaver accompanimental figure.

      {p. 100} Understanding now the role of the rocking semiquavers, we can return to the fourth section of the development. Whereas so far the developmental technique has been notably Beethovenian in its thematic manipulations, it now becomes Bachian in its contrapuntal combinations (of which Beethoven, of course, also often availed himself). Again the formation is one of 2 + 2 bars. The angular figure is played by the left hand. In the "soprano", each 2-bar portion begins with the neighbour-note figure; the first time the step-down figure follows (bar 122), while the second time this is logically transformed into the stepping-pairs figure (bar 124). At the end of each portion the neighbour-note figure is inverted (bar 122b and, more freely, bar 124b). This section is thus a considerable developmental working-out involving both motivic fusion and contrapuntal combination, but its crescendo leads to a still greater developmental feat.

      The fifth and final section (bars 125a-128b) sees the return of the repeated-note figure of the introduction in a grand synthesis of all the main theme's elements compressed within two-bar units and, thus, near-simultaneity. Even more, a hint of imitation between "soprano" and "tenor" is included, anticipating what will occur in the recapitulation. This tour de force ends the development, after which the subsequent ritardando and diminuendo are natural. We have looked at the workmanship of Chopin's development in order to draw attention to its similarity to Beethoven's typical procedures, though proposing no one model.

      In tracing the development's tonal course, it will be remembered that the exposition ended in B flat major. From that starting-point the development's first sequence moved from G minor to A minor, and the next from G minor to F minor extended to A flat major. In the midst of the rich final development section Chopin also modulated from A flat major to A major. The introduction to the main theme is next recapitulated (bars 129-134); it is in that key, A-major, rather than the C-major of bars 1-7, for a reason that will soon become apparent. The cadenza in double-notes recalls the sixths of the development's figuration. The recapitulation of the main theme itself is arranged in contrapuntal imitation with three presentations (Ex. 6). As the opening presentation rises a minor 3rd, we now see the reason why the introduction (bars 129-134) was in A major: for that is the dominant of the key a minor third below the tonic F minor, thus allowing the extra presentation of the opening statement. After the added initial presentation, the tonality follows that of the exposition; however, a deeper reason for the choice of A major will appear later.

      Having the recapitulation's tonality to that extent under our belt, we now look at its construction. The theme, or subject, has been slightly modified in its first two {p. 101} notes to allow the imitation to work.⁶  The first presentation of the imitation is in just two voices, the next is in four, and in the final presentation the number is increased to five, with the aid of a pair of entries in parallel sixths in bar 143. ⁷  That number, five, alerts us to a most interesting fact: the five-voice stretto suggests an association between this work and Bach's five-voice stretto Fugue in B flat minor, WTC I/22, the companion piece to the very Prelude referred to earlier. Moreover, Bach had first presented a pair of entries in vertical double-notes (Bach's bars 55-58), just as we saw Chopin do in his bar 143. Chopin would undoubtedly have been impressed by the stretto maestrale which concludes that Fugue (Bach's bars 67b-72b).

      Comparing the two composers' strettos more closely, we see that the distances in both cases are a half-bar. Bach's stretto incorporates his whole three-bar subject, Chopin's only his one-bar motif, and this provides a possible reason for the repetition in Chopin's theme (bars 8b-9a, 9b-10a): by this means he gained extra length, in effect doubling the returns for his smaller contrapuntal investment. Thus, Chopin did not match his model on Bach's terms, but adapted the technique to his own terms, achieving something like the freer stretto appearing earlier in the Bach Fugue (bars 50-55). Chopin was in any case writing not fugue but fugato.

      Realizing that Chopin intended to show his theme in stretto, we must ask how he constructed his theme in the first place, and we can no longer avoid bringing into comparison the subjects of the two works now under discussion (Ex. 7).

