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Opposition as a guiding principle for performance in J.S. Bach’s Die Kunst der Fuge Florence, Dominic 2006

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OPPOSITION AS A GUIDING PRINCIPLE FOR P E R F O R M A N C E IN J. S. B A C H ' S DIEKUNSTDER FUGE by DOMINIC FLORENCE B.Mus., The University of Western Ontario, 2000 M.Mus., The University of Southern California, 2002 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF MUSICAL ARTS in THE F A C U L T Y OF G R A D U A T E STUDIES (In Piano) THE UNIVERSITY OF BRITISH COLUMBIA April 2006 ©Dominic Lewis Florence, 2006 Abstract In standard fugal analysis, too much time is spent naming sections and simply describing events as they occur. The misleading labels (such as "episode") create problems by implying levels of importance where none exist. These analyses will only hinder performances by emphasizing form instead of process. Also, the variety that is possible between different fugues is not suggested by textbook analyses; in fact, they attempt to fit each fugue in to one specific mould. By studying Contrapuncti 1, 2, 3 and 5 from J. S. Bach's Die Kunst der Fuge, this document will show that greater understanding of each fugue can be gained by a different method of analysis. This new analysis will focus on processes and rates of change in rhythmic density, modulatory sections, and other aspects that provide insight to levels and changes in intensity (for example, the harmonic reinterpretation of each statement of the subject). A more sensitive approach to distances between keys and the affects of contrast will also be discussed. To achieve insight to these disparate elements, the all-encompassing notion of opposition will be used. Opposition is a basic concept that can be applied in many ways and on many different levels simultaneously. A l l of the conclusions drawn will be directed toward establishing a perceptive performance of fugue. Table of Contents Abstract . . . . . . . . . . i i Table of Contents . . . . . . . . . i i i List of Musical Examples . . . . . . . . iv List of Figures. . . . . . . . . . vi Preface . . . . . . . . . . vii Acknowledgements . . . . . . . . . viii Dedication . . . . . . . . . . ix Introduction . . . . . . . . . . 1 Contrapunctus 1 . . . . . . . . . 9 Contrapunctus 3 . . . . . • • . 2 0 Contrapunctus 2 . . . . . . • . . 29 Contrapunctus 5 . . . . . . . . . . 3 8 Tonal Opposition Between Contrapuncti 1, 3, 2, and 5 . . . . 4 6 Conclusion . . . . . . . . . . 50 Notes . . . . . . . . . . . 53 Bibliography . . . . . . . . . . 54 i i i List of Musical Examples Example 0. J. S. Bach, Das Wohltemperierte Clavier, Il/vi, mm. 16-19 . . 6 Example 1. J. S. Bach, Die Kunst der Fuge, Contrapunctus 1, mm. 1 - 1 1 . . 9 Example 2. Contrapunctus 1, mm. 16-24 . . . . . . 1 2 Example 3. Contrapunctus 1, mm. 33-40 . . . . . . 1 4 Example 4. Contrapunctus 1, mm. 45-53 . . . . . . 1 5 Example 5. Contrapunctus 1, mm. 64-73 . . . . . . 1 7 Example 6. Contrapunctus 3, mm. 1-10 . . . . . . 2 0 Example 7. Contrapunctus 3, mm. 19-22 . . . . . . 2 2 Example 8. Contrapunctus 3, mm. 23-26 . . . . . . 2 3 Example 9. Contrapunctus 3, mm. 31-34 . . . . . . 2 4 Example 10. Contrapunctus 3, mm. 51-54 . . . . . . 2 5 Example 11. Contrapunctus 3, mm. 47-50 . . . . . . 2 6 Example 12. Contrapunctus 3, mm. 43-46 . . . . . . 2 6 Example 13. Contrapunctus 3, mm. 55-58 . . . . . . 2 7 Example 14. Contrapunctus 3, mm. 63-67 . . . . . . 2 7 Example 15. Contrapunctus 2, mm. 17-23 . . . . . . 3 0 Example 16. Contrapunctus 2, mm. 24-28 . . . . . . 3 2 Example 17. Contrapunctus 2, mm. 34-38 . . . . . . 3 3 Example 18. Contrapunctus 2, mm. 44-53 . . . . . . 3 4 Example 19. Contrapunctus 2, mm. 69-84 . . . . . . 3 6 Example 20. Contrapunctus 5. mm. 1-6 . . . . . . 3 8 i v Example 21. Contrapunctus 5, mm. 29-38 . . . . . . 4 0 Example 22. Contrapunctus 5, mm. 44-57 . . . . . . 4 0 Example 23. Contrapunctus 5, mm. 34-43 . . . . . . 4 1 Example 24. Contrapunctus 5, mm. 63-71 . . . . . . 4 2 Example 25. Contrapunctus 5, mm. 86-90 . . . . . . 4 3 v List of Figures Figure 1. Comparison of tonal remove over time in Contrapuncti 1, 3, 2, and 5 . 49 vi Preface I feel there is reluctance on the part of pianists when it comes to playing Bach. As students, we are generally afraid to offend people such as teachers, jurors, and the composer himself. There are seemingly too many possibilities of performance and the choices are almost endless. Instead of feeling burdened by all of the decisions to be made, we should be content with the freedom that it entails. We can explore the music while not being constricted by our means of expression. With no implied barriers in mind that arise from an apprehensive approach, we can more easily convince ourselves and our audiences. This document attempts to provide some guidance by describing fugue in a less hierarchical fashion. It is certainly not meant to illustrate the only method of achieving a convincing performance, as there are many other facets of performance that need to be considered. Also, by writing this thesis I am not implying that other analyses are wrong; I am merely trying to derive new possibilities through flexible analysis. My analysis is neither technical, nor absolute. I try to use basic, direct and simple means of discovering what is in the score. The fundamental idea of opposition as a generator of interest and evolutionary drive is applied to many elements of composition, in an attempt to provide an underlying principle. It is meant to encourage individual thinking and individual interpretation. This information can help to provide us, as performers, with rational options. We need not fear our choices when our reasoning is logical. Acknowledgements I would like to acknowledge my research advisor Dr. Gregory Butler for his advice, editing and guidance in the preparation of this document. I would also like to thank my piano teacher, Jane Coop, for her commitment to her students, the endless encouragement I have received and for helping me to better myself as a performer. viii Dedication I dedicate this document to my parents, John and Catherine. Their love is the cornerstone of my life. ix Introduction Most analyses, rather than giving insight, merely provide a direct, measure-by-measure account of a given fugue. Donald Francis Tovey's A Companion to "The Art of Fugue " is a perfect example in dutifully specifying each entry of the subject along with the key and voice in which it appears. The episodes are referred to only in passing, usually as interludes between entries of the subject. The labeling of each entry of the subject and the cataloguing of episodes is misleading in that it gives only a skeletal synopsis. Implicit in such an approach is a hierarchy of importance — statements of the subject are elevated above the episodes which are seen to function merely as fillers between expositions. But simply taking into account such parameters as the harmonic rate of change (the speed at which the local tonality changes), reveals episodes to be more unstable and hence, more laden with tension than the more tonally stable segments in which the subject is being stated. Episodic material, besides leading the music to new keys, often showcases textural contrast as well as intensification of the subject by fragmentation. The term "episode" then, is seen to be highly unsatisfactory, i f for no other reason than it implies a break in the discourse and a relaxing of tension when in fact, what takes place is precisely the opposite. Analyses are essential for anyone embarking on a performance of a fugue of Bach's. But those perpetuated by the academy, like Tovey's, provide only a synoptic framework; one must look elsewhere, to find relevant analytical models, both in contemporary theoretical discourse as well as in treatises from the time of Bach. Present day analyses can be divided into two groups ~ those which are purely theoretical in 1 nature and those which focus on questions of performance practice. Daniel Harrison presents an extremely thorough exploration of the fugue from Bach's G-minor toccata B W V 915 but he fails to pursue the significance of his analytical findings for performance of the work in spite of his declaration that "composers design music for performance, building within their compositions rhetorical artifices that make sense and become effective only in performance."1 Likewise, Hans Heinrich Eggebrecht's fugal analysis takes him into the realm of symbolic speculation. Chromaticism is explained in exegetical terms as "the sinful and troubled condition of the human soul," but the actual projection of such passages in performance is left to speculation. For an example of fugal analysis from the point of view of the performer, one has Ralph Kirkpatrick's Interpreting Bach's "Well-Tempered Clavier". Although he spends more time on analysis of the preludes than the fugues, in presenting several different approaches to interpreting Bach at the keyboard, Kirkpatrick