Ex. 7. (a) Chopin: fourth Ballade, bar 9  (b) Bach: WTC, I/22, Fugue, bars 1-3

The comparison is summarised in Ex. 8:

Certainly Bach's final stepping-up proceeded an extra note—to the f''—but the outline of Chopin's theme is visible in Bach's first three bars. Whereas Bach's harmonies were tonic and dominant, Chopin has adopted tonic and diminished seventh, an interesting innovation. Thus Chopin's main theme is derived as follows: the antecedent from Bach's Fugue and the consequent from the corresponding Prelude (Ex. 9).

Ex. 9. (a) Chopin: fourth Ballade, bars 9-12  (b) Bach: WTC, I/22, Fugue, bars 1-3; Prelude, bar 1

      {p. 102} Digesting this discovery, we can first confirm that Chopin had in mind his theme's adaptability to stretto.⁸  It was also natural enough that he would reduce the antecedent to equal notes befitting the "head" of a common type of subject, by comparison with the faster notes of the "tail". Looking back to the first variation on the main theme (bars 23-37), we now see that the diminution was applied to fill in the upward 3rd interval (bars 24b, 29a, 34b), incorporating even the upper note ending Bach's complete subject; the filling-in of the tritone interval will later be seen, too. Certainly the filling-in of an interval is a standard resource, but Chopin's initial perfect fourth always remains open, and these features correspond to Bach's theme. In reviewing the source of the main theme and that of its counterpoint (appearing together in bars 58-61), it might seem extraordinarily clever of Chopin to have found that part of one Bach Fugue subject could act as counterpoint to part of another; but this was assisted by the conformable nature of the "stepping-pairs" material, which could serve to accompany a wide variety of subjects. A more far-reaching consequence of our discovery is that we now see a possible factor leading to the main theme's ending (at bar 22a) in the subdominant, B flat minor: for that is the key of its pair of models. This raises the further question why Chopin chose F minor rather than B flat minor for the key of the piece—that question, too, can only be answered later.

      In view of all that has been said up to now, it is incontestable that Chopin closely studied the Bach Prelude and Fugue in B flat minor, WTC I/22, and based many {p. 103} features of his fourth Ballade upon them. This mixture of homage and emulation is profound and moving.

      After the highly intellectual contrapuntal phase just examined, the Ballade returns to the original song-like texture for the remainder of the theme.⁹  The following version of the theme uses a new counter-metrical left-hand figuration against the right hand's highly-wrought fioritura (bars 152-168). Here again the ascending end of the main motif is filled in—an intensification of the first variation of the theme referred to earlier. Except for the coda, this is the last of the variations upon the main theme;¹⁰  it is dissolved to modulate by the simplest of means—a continued chromatic scale—from B flat minor to the new key of D flat major.

      Now follows the recapitulation of the subordinate theme (bars 169-191), and it is at about this point that the listener might suspect that the piece will be in sonata-allegro form, with the subordinate theme in the unusual keys of the subdominant major and flattened sixth. Indeed, the form of the Ballade can be summed up in no better terms than Abraham's "a masterly deformation of sonata form". ¹¹  In the exposition this theme used the weaker triads (ii, iii and vi), giving a tentative or restrained impression, but now the strongest harmonies are used. The left-hand material is still further enhanced, and Chopin's well-known desideratum of a steady bass with independently delivered melody is nowhere better illustrated than in bars 175-176.

      The piece is now heading for an end in the wrong key of D flat major: the denouement is at hand. This consists, in a word, of a breaking-up. The established texture is abandoned for improvisatory material as the D flat key gives way to F minor (bars 191-210). At the beginning both hands sweep up the keyboard. Rapped-out chords follow in which traces of the main theme are present—Samson has pointed out that the passage and its sequel are similar in texture to a passage in the Hummel Fantaisie, op. 18 of 1805. ¹² 

      Finally, the thematic material itself is broken up in an F minor coda (bars 211-239). We will not need here to trace all its intricate details; but it is relevant to note the filling-in of the tritone interval and its inversion (bars 212b, 214b and 215-216) as if to refer again to Bach's version of the theme, in which that interval was filled in (see Ex. 7 and compare the last reprise of the main theme, bars 152-168, referred to earlier). It is also relevant to note that the prominent unresolved progression of the main theme, f - e natural, is at last resolved in bars 224b-225a in the reverse progression, e natural - f.¹³ 

      {p. 104} For Chopin's concluding bars (227-239) a relationship to a work of Beethoven will be put forward. As indebtedness of Chopin to Beethoven has not often been suggested, the way will be prepared by a digression examining another of Chopin's most powerful works.

      The Prelude op. 28 no. 24 in D minor was composed between 1836 and 1839, and thus a few years before the fourth Ballade. (The fact of Chopin's having written a set of 24 Preludes incidentally reminds us once again of his emulation of Bach.) One of the first things to notice here is the indication Allegro appassionato. This indication calls to mind Beethoven's Sonata in F-minor, op. 57, of which the title Appassionata was given by the publisher in 1807 and so would have been well-known to Chopin. We look first at the opening period of the Prelude, in which both the antecedent and consequent are doubled. When this is put up against the opening of Beethoven's first movement the relationship becomes clear: the initial triadic fifth falling to a long note followed by a rising arpeggio and trills obviously match (Ex. 10). Chopin has shifted the initial motif by a half-bar, the metrical change no doubt having the effect of camouflaging the derivation somewhat. Chopin's upward-rushing scale (bar 14) might be his replacement for Beethoven's cruder upward-pounding chords (Beethoven's bars 17-18 etc.); Chopin's later downward-rushing passages (bars 35, 55-56, 66, 70 and 74) might correspond to Beethoven's bar 14.

Ex. 10. (a) Chopin: Prelude, op. 28 no. 24, bars 3-19, 74-77  (b) Beethoven: Sonata, op. 57, I, bars 1-24, 258-262

      Both movements end with three low repeated notes following a long descent of the main falling triadic motif, which Chopin has intensified with an added flattened-sixth appoggiatura. (In this and the Ex. 11 leger lines are retained to represent patterns graphically.) The dynamics, certainly, are different, Chopin's piece being forte almost throughout, but we have seen enough to establish the derivation; because the Prelude is so furious, this might be considered neither homage nor emulation so much as competition, as if Chopin thought "I'll show you something really appassionato". Chopin has borrowed Beethoven's material and mood, but not his form. It is curious that the derivation has apparently not been reported before and that commentaries seldom mention an influence of Beethoven upon Chopin.¹⁴ 

      Having concluded our digression and armed ourselves with the knowledge that Chopin had already referred closely to Beethoven's Appassionata Sonata, we can continue our study of the fourth Ballade, comparing the two conclusions (Chopin's bars 227-239, Beethoven's bars 325-361: Ex. 11).

Ex. 11. Upper staff of each pair: Chopin: fourth Ballade, bars 227-239  Lower staff of each pair: Beethoven: Sonata, op. 57, III, bars 325-361

A parallel organisation appears, and the five pairs of staves in the example will now be considered in turn:

      (1) and (2) First, thematic passage-work rises sequentially to the top of the keyboard; Beethoven's left-hand arpeggios, which are also thematic, become in Chopin the counter-metrical arpeggios that he had used already in bars 152-164 (the second version of the main theme in the recapitulation).

      (3) Next, the left-hand makes forceful two-note gestures (distinguished in the example by downward stems) striking four times with flight on a fifth strike. Chopin has, typically, reversed the metrical orientation of the note-pairs from that of his model; compare in this metrical respect his derivation of the main motif in the Prelude op. 28 no. 24 discussed earlier.

      (4) {p. 105} At the top (Beethoven's bars 341-352, Chopin's bars 231-233a), Chopin characteristically replaces a figuration of Beethoven's that he, Chopin, would have found awkward by an elegant one; such replacements were seen also in the Prelude op. 28 no. 24.