directly relates his analysis to performance. But even here, an all-encompassing approach to the interpretation of fugue is lacking. What is needed is a general analytical approach that is flexible enough that it can be adapted to fit any fugue, but at the same time directly applicable to its performance. A study of rhetoric and its application to music will prove useful. Rhetoric has a long history, both generally, as a tool for musical analysis and specifically, in elucidating the structure and technique of fugue4 As one of the three subjects of the Medieval arts curriculum (the trivium), rhetoric was taught along with grammar and logic in schools so that Bach and his contemporaries would have been very familiar with it. As the art of persuasion and the basis of oratory and along with its sister art logic, of argumentation, it 2 is reasonable to assume that it influenced a music whose power lay in expressing the passions convincingly. Fugue was considered to be highly intellectual but also highly expressive and its interpretation as a musico-rhetorical genre is well-founded in writings of the Renaissance and Baroque. The five branches of rhetoric are: memory (memoria), invention (inventio), disposition (dispositio), elaboration (elaboratio, elocutio), and delivery (pronuntiatio). The third of these (elaboration or elocution), the filling out of the unadorned structure by the use of rhetorical figures and tropes, is the basis for most of the present discussion. This follows the trend beginning in late Renaissance music theory of relating rhetorical tropes and figures to techniques of musical composition. The intention here is to present an analysis based on a group of techniques related by theorists of the late Baroque with rhetorical figures of opposition. Musico-rhetorical opposition as it applies to fugue can be broken down into the following musical procedures.5 Contrary Motion The first and principal of the musical elements of opposition listed by the German theoretician Johann Mattheson, melodic inversion, has direct implications for fugue. His example, consisting of a melodic phrase with text, which is inverted note for note and set to a text with the opposite meaning, parallels closely the inversion of the subject of a fugue. Besides such opposition by contrary melodic motion which is horizontal, the simultaneous juxtaposition of melodic phrases moving in opposite directions is just as important. Contrary Time Marpurg in his reference to "imitation on opposed or mixed parts of the measure, 3 imitatio per arsin et thesin or in contrario tempore" is describing a particular approach to syncopation in which an initial entry of a subject on the strong downbeat is imitated in canon by a subsequent entry on the weak upbeat. In his definition of the musico-rhetorical figure climax (gradatio), Johann Gottfried Walther uses the same terminology as Marpurg, per arsin et thesin, in referring to a canonic sequence. In both cases, strict contrapuntal imitation is involved but any two-part counterpoint in which one part is unsyncopated and the other is syncopated creates the same effect of musico-rhetorical opposition. Juxtaposition of Opposites The juxtaposition both contrapuntal (vertically) and melodic (horizontally) of contrasting musical passages is another type of opposition referred to by theoreticians. A specific application of this aspect of opposition to fugue is the juxtaposition of a subject and a contrasting countersubject. Mori tz Vogt, Meinrad Spiess, and Johann Adolph Scheibe all see this fugal technique in terms of musico-rhetorical antithesis. However, the same figure is defined as the horizontal juxtaposition of highly contrasting passages referred to by Walther as "foreign passages" and Mattheson as "strange seeming passages." Tonal Opposition Mattheson includes "change of tonality" in his list of elements of musico-rhetorical opposition. This can entail the immediate juxtaposition of passages in contrasting tonalities as, for example in the initial statement of the fugue subject in the tonic (dux) followed immediately by a statement in the tonic (comes). Mattheson likens these to "two principal combatants" (zwei Hauptkdmpfer), the analogy arising out of the 4 fact that "this succession or accompaniment occurs in different keys, ... thus expressing a certain rivalry." The same opposition with its resulting tension is created on the larger scale of an entire movement by the modulation from one key to another, a tension which is underlined by analysis of sonata form by theorists today. This idea of long-range tonal opposition and its resolution by a return to the home key is referred to by Mattheson in his reference to conciliatio modorum as the process of "bringing itself [foreign key] into agreement with the key: because it had, as it were, fallen out with it over some matter." Harmonic Opposition The opposition created by sharp dissonance between two voices is related by a number of theorists, among them Brossard, Mattheson, and Spiess to musico-rhetorical opposition. For Brossard, "opposition is when one places something against another although this is not naturally its place ... above all in the preparation of cadences where one places by opposition the 6 t h thus 6s" while for Mattheson, "opposites can be expressed in music ... through intervals which run against one another," while according to Spiess, "opposition occurs whenever ... dissonances are set against anticipated consonances." In addition, there are other kinds of opposition to be considered. Contrasting registers create opposition, vertically between two voices or horizontally between passages where there is a shift of the entire musical texture to a contrasting register. Texture is also an important element, as changes in the density can be considered in terms of musico-rhetorical opposition. There is a precedent for the kind of analysis of fugue, and more specifically the fugues of J. S. Bach, approached through musico-rhetorical opposition that is embarked 5 upon in this document. In his Abhandlung von der Fuge (1753)6 the German theorist Marpurg, in his analysis the D-minor fugue from Das wohltemperierte Clavier, II comments on the passage at mm. 17-18 as follows: The alto takes it [the subject] up at that point in contrary motion a quarter note later and therefore on the weak beat (arsi). The bass follows in the same motion by means of close imitation. The discant also seems to be willing to engage in this dispute ..."7 Example 0. J. S. Bach, Das Wohltemperierte Clavier, Il/vi, mm. 16-19. —m. m ^ T f 1 I 5 -m m r 0 - r i f For Marpurg, the main source of opposition here is clearly the entry of the subject at m. 17 in stretto on the weak upbeat and therefore in contrary time. In addition, the subject is inverted here, thus setting up opposition by contrary motion horizontally on a large-scale structural level. The opposition he refers to in the discant involves the statements of a fragment from the incipit of the fugue subject in contrary melodic motion both on the large scale of recta versus inversa entries and on the small scale as immediate juxtaposition of recta and inversa fragments in close succession. An important aspect of this opposition in the discant is also harmonic since the statements introduce diminished fifths into what is otherwise a consonant environment. 6 There are other elements of opposition setting up conflict in this passage. The truncated version of the subject here is clearly divisible into two segments in opposition to one another, one consisting of triplet sixteenths and the second made up of longer eighth note values. The opposition between these segments is clearly rhythmic but also involves the horizontal juxtaposition of ascending diatonic and descending chromatic melodic progressions. This example shows that different types of opposition appear concurrently, and therefore, that the rhetorico-musical process of opposition is both complex and multi-layered. Opposition also exists on a structural level involving an entire work and here the third branch of rhetoric, disposition comes into play. As a musico-rhetorical genre the fugue comprises only the last four sections of the disposition scheme - proposition (propositio), refutation (refutatio, confutatio), confirmation (confirmatio), conclusion (conclusio, peroratio) - and for theorists the second of these, refutation, is linked closely with opposition. For both Christoph Weissenborn, a leading German rhetorician of the late Baroque and Johann Christoph Schmidt, the first composer to explicitly link the rhetorical disposition scheme to fugue, opposition (a contrario, oppositum) is mentioned first as the rhetorical element basic to refutation. This is logical since in this section of the oration arguments are raised against the proposition. Since the third section, confirmation, involves the resolution of these arguments by counterarguments, it also involves opposition, in this case to opposition in order to resolve the