      (5) Finally comes a long thematically-derived fortissimo descent. Chopin has replaced Beethoven's "square" pattern with his own typical counter-metrical arrangement; he has also chosen a figure closely related to both composers' works: the main motif derived from Bach is probably the primary one to be reflected in performance, but Beethoven's descending arpeggio is present too, arranged with an appoggiatura (Ex. 12).

Ex. 12. Chopin: fourth Ballade, bars 233-234

No other reason seems to explain this sudden appearance of the close-position descending arpeggio in Chopin's piece. We also note that it was with a different arrangement of the same figure that Chopin ended his Prelude op. 28 no. 24 (see Ex. 10(a) bar 74). Chopin has arranged his final four chords to show once more a logical resolution of the progression of the main theme's first motif, the angular motif; whether intentionally or not, there is again a hint of "crab" reversal (bass d flat - b flat - treble e natural - f). A summing-up of the tonality debate might be found in those four chords too, as if they say "Is it D flat or B flat? No, it's F minor!".

      The comparison in Ex. 11 shows not only that the organization is parallel between the two pieces, but also that Chopin kept very closely to Beethoven's sectional proportions, departing only in the small section before the final descent. {p. 107} The control of such proportions was a Beethoven trademark and was evidently recognised as such by Chopin. Both pieces end in F minor, and there is no music better able to justify the term appassionata than the end of the F-minor Ballade. ¹⁵ 

      Certainly the endings of two works may show parallelisms without arousing claims of actual derivation; but in the present case we believe the cumulative evidence outlined here is fully convincing.¹⁶  Whereas in the Prelude op. 28 no. 24 Chopin borrowed Beethoven's material and mood rather than his form, here he has borrowed the mood and form of the ending with only such a hint of the material as his Ballade, with its already chosen materials, allowed him. Thus the remarks of Liszt, Niecks and Lenz (see footnote 2) seem to need qualification, for Chopin has now been seen to have admired several aspects of Beethoven's Appassionata Sonata sufficiently to emulate them. Of course, this derivation immediately suggests an answer to the question as to why Chopin's piece is in F minor rather than B flat minor, to which latter key the main theme was seen ultimately to belong.

      We have now reached the end of the Ballade, but that is not the end of the story, for we next look back to seek further implications of the derivations discovered so far.

      The competition between F minor and B flat minor for the role of the main theme's key had very interesting structural consequences of which Chopin naturally took advantage. On a medium scale, the performer will be reminded of them when playing the single dominant 7th chords needed to restore normalcy in bars 22b, 57b and 151b. On a large scale, Chopin had gravitated to B flat minor in the main theme for the reason already indicated; for the subordinate theme keys he used instead, very logically, not B flat minor itself but its tonic major (B flat major) in the exposition and its relative major (D flat major) in the recapitulation. From this point of view Chopin set himself the large-scale task of reversing the usual key-scheme, which could have been B flat minor for the main theme and F minor or D flat major for the subordinate one. Somewhat similar key-twistings occur in the other Ballades.¹⁷  By classical convention one refers to only one main key, here "the F minor Ballade", but one might with little exaggeration regard it as "the B flat minor - F minor Ballade". Chopin had already departed from the one-key convention in several other works, including the second Scherzo (1837) in B flat minor - D flat major and the second Ballade (1839) in F major - A minor; the present design is, however, more subtle, with F minor not only following but also preceding B flat minor.

      As F minor was not Chopin's intended "real" key for the main theme—but rather B flat minor—we can see his anticipation of that key-relationship by placing {p. 108} the introduction not just on the dominant of F-minor but in C major. One could therefore well begin the piece with a bird's-eye view of the progression of rising 4ths C → F → B flat. That anticipation at one remove in the exposition of the main theme is taken a step further to two removes in the recapitulation of the main theme, with the progression A major → D minor → F major/minor → A flat major/minor → B flat minor. Here the rising third through which the theme first progresses in the exposition, F minor → A flat major, has been anticipated in the progression D minor → F major (Ex. 13).¹⁸ 

Exposition:                                      
    Introduction:        C  →                      
    Theme:                          F  → (Ab) →  Bb
                         └——————————┴————————————┘ 
Recapitulation:                                  
    Introduction:  A  →       ┌—————┬—————┐        
    Theme:                    D  →  F  →  Ab  →  Bb
                   └——————————┘     └————————————┘ 

Also available to Chopin for the anticipating key was the closely related D flat major or minor rather than the very distant D minor, but he clearly welcomed the opportunity for fresh blood and the resulting unusual A flat to A major modulation at the end of the development. This wonderful handling of the medium-range tonal relationships, indicated by the interlocking brackets in Ex. 13, constitutes the deeper reason referred to earlier for the appearance of A major.

      Having seen Chopin's adherence to the tonalities of his models, we now know where to look for a model for the subordinate theme, which is in B flat major: Bach's Prelude in that key, WTC I/21 (Ex. 14).

Ex. 14. (a) Chopin: fourth Ballade, bars 85-87  (b) Bach: WTC, I/21, Prelude, bars 1-3, 3

This clue is confirmed when we notice that each melody follows the same outline in half-bar units—d'', b' flat, g', f', and that each note appears twice; indeed, the insistence of those repetitions in Chopin's theme are a little puzzling without the aid of this source. Even Chopin's falling 3rd, d - b flat (bar 86), otherwise unexplained, finds its place. Chopin has, as we saw him do in his D minor Prelude, changed the metrical orientation of the thematic elements between the model and his own composition—there from approximately ( ˘ ˘ ˉ ) to ( ˉ ˘ ˘ ) , here from ( ˉ ˘ ) to ( ˘ ˉ ) —and it is by now clear that metrical manipulation is one of his favourite devices. Chopin's theme proceeds to a turn (bars 87, 95) seen also in the Bach theme (bars 3-4), while the weaker triads (ii, iii and vi) referred to earlier in Chopin's theme appear also in the model.

      Finally, an explanation can be sought of the introduction to the subordinate theme (bars 80b-84a). Its three components, described earlier in Ex. 5, are reproduced in Ex. 15 (a).

Ex. 15. (a) Chopin: fourth Ballade, bars 81-84  (b) Bach: WTC, I/21, Fugue, bars 1-3

The first and last of these belong to the theme proper and have just been identified in the WTC I/21 Prelude. But the middle figure is harder to assign, for it is not used in Chopin's theme proper; the presence of this figure is perhaps the only case in the piece where Chopin's thematic logic might be {p. 109} questioned. We note the distinctive feature of the falling 6ths being followed by a step down, rather than more regularly moving back up within the wide interval. Although the demisemiquaver figure in the same Bach Prelude does include falling 6ths, it does not contain the following step down (see Ex. 14), so the real source of the figure appears to be the subject of the corresponding Fugue WTC I/21 (Ex. 15 (b)).

      Taking stock, we have seen Chopin's adoption of the B flat major and minor works from the WTC. There are eight such works, among which some figures {p. 110} naturally reappear, slightly confounding the assignments (Ex. 16).

Bach WTC                  Chopin fourth Ballade            

 I/21 B-flat major Prelude       Subordinate theme                            
 I/21 B-flat major Fugue         Subordinate theme introduction: middle figure

 I/22 B-flat minor Prelude       Main theme: consequent                       
 I/22 B-flat minor Fugue         Main theme: antecedent                       

II/21 B-flat major Prelude      —                                           
 II/21 B-flat major Fugue (*)    Main theme: counterpoint                     

II/22 B-flat minor Prelude (*)  —                                           
II/22 B-flat minor Fugue        —                                           

(*) Contains additional material somewhat similar to Chopin's.

Chopin's drawing from Bach's works having one particular tonic might have been arbitrary, but more likely it reflects his notion of the unification of key and mood referred to earlier.