conflict. For both these reasons these two sections of the musico-rhetorical oration are linked and were often subsumed by rhetoricians under the rubric contentio, a term which underlines the argumentation through opposition which characterizes this segment of the disposition 7 scheme. Musically, this involves the creation of tension and conflict through opposition and its subsequent resolution, a concept which will be central to the treatment of fugal structure presented here. Finally, the sequence of statement of a proposition, opposition to the proposition and the resolution of the conflict set up by that opposition, and the restatement of the proposition as having been proved, manifest in the musico-rhetorical disposition scheme propositio, refutatio, confirmatio, conclusio and applicable to a single fugue, can be applied on an even larger scale to extend through a series of fugues linked as a group. In the analysis which follows, this macro disposition will be applied to Contrapuncti 1, 3, 2, and 5 of J. S. Bach's Die Kunst der Fuge. 8 Contrapunctus 1 Contrapunctus 1 has a special function -- to introduce simple material in a manner that can eventually be elaborated in more complex ways. Bach has the uncanny ability to write subjects that are highly flexible and the opening subject that drives the entire Die Kunst der Fuge is no exception. What makes the first fugue so special is that while it dutifully presents a simple fugue from every analytical viewpoint, it also manages to create interest on the foreground and background levels. Not only are there no entries of the subject in stretto or inversion, in fact, there is no entry in any key but the tonic or dominant and no other key is introduced but the subdominant. Also, the first four statements of the subject enter one after the other without a break and the next four entries appear in the same voice order. The only departure from this striking regularity is provided by the abbreviated entries of the incipit of the subject at mm. 29-30, 48, and 55 which hint at stretto. This brief discussion of the entries of the subject, while it reveals a simple and rather regimented plan, neither presents an explanation of the deeper substance of the piece, nor does it offer suggestions for a cohesive performance. First, the subject itself needs to be dissected. Example 1. J. S. Bach, Die Kunst der Fuge, Contrapunctus 1, mm. 1-11. r *r r r ' I - E L F — a ^ { [ [ E2: arc? 3p£ 9 ""* O r f r I'c "r n It is truly simple, yet exceedingly effective. It can be broken down into two two-measure segments (the second segment is actually occupies two measures plus the downbeat of a third measure). The first segment presents an arpeggiation of the tonic chord beginning and ending on the first scale degree. It can be thought of as a very local presentation of the departure and return scheme — one of the basic tenets of tonal music. Also, each interval between successive notes is larger than a second in contrast to the second segment in which no interval between successive notes is larger than a second. The intervallic opposition set up between the opening and closing segments of the subject plays a very important role in this fugue. The performer must be sensitive to the size of each interval and to the dominating interval class not only in these two segments but in each and every passage in a fugue. Bach thus raises the issue of opposition right away in the first statement of the subject. Since, it is the combination of the subject with the counter subject which constitutes the "contrapunctus," the countersubject is a vital component both in setting off the subject and in giving each fugue its own character. Many fugues have countersubjects which appear in combination with the subject at each entry. These counter subjects (as noted in the Introduction) change the affective impact of the subject depending on whether or not they are in conflict with it. The countersubject in Contrapunctus 1 is less remarkable in this respect than in other of the contrapuncti. It does not appear with the subject at every entry, it sometimes is shared between two 10 voices, and often the melodic structure is altered. What is more important is the formation of the countersubject during its first appearance at m. 5 in the alto. As with the subject, this countersubject is broken down into two distinct halves, each two measures long (see Example 1, alto, mm. 5-8). While the subject involves intervallic opposition, the countersubject utilizes rhythmic opposition. In mm. 5-6, the countersubject with its regular quarter-note pulse is in rhythmic accord with the subject. The second half in mm. 7-8 is syncopated and thus, in rhythmic opposition to the subject. The divison of the countersubject into unsyncopated and syncopated halves (rhythmic accord versus opposition) coincides with the intervallic opposition between the two halves of the subject and thus underlines it. Besides this underscoring of the horizontal opposition already introduced with the first entry of the subject, simultaneous vertical opposition is introduced, both rhythmic and harmonic, as a result of the dissonant intervals engendred by the syncopation. Bach uses syncopation as a device for producing rhythmic opposition between the subject and another part throughout this fugue. Notice, for instance, the syncopation of the soprano through mm. 9-12 during the entrance of the subject in the bass. On the other hand, it should be noted that syncopation and the rhythmic conflict between subject and countersubject are perhaps not quite so acute as in Contrapunctus 3 where a fuller discussion is warranted. For the lack of better terminology, the word "episode" will be used here to refer to any part of the fugue where no subject entry is present in any voice. However, it must be stressed again that episodes are by no means secondary; they often provide greater harmonic interest, heightened textural contrast and lead the fugue in new directions. The episodes in the first contrapunctus contribute in many ways to the overall growth of the 11 fugue, and at the same time echo and extend the opposition noted between subject and countersubject. The first episode (mm. 17-23) revolves around smaller intervals — the major and minor seconds of the second half of the subject. In mm. 17-20 the upper two parts of this three-voice structure constitute a canonic sequence in which the tenor imitates the soprano at the lower seventh at the distance of a half measure. The sequential unit in each voice rises by a third at each repetition. Example 2. Contrapunctus 1, mm. 16-24. 16 )4=i y J 9 0 * — • — # -Tr- cjir rr*r rn — The result of this is one of the most intense dissonant combinations in the entire fugue with the clashing of ninths and sevenths which are resolved by the upward leaps of a fourth. The lightly ornamented rising quarter-note chromatic scale in the bass is in sharp intervallic opposition to the upper voices. Taken in combination, the half notes which alternately appear in one of the two canonic voices rise by step (ninth in octave transposition) starting with the A in the tenor on the downbeat of m. 17 and concluding with the G in the tenor on the downbeat of m. 20. After reaching this high point, the canon between the upper voices is broken and the episode descends by step through the interval of a seventh. At the same time, the bass voice in this measure gains prominence, completing the ascent by step between the tenor and soprano with the A on the downbeat of m. 21. This note acts as a strong dominant preparation (it is transferred an octave higher to the soprano a measure later) for the beginning of a new series of entries of the subject starting in m. 23. The element which gives such prominence to the bass voice at the end of m. 20 is the dissonant interval of the diminished fifth on the fourth beat (D to G-sharp). From the middle of m. 17, every eighth note movement is by major or minor second. This descending tritone in the bass at m. 20 is quite clearly in opposition to the ascending chromatic scale immediately preceding it. A logical performance of this episode will need to encompass all of these points. Identical treatment of each statement of the sequential unit in soprano and tenor is necessary in rendering audible not only the precipitous rise at mm. 17-20 but the grinding dissonances with their resolutions. In addition, the tritone in the bass at m. 20 will need careful attention in order for the listener to appreciate the new turn of events harmonically. Clear articulation is of utmost importance here; the repetitions of sequential units played with exactly the same touch with a new touch for the tritone will bring out the drama of this episode for the audience. The next episode (not counting the very short episode at mm. 27-28) continues to build on this aspect of opposition in intervallic relationships. This episode beginning in m. 36 presents the same canonic sequence as the first episode. The canon now appears between the bass