      Our unravelling of the sources of the Ballade has, as was foreshadowed at the outset, followed the order of our reasoning rather than that of the piece, for some of the derivations, such as that of the subordinate theme, could not otherwise have been found. More detailed relationships could be exposed than have been here, and other works of Chopin could be approached similarly. Further, the identification of sources is only a first step to a fuller analysis and appreciation, and the closest derivations provide an opportunity for instructive comparisons of the composers' styles. A review of earlier commentaries on the Ballade in the light of our findings would also be of some interest; but our present purpose has been completed and it is time to reflect upon the results.

      In so reflecting we naturally ask why the derivations shown had remained unnoticed in the 150 years since the work's publication, and two points of view can be considered: the composer's and the musicologists'.

      From Chopin's point of view, the hiding of the relationships may be explained by the artistic process transforming the sources or by a deliberate desire to cover his tracks. Beginning his main theme in the key of his piece rather than of his model had a covering-up effect, whether deliberate or not, as did the subtlety of some of his transformations, such as that shown in Ex. 7. The question is often raised as to what extent borrowing is conscious: here the very careful workmanship suggests full consciousness—indeed, a theme suitable for five-voice stretto could not otherwise be written. There is no record of Chopin the teacher mentioning such derivations to his students. "He had an almost pathological dislike of talking about the way he composed. He rarely missed an opportunity of keeping quiet about it."¹⁹  Probably, then, the two suggested explanations operated in tandem.

      From the musicologists' point of view, a grasp of the piece as a whole and of Chopin's likely attitudes to Bach and Beethoven was needed. The individual borrowings could not have been fully established alone, but depended upon the {p. 111} whole skein of derivation. Vladimir Protopopov studied the polyphony in this Ballade more or less separately from the whole picture. As the fugato started in D minor with a modified version of the main theme (bar 135), he took that to give its key and melody and so produced mainly D minor models, all starting with the notes a - b flat. To be fair: his purpose was to illustrate the character of certain fugue themes, but he was thus not in a position to find the true models.²⁰ 

      The fourth Ballade has, then, been shown to be the product primarily of Bach and Beethoven. The debts involve both technique and borrowing: the technical contributions were Bach's counterpoint and Beethoven's developmental logic, while the borrowing was of Bach's subjects and Beethoven's final phase. Each composer's tonality and mood were respected as well. In sum, Chopin has used not just a double-key, double-theme, double-mood and double-technique procedure, but a double-model one. What a heroic act this was, for the models were chosen from some of the greatest existing works: few have aspired to Bach's counterpoint at its highest, and probably no other composer has dared to say, on hearing the Appassionata Sonata, "I can exceed even that!".

      I believe that a recognition of the way the fourth Ballade has been put together, as here shown, can lead to a much more understanding performance. More broadly, I conclude that some of the greatest musical masterpieces have closer debts to one another than had previously been supposed. Without my wishing to open a wider debate, the present paper can finally be held to support the view that the best compositional results may be achieved not by seeking to eliminate the past but by building upon its own highest peaks.

      Since writing this paper I have learnt of the close derivation of Chopin's Fantaisie-Impromptu of about 1834 from Beethoven's Sonata quasi una fantasia (Moonlight) of about 1802. This was established in a fine paper by Ernst Oster.²¹ 

      The manner of Chopin's derivation there was very similar to that shown here for the fourth Ballade (and, to a lesser extent, for the D minor Prelude). Both derivations include key-relationships, motivic manipulation, a "crab" reversal, a single notatim quotation, Chopin's close attention to Beethoven's coda and an undeniably conscious implementation. These common features add to the significance of both papers.

      After asking why Chopin had declined to publish the Fantaisie-Impromptu—it was published posthumously against his wish—Oster answered that the close derivation would have been embarrassing. In view of the close derivations shown in the present paper of works which Chopin published without reservation, Oster's explanation now loses its likelihood; but his paper otherwise retains all its instructional value.