and alto at the upper ninth. However, the free voice (soprano) is in marked contrast to that in the first episode. Notice especially the prominent ascending sixths followed by falling fifths to each downbeat starting with the pickup to m. 37. This 13 seemingly minor change makes quite an audible difference in diatonicising the rising chromatic scale in the free voice of the first episode. Example 3. Contrapunctus 1, mm. 33-40. Here the episode terminates after four measures, that is, without the descending sequential segment which concludes the first episode and the subject enters abruptly in the tenor. While these two episodes (mm. 17-22 and mm. 36-39) employ the identical canonic sequence, they are actually quite unlike each other. They oppose each other in their harmonic goals, intervallic relationships and melodic contour. By m. 35 the fugue has come to the point of furthest remove tonally. Given the fact that it does not stray far from tonic and dominant, the move to another tonal centre at this point is striking and all the more so given the dramatic entry of the subject in the bass in stretto at m. 32. With its radical melodic alterations, the music is wrenched from the tonic into the subdominant. This point in the fugue also marks the beginning of dramatic, audible heralding of subject entries. There are longer rests before nearly all of the remaining entries, increasing the listener's anticipation. Further underlining this pivotal point is the forceful entry of the subject in the tenor at m. 40. It is the texture here which 14 is notable for it is the first time in the fugue that all the voices are present for every note of the subject. One final significant detail with regard to this episode is that the climax reached on the downbeat of m. 40 happens to be the exact mid-point of the fugue. Although this may not have been planned by Bach, given the confluence of so many significant features at this particular point in the fugue, such a conclusion is inescapable. At m.48 (as later at m. 55) there is a false entry of the subject. The first two notes of the subject enter in the alto, but the second is suspended and resolves to a half cadence in the tonic at which point it is interrupted by the entry in the soprano. Example 4. Contrapunctus 1, mm. 45-53. •Lyr~CrMc.rf~trr J- M J i illi Li" i CJ r ,pi T One experiences the entry of the subject in m. 48 as a logical place to begin a new statement after four measures of episode. Because it is delayed for a measure there is a certain amount of tension and ambiguity surrounding the soprano entry. The harmonic context of this entry adds further to the tension for instead of entering in the tonic harmony as expected, the subject here enters in the dominant. Taken together, all of these things serve to delay the return to the tonic. In a fugue that barely moves away from the home key, all other factors involving anticipation and of undermining a sense of tonic 15 confirmation are carefully controlled. True affirmation of the tonic key (and resolution of harmonic opposition) arrives only at m. 56 with the now eagerly anticipated bass entry of the subject in the tonic. The sense of anticipation is even further heightened as the bass has dropped out for almost seven measures, the first time since the opening of the fugue that it has fallen silent for more than one measure. Since the bass is the acoustic foundation for the overtone series, its absence lends to a sense of thinness and loss of groundedness so that when it finally enters, the sudden fullness and sense of relief is almost palpable. This leads to interpreting this entry harmonically as initiating the conclusion of the fugue for it restores the original harmonic interpretation with a minimum of chromatic colouring. For the moment, the harmonic conflict seems to have been resolved. The episode at mm. 60-73, by far the longest in the fugue, breaks down into three distinct segments. In the first, the approach to the dominant pedal at m.63, the outer voices move precipitously in contrary motion — the most blatant and dramatic use of this particular type of opposition in the fugue. In the second segment, for three measures over the pedal in the bass the soprano presents a descent by step with syncopation at the quarter-note level thus increasing the rhythmic opposition to a higher plane. Finally, this final episode concludes with a third statement of the four-measure canonic sequence stated previously at mm. 17-20 and mm. 36-39. In this final statement the canon is at the upper sixth and thus, far less dissonant so that it represents a clear resolution of the intervallic opposition in the first two statements. The passage at mm. 64-73 presents the most dense music heard thus far. Not only is it the first time all four voices have sounded together in an episode but also, the attack 16 density has increased, that is, there is a sudden flood of notes of shorter duration. Thus while there is a resolution of the tonal conflict built up during the fugue at m. 56 with the forceful and long-anticipated tonic entry at that point, on another level of analysis the fugue is still arriving at its motoric climax at mm. 67-70 with the heightened rhythmic drive and greater attack density. Example 5. Contrapunctus 1, mm. 64-73. There are two seemingly divergent, but ultimately compatible, ideas at work in Contrapunctus 1 — simplicity (or regularity) and organic growth. The fugue reflects simplicity in various ways. The first four entries of the subject are stated without a break and most appear at anticipated junctions. In other words, there are no hidden entries and almost all entries are heralded by long rests; there are no syncopated or rhythmically altered statements of the subject nor does augmentation or diminution of the subject occur. There is only a hint of stretto. The episodes, three of which are based on the same two-voice canonic sequence, are also models of simplicity, each with an unwavering drive toward the next subject entry. Perhaps the simplicity of this fugue is at its most audible in its tonal scheme and harmonic combinations. Rarely does the tonality stray 17 from the tonic or dominant and chromatically dissonant notes are carefully prepared, controlled and resolved. This simplicity serves to complement and even to highlight the levels of opposition at work in the fugue. Rhythmic, harmonic, melodic conflicts as well as those of density — all are in flux here. In performing the work, one must explore the ebb and flow of these oppositional parameters and interpret the appropriate degree of tension in each case. The work is as notable for its organic growth as it is for its simplicity. There is a general increase in the number of voices heard at any given point with no rests longer than one measure's duration in any voice beginning in m. 56. During the course of the fugue, the voices gradually begin to move more closely in tandem with each other rather than in opposition. The fugue also increases in rhythmic density as it unfolds. The music then, is always building upon itself, taking into account all that has come before. A perceptive performer of Contrapunctus 1 would need to be aware of these concomitant processes. It must be made clear that the ideas presented are simple in nature but that they build organically in the course of the fugue to a convincing conclusion rhetorically. A performer could conceivably focus on small motives, making sure that all similar motives are presented with a controlled articulation and intention (taking in to account the context of each motive). The intervallic opposition in the subject between large and small intervals could be shown in such a way as to make it the focus of attention. These minute details would then drive the music and create a larger impression of the fugue. Conversely, a performer could start by imagining the piece in three broad sections, each with its own goal. Then the planning could continue by exploring the details that arise out of visualizing the larger sections. 18 A n y performance of this fugue also requires an awareness of its place in the large-scale projection of opposition and its resolution in Die Kunst der Fuge as a whole. Since this is the very beginning of this project, one could imagine a performance presenting the material in a relatively dispassionate manner giving only hints of the processes of opposition at work in the cycle. Bach has laid out this fugue so convincingly and with such a sense of inevitability, that over-emphasizing the ebb and flow of the music may detract from its inherent intensity. The performer might well decide to set aside overemphasis of the conflict and let the fugue live and grow by itself. 