      ¹ "[In the last compositions] one notices a new strength and additional interest supplied by the fresh contrapuntal element, presumably the belated fruit of long study of Bach's 'Forty-eight' and of more recent study of 'Cherubini's traité' [which he had requested in 1841]." (Gerald Abraham, Chopin's Musical Style (London: Oxford University Press, 1939), p. 102). Abraham's word "presumably" indicates that specific relationships were not known.

      ² "Whatever admiration he entertained for Beethoven's works, certain portions seemed to him too roughly hewn . . ." (Franz Liszt, Frederic Chopin (New York: Vienna House, 1973 [1852]), pp. 143-144).
        "All accounts agree in that Chopin was far from being a thorough-going worshipper of Beethoven . . ." (Frederick Niecks, Frederick Chopin (Third edition, London: Novello, 1902), Vol I, p. 213.
        "He never cared very much for Beethoven. He knew only his great compositions . . ." (Wilhelm von Lenz, The Great Piano Virtuosos of Our Time (London: Kahn & Averill, 1983 [1872]), p. 48).
        Yet evidence to the contrary is not entirely lacking:
        ". . . Beethoven's last Trio [was played]. I've never heard anything so great: in it Beethoven snaps his fingers at the whole world. . . . [some minor works of other composers] did not suffice to efface the enormous impression which the Trio made on me . . ." (from a letter of 20th October, 1829 from Chopin to Titus Woyciechowski, in Arthur Hedley (translator and editor), Selected Correspondence of Fryderyk Chopin (London: Heinemann, 1962 [1955]), p. 36; see also pp. 111, 225, 265).

      ³ In an abandoned partial autograph the initial figure was modified differently, according to Jim Samson, Chopin: The Four Ballades (Cambridge: Cambridge University Press, 1992), p. 25.
        A very similar procedure of modifying in turn each component of a model theme was seen also in the case of Schubert's Drei Klavierstücke D 946/2 (second theme), where the model was the first theme of Beethoven's Sonata, op. 2 no. 3 (Nettheim, "Schubert's Drei Klavierstücke: how he learned from Beethoven", forthcoming). The use of such a procedure by both Schubert and Chopin suggests that it may be advantageous to students of composition.

      ⁴ A convention associates ballades with 6/8 or 6/4 metre (Samson, Ballades, p. 11), but Chopin's musical intentions could sometimes be represented equally well in more than one notated metre:

"I don't know whether it [a Rossini Tarantella] is written in 6/8 time or 12/8. It can be written in both ways, but I should prefer it [my Tarantella Op. 43 of 1841] in the same way as Rossini. So if it is written in 12/8 or possibly common time with triplets, you should make two bars into one when you copy it out."

—from a letter from Chopin to Julian Fontana, 20 June 1841; Hedley, Correspondence, p. 196.
        Similarly, the E flat Nocturne, op. 9 no. 2 of 1830-31 was published in 12/8, but Chopin later wrote out its first few bars in 6/8—see Maurice J. E. Brown, Chopin. An Index of his Works in Chronological Order (second edition, New York: Da Capo, 1972), p. 59.

      ⁵ Josef Hofmann emphasised those neighbour-note figures in a recorded performance: "Casimir Hall Recital, 1938", LP IPA-5007.

      ⁶ This is a normal procedure in constructing a stretto and was discussed in the work which Chopin consulted, Cherubini's A Treatise on Counterpoint and Fugue (New York: Belwin Mills [Kalmus], n.d.), p. 66: "In order that the response and subject may be brought closely together, it is permitted, no other course being possible, to change some notes of either the one or the other; or, if not to change the notes, to change their value . . .".

      ⁷ The number of voices represented in Chopin's treatment is indicated not by the number of distinct registers, but by the number of entries. As the intervals between his entries were octaves rather than the fifths arising in fugues, he had to compress the music to lie within the span of the two hands and thus place some entries in the same register. This point was unfortunately not taken into account by Vladimir Protopopov, "Polifonia w Balladzie F-moll Chopina", Rocznik Chopinowski 7 (1968), p. 39, who erroneously considered the number of voices in the three presentations to be 2, 3 and 3.