19 C o n t r a p u n c t u s 3 In Contrapunctus 3 new levels of opposition emerge. Progressive alterations of the subject, textural density in the episodes, and continuous growth of chromaticism almost to the end of the fugue, all contribute to the building of intensity. A recurring countersubject controls much of the new opposition projected and even penetrates into the episodes. Further, the simple four-note upbeat motive which concludes the subject saturates the music. The reason for Bach's originally having placed Contrapunctus 3 before Contrapunctus 2 in the earlier manuscript of Die Kunst der Fuge, will begin to become apparent in the course of analysis of this fugue. It is necessary to begin by discovering the internal conflict in Contrapunctus 3 while keeping in mind that this fugue has many features that place it in direct opposition to Contrapunctus 1. The melodic inversion of the subject in Contrapunctus 3 has the effect of creating a mirror image of the melodic contour with the mid-point of the subject the highest note, rather than the lowest. A very basic form of opposition, it sets all the expository material in this fugue in opposition to that in Contrapunctus 1. Example 6. Contrapunctus 3, mm. 1-10. 20 Importantly, the sequence of entries in Contrapunctus 3 (dominant-tonic, dominant-tonic) reverses that in Contrapunctus 1 and in doing so acts in tonal opposition to it. The dominant entries are unstable tonally, modulating in both cases back to D minor for the stable tonic entries in the episode. Along with the C/C-sharp juxtaposition in the second and fourth measures of the dominant entries, this highlights the internal tonal conflict between the pairs of entries. Counter subjects, by their very nature, are placed in conflict with the subject and the interaction between these two voices is at the very heart of fugal writing. Whether the voices are in conflict with one another is a crucial factor in creating the tension, drive, focus, and ultimately, the interest in a performance. The recurring countersubject in Contrapunctus 3 is the essence of opposition (see Example 6, tenor, mm. 5-9). While the subject relies on diatonic intervals, the countersubject is highly chromatic and dissonances between the two voices created by this chromaticism are quite clear. At the same time the countersubject is strongly syncopated and thus in direct rhythmic opposition to the subject. For all of the opposition, there is agreement as well. The general melodic contour of each voice is similar (first a descent, followed by an ascent, and so on). Significantly, much of the conflict generated is resolved by m. 9. The two voices share quarter notes in m. 7 and eighth notes in m. 8. Also, the chromaticism of the countersubject now turns to diatonicism in accord with the subject. A performer must be sensitive to both elements of opposition and accord between the voices and at the same time be aware of the point at which opposition is resolved. This countersubject not only reacts with and against the subject, but also prepares the listener for the chromatic disposition of the episodes. 21 In the first episode at m. 19 and repeated again at m. 39 (the preceding episodic material in mm. 13-14 occurs as a two-measure delay for the bass entry) there is a significant change in texture. Example 7. Contrapunctus 3, mm. 19-22. -rjiJ j Jv _ l;p - hm im 7 ' r t-^—U - j -V l l 4 Lr Lr Soprano and alto work in close imitation with one other. Every two measures two contrasting motives — a chromatic conjunct one derived directly from the countersubject and a diatonic disjunct one are juxtaposed vertically and then inverted contrapuntally. The effect is to create simultaneously strong vertical and horizontal opposition. The bass, also with chromatic material reminiscent of the countersubject, is very separate in the lower register and thus removed from the conflict between the alto and soprano. This is somewhat suggestive of a trio sonata, where two upper voices converse over an impartial bass. Thus Bach, while evoking a completely different style of writing, manages to adapt it into a strict fugue. This new texture brings about yet another kind of opposition. The trio sonata episodic material creates textural opposition and since structurally it occupies a central position, it contributes as departure to the tripartite scheme of statement, departure and resolution. At m. 23 in the soprano a syncopated form of the subject appears in which the strong stresses on the half-note downbeats have been shifted off the beat. At the same time eighth-note passing tones fill in the thirds of the broken triad. The rhythmic shift is 22 blurred because the effect of the offbeats in mm. 24 and 25 is defused by the passing notes. The true downbeat is restored at m. 26 through the diminution of the two preceding pitches, A and G. While the subject is displaced by one quarter note, the countersubject is presented in its original syncopated form. Thus at m. 23, instead of working against one another as in the opening exposition, the two now work together. At the same time, by eliminating most of the larger intervals and introducing a dotted rhythm, the inherent disjunct/conjunct opposition between subject and countersubject has been eliminated and as a result the performance of the subject must change, giving way to a more flowing and less stolid interpretation. Example 8. Contrapunctus 3, mm. 23-26. 2 • F 3 r c r In performance, the syncopation of subject and countersubject must be clearly projected without a strong articulation on the second beat of m. 23. Due to the accord between varied subject and unvaried countersubject this temporal displacement is even more apparent. This working together, while it implies a lessening of opposition locally, generates conflict on the macro scale. The three syncopated statements of the subject at mm. 23, 29, and 35 acting as they do in opposition to the non-syncopated statements preceding and following them, support the scenario of a large-scale musico-rhetorical statement, departure, resolution disposition scheme at work here. The four-note motive (hereafter referred to as motive X) which concludes the subject dominates much of this fugue. (See Example 6, the last three notes of m. 4 and 23 downbeat of m. 5 in the tenor). It is a simple upbeat scalar motive in eighth notes, but it forms the basis of dramatically and structurally important gestures and creates heightened opposition in this fugue. Motive X permeates the countersubject almost entirely. The countersubject can be seen to be made up of three statements of X , as well as several other motives suggestive of the scalar upbeat figure. The permeation is at its most intense at the end of the countersubject, when motive X appears twice in succession and in vertical juxtaposition with the end of the subject. This motive acts as an important modulator of intensification throughout the fugue. From m. 26 motive X , in both its descending and ascending forms, begins to permeate the texture of the fugue, first juxtaposed horizontally for the most part. This turn of events is marked by the most dramatic episode of the fugue. Beginning with the upbeat to m. 27, three statements of the descending form of motive X emerge in the bass. Each repetition appears a fourth lower at each repetition and with vehement trill figures on the downbeat arrivals. The third descent occurs in the bass leading to the downbeat of m. 27 and the music plunges down to G-sharp. The music has been torn away from D minor and thrust into the dominant, A minor, in a matter of moments by this precipitous descent. Beginning in the episode at m. 33 there is an intensification as the descending and ascending forms of motive X are juxtaposed vertically in pairs of voices every two beats. Example 9. Contrapunctus 3, mm. 31-34. 1 =]- — i « ~ L f ' is f-ji —y.Lj _ J ^ » r — fT •0- ^= rr 'W \'{- rjrr- Ptf -^ Ir"—1 24 The contrary motion set up, both horizontal and vertical, increases the conflict and draws the attention of the listener to this important departure phase of the fugue. The intensification of contrary motion here at the mid-point of the fugue and repeated nowhere else affects the rest of the fugue. Although motive X is employed in all voices at other points in the fugue, in these cases at least two of the voices work in parallel motion which tends to damp down rather than to kindle opposition. Toward the end of the fugue at measure 51 in conjunction with the entry of the subject in the bass, there is a precipitous ascent in the soprano with three statements of the ascending form of motive X continued by the second half of the countersubject. Example 10. Contrapunctus 3, mm. 51-54. 1 i 7 f -r This impressive gesture parallels the earlier descent in the bass both in its overall dramatic effect and also functions as an important structural articulator in preparing for the return to D minor in m. 55. While important structural divisions are often delineated by major cadences, it is notable that in fugue other elements such as exclamatory motivic outbursts may function as articulating agents. Starting in m. 47, there is an almost complete saturation of the music by motive X as it is taken up by all four voices. The intensification here is precipitated by the increase in rhythmic density. More statements of motive X with the attendant opposition (by now mainly horizontal rather than vertical) between ascending and descending forms leads to and is resolved by the aforementioned passage at m. 51. The performer may begin to feel 25 saturated by this motive as well. However, one must remember that Bach was not using these motives carelessly but in a very controlled way, and his attempt to sway the listener should not be played down in performance. The music demands intensification, and the distinct articulation of this motive each time it appears is an essential part of this process. Example 11. Contrapunctus 3, mm. 47-50. w. m The intense chromaticism involved in Contrapunctus 3 is one important element not concentrated in the middle of the fugue. Instead of the markedly symmetrical placement of elements of textural, rhythmic, and melodic opposition, the dissonance and harmonic instability arising from chromaticism seem to increase almost to the end of the piece. The return of the original form of the subject at m. 43 follows the entry at m. 35 in F major which, harmonically speaking, is at the point of furthest remove. One would expect a more stable entry to follow and indeed, the entry itself clearly defines A minor, and unlike the dominant entries at the beginning of the fugue it does not modulate. Example 12. Contrapunctus 3, mm. 43-46. it y fJrt " »c!f'rifr 'rr ' r -i k \ ' ^ i / i r 7 i V j i However, this apparent return to tonal and expositional stability is undermined, not only by the ever present chromatic countersubject, but by the other accompanying voices 26 which grows out of the preceding chromatic episode. The instability constantly generated by pervasive chromaticism continues as the true return of the tonic key is delayed. A l l of the last four entries of the subject in the fugue feature the same sort of tonal instability as the opening dominant entries. Also, Bach injects an extra dash of chromaticism and rhythmic instability by means of syncopation at the quarter-note level (note the last two beats of mm. 57 and 60) and by overlapping the two entries beginning in mm. 55 and 58. Example 13. Contrapunctus 3, mm. 55-58. r p r p err X T T P 7 ^ ^ ^ J ^ J ^ ^ I J - ^ rrrrr »r ir - ^ w ^ p The final entry should be the most stable of the fugue, confirming D minor and preparing all elements for closure. Instead, the extreme chromaticism in the accompanying voices threaten to drown the subject. Example 14. Contrapunctus 3, mm. 63-67. I F In fact, only during the last five measures of the fugue is there any resolution of the tonal instability and even here, the opposition between the ascending and descending forms of motive X extends to the final cadence. Since Bach has pushed the final tonal resolution as close to the end as possible, the performer of this fugue cannot relax the intensity too 27 soon. The conflict unleashed by the pervasive chromaticism has had the affect of tonally destabilizing the entire fugue. Contrapunctus 3 represents a major departure from Contrapunctus 1 in many respects. Different kinds of opposition are utilized. While syncopation emerged in the first fugue was a subtle element, here it takes on macro-level dimensions. The syncopation of the entire subject in the middle of the fugue along with the inherent syncopation of the countersubject play crucial roles. Also, the melodic opposition built up in Contrapunctus 3 raises the conflict to a higher level, both locally and on the level of structural definition. The chromaticism intensifies throughout the fugue, pushing any sense of climax or resolve from its expected point of arrival about two thirds of the way through the fugue to the very last measures. The opposition in Contrapunctus 3 is palpable, in contrast to the modest conflict of the opening fugue in the collection. 28 Contrapunctus 2 Unlike Contrapunctus 1, Contrapunctus 2 features extensive opposition and highlights new levels of fugal process requiring a different performance. Nevertheless, the two fugues have in common a number of features marking the latter as a return after the extreme departures noted in the intervening fugue, Contrapunctus 3. It is the new approach to opposition in Contrapunctus 2 which makes it so unique. In the opening exposition, the melodic formulation and tonic-dominant-tonic-dominant sequence of entries encountered in Contrapunctus 1 reappear. However, the concluding four-note downbeat motive has been rhythmically altered — pairs of eighth notes have become dotted eighth- and sixteenth-notes. This new rhythm dominates the entire fugue and influences the interpretation of the fugue in a number of ways. The episodes in Contrapunctus 2 are half as long on average as those in Contrapunctus 1. Also, the concluding segment of Contrapunctus 2 is permeated by entries of the subject and because the episodes are so brief, it is the expositions rather than the episodes which take over the function of building conflict in this fugue. How do these fundamental differences in the two fugues affect performance? Following the initial set of four entries of the subject at m. 17, there is a six-measure episode, the same length as the initial episode in Contrapunctus 1 which also begins at m. 17 after the first set of four entries. In both cases, this initial episode ends in a strong half cadence which articulates the introductory segment of the fugue with the subsequent exposition of the subject. The half cadence in Contrapunctus 1, however, is delayed by two measures and appears at m. 25 in the middle of an entry. 29 Beyond this however, the two episodes are entirely different, and warrant contrasting interpretations. The episode in Contrapunctus 1 (see Example 2) has a rising trajectory to the midpoint at m. 20 and then falls toward the end at m. 23. The episode in Contrapunctus 2 has the opposite shape, first descending to m. 21 and then ascending toward the cadence. Example 15. Contrapunctus 2, mm. 17-23. -^FL— "•*r - j l l p. m • r N- 3 J-tPJ j—hj ll j JTii J =j —1 1 U £ T 1 This difference will strike the listener quite clearly, as keyboard instruments in general (and especially the clavichord and harpsichord) have different colours depending on the register. The textures of the two episodes are quite different. In Contrapunctus 1 the same texture is retained throughout the six measures ~ that of a trio for two treble voices working together and a somewhat independent bass. In contrast, the texture in Contrapunctus 2 changes significantly at m. 21. At the beginning the two middle voices move in parallel motion while the bass echoes them motivically and the soprano has two sustained pitches, dominant to tonic. At m. 21 the alto and tenor drop out, leaving the bass on a low sustained E; meanwhile, the soprano has quite a unique solo passage which can only be described as "cadenza like." This is highly unusual in a fugue, evoking 30 instead, the aria but it definitely underlines the strong cadential function of this episode. The contour change and the different approaches to texture in these two episodes will immediately become apparent in almost any performance. While in the first case the articulative effect of the cadence is blunted by its overlapping with the first statement of the subject in the new exposition, in the second there is a clear caesura. The performer might underline the overlap in the first case by adopting a motivic consistency through to the end, the strong articulation of the episode in Contrapunctus 2 from the subsequent exposition could be highlighted by a more intense tone or innovative articulation to highlight the soprano cadenza while a slight slackening in tempo at the cadence might underline the caesura. Consistency in articulation should aid in underlining the relation between similar motives and continuity of an idea while variation in articulation will emphasize discontinuity and change. A l l choices in articulation, dynamics, tempi, tone, etc., must be correlated to what is happening on the score or meaning will be lost. A change in articulation in the repetition of a motive for no good reason is contradictory to the projection of process and will dull the keen blade of opposition. The entry of the subject in the alto at m. 23 is disguised; the first note, E, which should fall on the downbeat coinciding with the cadence appears in the tenor an octave too low. The correct transposition then appears as the sixteenth note which begins the upbeat figure derived from the concluding motive of the subject. Although the listener will understand retroactively that an entry has taken place, it is nevertheless quite different from one that has been more prepared. The status of the subject as the fugal imitation mechanism has been weakened as the upbeat motive takes over this role with 31 imitative entries in tenor and bass. The entries of the subject in this exposition have also been weakened tonally since the key in each case becomes clear only in the second measure. With the first measure of the subject