      ⁸ ". . . in composing a subject, therefore, the difficult combinations of stretto ought to be pre-considered" (Cherubini, Treatise, p. 66). It is now easy to understand the report from about this time of Chopin's "days of nervous strain and almost frightening desperation . . . He alters and re-touches the same phrases incessantly and walks up and down like a madman"—from a letter of Joseph Filtsch, 8 March 1842; Hedley, Correspondence, p. 217.

      ⁹ The poignancy of this transition from counterpoint to song was very sensitively portrayed by Heinrich Neuhaus, The Art of Piano Playing (London: Barrie & Jenkins, 1973 [1967]), p. 176.

      ¹⁰ The effect of making each appearance of the main theme a new variation upon it was to achieve greater forward momentum by avoiding the return to the original version that would occur in a classical sonata form; this aspect of Chopin's form was discussed by Vladimir Protopopov, "A New Treatment of Classical Music Forms in Chopin's Compositions", Chopin Studies, 1 (1985), pp. 21-26. The varied restatements also conform to the rhetorical device of "incremental repetition" belonging to poetical ballad form (see David Witten, "Ballads and Ballades", Piano Quarterly (1981), pp. 33-37).

      ¹¹ Abraham, Chopin's Musical Style, p. 108. For simplicity I have used standard terminology for the formal sections of the Ballade, even though Chopin treated these in a non-standard way.

      ¹² Samson, Ballades, p. 18. (Samson's example omits the first bar of Hummel's passage: the correct bar numbers are 612- 621 from the Leduc edition or 579-588 from Peters.)

      ¹³ A "crab" reversal in bars 200b-201a was pointed out by Badura-Skoda in Walker, The Chopin Companion (New York: Norton, 1973), p. 271. Such reversals may be seen as a combination of Bach's and Beethoven's logic.

      ¹⁴ "That Chopin assimilated something of Beethoven is of course more likely than not; but if a fact, it is a latent one" (Niecks, Chopin, Vol I, p. 213). Abraham, Chopin's Musical Style, does not mention Beethoven.

      ¹⁵ Neuhaus, Piano Playing, p. 189, related the two works in respect of their mood, but carried the comparison no further:

F minor I would call the tonality of passion. . . . To name but a few examples: . . . Beethoven: . . . "Appassionata"; . . . Chopin: . . . everything, from the recapitulation to the end, in the Fourth Ballade in F minor, including the Coda which could be called "passion as a catastrophe".

      ¹⁶ Other works of Chopin's also have a somewhat similar ending scheme to that of the Appassionata, as, for instance, the third Scherzo, op. 39 of 1839. If we look back to the rapped-out chords of the Ballade (bars 195-202) mentioned above as similar to Hummel's, some resemblance might now be seen to the chords appearing at the denouement of the last movement of Beethoven's Appassionata Sonata (bars 308-325), but that relationship seems too distant for any certainty.

      ¹⁷ The first Ballade shows G minor - E flat major - E flat major - G minor, the second F major - A minor - F major - A minor, and the third perhaps A flat major - F minor - C sharp minor - A flat major.

      ¹⁸ The last progression (bar 144) at first climbs to C-flat, extending the series of minor 3rds at its end just as at its beginning; it is rescued by a beautiful modulation to B flat minor (see footnote 9).

      ¹⁹ Walker, Companion, p. 249n.

      ²⁰ Evidently searching through the WTC, Protopopov (Polifonia, p. 39) settled upon the fugue subject I/16 in G minor, transposing it to D minor. The fact that Protopopov must have considered and rejected the B flat minor works from the WTC shows once more how covert was Chopin's derivation.

      ²¹ Ernst Oster, "The Fantaisie-Impromptu: A Tribute to Beethoven" (in David Beach, editor, Aspects of Schenkerian Theory, New Haven: Yale University Press, 1983, Appendix, pp. 189-207; reprint of the original in Musicology 1 (1947), pp. 407-429). I thank Roger Lustig for drawing my attention to that paper.