now in the dominant, the tonal stability of the subject is undermined and it can no longer be discerned in terms of the strict tonic-dominant polarity of the archetype. Thus the tonal opposition engendered by it is softened. The tonal blurring and lack of clarity is exacerbated by the alterations to the concluding upbeat motive of the subject. Since it overlaps with the tonally altered first measure of the next entry, it has been distorted in order to affect the requisite modulation. In turn, this has the effect of speeding up the harmonic rhythm in each entry of the subject. Example 16. Contrapunctus 2, mm. 24-28. • 21 dl. • 1 i — i — i Ti 1 hJ I, 'V r r t r r r ^= i • r J. J n i -i rict'i In general, the harmonic rhythm in statements of the subject in Contrapunctus 2 is faster than that in Contrapunctus 1. Instead of harmonic change once per measure, most often the harmony changes twice per measure. This raises the intensity of horizontal opposition, imparting to Contrapunctus 2 a more driven feeling. Another factor that adds to the drive of Contrapunctus 2 is the emergence of the sixteenth note as the smallest rhythmic unit in the dotted eighth-sixteenth note combinations. At m. 32 the original three-note upbeat is expanded to seven notes and imitated in contrary motion in tenor and alto after which a five-note version appears in all four voices. Both the expansion of the motive, its inversion, and its permeation of the 32 fabric heighten the opposition at this point. Example 17. Contrapunctus 2, mm. 34-38. A comparison of the point of furthest remove tonally in Contrapuncti 1 and 2 underlines the different functions of these two works in the rhetorical disposition of the collection as statement and return. Normally at this point there is a marked shift to a remote harmony and a change of texture as part of the climax of opposition in the fugue. In many of Bach's fugues, the most remote harmony is a local tonic based on the relative major or minor of the subdominant or dominant (for D minor, those keys would be B-flat major and C major). After the point of furthest remove, Bach usually sets up a strong return to the home key as the confirmation of the argument begins. The elements which lead to the climax may not coincide. For example, the most remote tonal area may be reached before the intensity of rhythmically overlapping motives has reached its peak. That is to say that opposition on different levels ebbs and flows in waves before the global resolution. Some waves are more intense and brief, while others may be sustained for many measures. In Contrapunctus 1, the point of furthest remove tonally falls at mm. 34-36, where there is a brief tonicization of G minor, the subdominant. As mentioned earlier, in Contrapunctus 1 the subject enters only in the tonic and dominant, and this brief reference to the subdominant is the only departure. However, the peak of rhythmic opposition occurs much later at mm. 64-70 (see Example 5). By staggering such 33 climactic moments, Bach avoids over-emphasizing any particular one. In Contrapunctus 2 the situation is much more complex. At the point of furthest remove in mm. 45-59, texture and weakened subject entries deflect a feeling of true climax. Example 18. Contrapunctus 2, mm. 44-53. 44 torn 1 ! • - . J r * -J - J J _ j J J * — ^ — r * r *r r -j\>m—— 1 J " l . I f r r I3J J l -• — - r r —9— —m Jj? L _ — 1 + — s — r i 1 Three entries of the subject without break in F major (soprano, m. 45), G minor (alto, m. 49) and B-flat major (bass, m. 52) take the fugue to the farthest point of remove tonally. The entries in G minor and B-flat major are weakened by beginning on a pitch not in the local tonic. The B-flat major entry is weakened further in that the first note has been lengthened to two half notes tied over the barline, thus obscuring the downbeat and disguising the entry. The permeation of the upbeat four-note scalar motive apparent in Contrapunctus 3 is absent. Instead, the downbeat motives here are twice as long, as at mm. 32-33. The articulations thus fall half as often and so the music is less disjointed and more flowing. The voices do not interrupt each other (as in mm. 35-37) and harmonically the music is more consonant. Although the fugue has reached its point of furthest remove tonally, the fluid contours of the extended upbeat scalar motives negate a sense of true 34 climax. The entries of the subject here, weakened as they are should not be attacked by the performer as the intensity level here must not be raised. This is rather a passage of an almost passive character and it serves as a foil to the driven strength of the conclusion to come. Thus, while Contrapunctus 2 certainly expands the harmonic boundaries of Contrapunctus 1, for Bach this is not an end in itself. It seems more like a moment of reflection in the course of the confirmation of the argument. In general, having arrived at the first tonic entry after the point of furthest remove tonally, a fugue enters its final stages. This concluding section can be filled with tonic-affirming entries, episodic material, or some combination of both but this occurs securely rooted in the tonic key. However, tension must be maintained so the creation of opposition within parameters other than tonality rises in importance. In Contrapunctus 1, a strong bass entry (m. 56) is followed by a long, intense episode. The confirmation of the second fugue also begins with a strong bass entry (m. 61), although there is but the briefest break in that part and the dominant preparation is minimal. This concluding entry also continues on at mm. 64-69 in much the same manner as in the first fugue, with an even more extended sequence growing out of the concluding upbeat scalar motive and descending by third at each statement with arrivals on F, D, B-flat, G, E, and C-sharp. However, instead of leading to a dominant pedal and an ensuing lengthy episode as in the opening fugue, here it ushers in a further entry of the subject in the tenor at m. 69. This statement is curious because unlike the fully syncopated entries in Contrapunctus 3, only its first four notes are syncopated while the remainder are unsyncopated. Just as the fugue as a whole can be viewed as a rhythmic resolution of the rhythmic opposition raised by the syncopated entries of the subject in Contrapunctus 3, here too on the micro level of a 35 single entry is the same resolution underscored one last time. The concluding measures leading up to the cadence are treated rather differently here than in Contrapunctus 1. In Contrapunctus 2, neither the climax in rhythmic intensity nor the concord of voices working together at the same juncture in Contrapunctus 1 is explored. Instead of rising precipitously in a restatement of the long opening episode to a dramatic exclamation at mm. 70-72, there is a sort of slow descent by step to an inconclusive cadence — not to the tonic major but to the dominant major, and in a markedly lower register. Example 19. Contrapunctus 2, mm. 69-84. 1=H -s-4 = i . ftp--'--j so til, 1 1 1= — = - ^ ^ -—rf rr~ ^ Y J r-—B = M * U m r r r I,, i j j |J J 5 3 ^ - — -uni ' " ' r > r c r j r ( -— t^cr ' r £ The dotted-note upbeat figures derived from the first countersubject generate both rhythmic and harmonic tension as the music drives even lower to the final cadence. Conflict through opposition and contrast constantly propel a fugue forward, even if it has reached its tonal goal. A performer must embrace this and plumb the rhetorical 36 conflict to the full, using them as the guiding force for a convincing interpretation. The conclusions of Contrapuncti 1 and 2 should strike the listener as a study in dynamic contrasts ~ the first emphasizing the complex of oppositional elements in the unexpected repetition of the episode in an expansive rising dynamic leading to a dramatic and conclusive full close while the second concentrates on an equally unexpected expansion of the motive which has generated rhythmic opposition throughout the fugue in a contractive falling dynamic leading to a less conclusive cadence. Significantly, the early manuscript version ends on a half cadence (a full close appears in the later print), emphasizing the idea of a link between the fugues. Contrapuncti 1 and 2 are dissimilar in several ways. The latter presents a more extended tonal departure, a stronger emphasis on the subject as a defining factor, and the much less dramatic manner in which the tonic key is finally confirmed. This is offset by the elements they share in common. The first two expositions are handled in a similar way, the tonal departure is essentially an expansion of the one found in Contrapunctus 1, in both there is no recurring countersubject, and changes in texture are minimized. A l l this is in direct contrast with Contrapunctus 3, which presents an entirely different approach to opposition with its obvious emphasis on syncopation and regular countersubject. But probably the greatest contrast is the pervasive use of chromaticism in Contrapunctus 3. It becomes more intense as the piece progresses, right to the last entry of the subject. The same degree of instability and conflict simply does not exist in the two other fugues. 37 Contrapunctus 5 In Contrapunctus 5, the subject dominates almost all elements of composition. The subject is present in all but three of the first thirty measures and in all, seventy of the ninety measures are taken up by entries of the subject. Episodes are short, averaging three measures in length, and have no clearly defined modulatory function or building of tension through opposition, serving rather as brief approaches to cadences and other articulations. That being said, though more subdued and less extensive, they do present the same sort of melodic opposition built on close imitation of the scalar upbeat motive which concludes the subject (as well as a variant in the form of a turn figure) as the episodes in Contrapunctus 3. Nevertheless, for the most part it is in the entries of the subject where tension through conflict is raised and ultimately resolved in this fugue. The main conflict here is between normal (recta) and inverted (inversa) forms of the subject and the resolution of this conflict is the focus of the fugue. In Contrapunctus 5 it is the elaborated form of the subject through the characteristic dotted quarter-eight note rhythm appearing first in syncopation in Contrapunctus 3 (mm. 23-27, 29-33, 35-39) which appears throughout. Using this form of the subject Bach is able to present entries in stretto with varying degrees of overlap. Example 20. Contrapunctus 5, mm. 1-6. Horizontal juxtaposition of normal and inverted statements of the subject for the 38 first time in the collection is the main element of opposition in the first exposition. At the same time the normal tension set up between alternating tonic and dominant entries is absent here as all four entries are in the tonic. It is unusual for entries of the subject in the opening exposition to appear in stretto, a technique reserved for the conclusion of a fugue. It has the result in general of blurring the strong articulation of subsequent entries and specifically, it takes away the strong rhythmic drive generated by the scalar, upbeat eighth-note motive which concludes the subject (see Example 20, alto, m. 4) that plays such an important role in the previous fugues. After the typically brief episode (mm. 14-16) constituting a descent by step in the soprano to a half close, there follows a second exposition (mm. 17-30) with the same alternation of inverted and normal entries of the subject overlapping by one measure. In this second exposition the first two entries are in the dominant, setting up the first tonal conflict in the fugue, a conflict resolved by the final two entries in the tonic which follow. This concludes the statement phase of the fugue and this structural point is underlined at mm. 28-32 by a precipitous sequential descent by thirds. Three paired entries of the subject in F major, G minor, and B-flat major follow at mm. 33-53. In the first two the alternation of normal and inverted forms of the subject continues but the entries now overlap by beginning half a measure apart. The elements which create opposition in Contrupunctus 5 — melodic inversion of the subject, degree of overlapping of entries of the subject, and remoteness of tonality coincide just before the point of furthest remove to create a stunning moment in this fugue. Where pairs of entries of the subject are presented in the more remote keys the overlapping is much more extreme, almost to the point of complete superimposition. Since this passage culminates 39 in the furthest point of remove tonally and presumably the climax of opposition in the fugue, the greater degree of overlap thus compliments the growing tension set up by the extreme remove in key. Example 21. Contrapunctus 5. mm. 29-38. 29 i - = - J i J'\ m m ^ J J ] J J ^ — v j j ] f . Ferr Y — L f f r 1 V — ij. j> j- —i tor r r r V r r JTT3jr> -r- Z — r r V 1 r - — - U L L - T r —-[Hr1 However, it is exactly at this furthest point of remove tonally with the paired entries in B-flat major, that for the first time in the fugue, both entries are inverted entries, that is, in the same melodic motion (as are all subsequent pairs of entries in the fugue) and they now overlap by beginning only one and a half measures apart. Example 22. Contrapunctus 5, mm. 44-57. fhr~— A JO, r m r m i . f r pr — -F 11^  \) n .: 1 r r r • M 1 J J >—^n9 4 = i f j T 1 " r- P ' I • Er i i j J j.,J>, *):, ? f. \,m . . u Tj-r- il£Jir J- vJ>J— Tr—-trr_f - r M r r =pz — r — m =—h-40 p r j J - J» Jrr > "4 It may be significant that this moment of extreme tension and onset of relaxation falls at almost precisely the mid-point of the fugue. The fact that the subject is heard twice in a row in the same melodic motion has the affect of resolution rather than opposition, relaxation rather than tension. Other contrapuntal techniques lead to an increase of intensity toward m. 53. The change of texture between m. 38 and m. 39 from a full four-part, pervasively imitative structure to a thin, three-voice trio (sounding because of the use of the stile brise as though it were in two parts) occurring as it does within an episode is unusual. In the first two measures of the episode (mm. 37-38), the eighth-note scalar upbeat motive which concludes the subject is presented in close imitation in all four voices in both similar and contrary motion while at m. 39 only the bass voice continues on with eighth notes, contrasting with the syncopated half notes in the upper two voices. Example 23. Contrapunctus 5, mm. 34-43. s 4> H P J ^ J j j j J-~JJ9^  ^ . j . , J f—r j . 41 In addition, the pair of entries of the subject in G minor at m. 41 is accompanied by an extremely angular and active soprano voice so that the subject is heard in an entirely new light. It is notable also that after these entries, the attack density increases with the eighth notes no longer present in one voice alone but distributed among all voices. The music literally stops on the dominant of B-flat major at m. 53. The constant eighth-note motion ceases and instead of driving through the point of furthest remove in an episode which resolves the harmony in the tonic, the music modulates rather abruptly to the tonic in a curious passage notable for its intense fragmentation and imitation. It is based on canonic imitation with entries in the same melodic motion and at the distance of a quarter note of the first five notes of the subject in diminution (mm. 53-56). Example 24. Contrapunctus 5, mm. 63-71. 63 —1 pi ] | i JJrf-'J" =?=?=•• * ' r p r ' P7--1 y r j A — -A 1 - - y i p L r i - - - L r r If " r 1 A 1 u l J u J. JU r == 'r This contrapuntal technique relentlessly drives the musical argument, but not through opposition; rather, this is obsessive affirmation. As such, the passage constitutes a strong confirmation of the subject. The same passage is repeated verbatim with all the voices inverted at m. 65, now transposed into the tonic key, serving to emphasize the process. Each imitative passage is followed immediately by a pair of entries of the 42 subject in the tonic; the first pair in its recta form beginning one measure apart, and second, the inversa form beginning one and a half measures apart. This constitutes a forceful confirmation not only of the subject, but of the tonic key as well. The effect is one of severe formal balance and symmetry at this most formal point in the fugue, as this section opens the second half of the piece. From m. 53 on to the end of the fugue the entries of the subject, eight in all, are in the tonic with a gradual increase in the amount of overlap. The fugue cadences in a full close with a tierce de Picardie at m. 86 and the five concluding measures simply extend this D major harmony over a tonic pedal in the bass. In a texture thickened to six parts, the alto and lower tenor parts present two entries of the subject beginning at the same time in contrary motion, constituting a maximum four-measure overlap. Example 25. Contrapunctus 5, mm. 86-90. J j 5 FTP A i7\ This total overlap seems inevitable, prepared from the beginning of the fugue. Even the countersubject in soprano and upper tenor are in simultaneous contrary motion doubling the concluding motive of the subject in the imposing six-part cadence. Bach has demonstrated here that the recta and inversa forms of the subject, while they are diametrically opposed melodically, are totally compatible harmonically. In the early manuscript endings of these four fugues, the full close at m. 85 is the only conclusive cadence. The fugue ends fittingly with the last notes of the subject in this canon sine pausis (canon without pause), seemingly with nothing left to say. Although 43 there has been resolution of both the tonal and melodic opposition built up in the first half of the fugue by this point, the contrary melodic motion returns suddenly and with a vengeance. Does this indicate a reconciliation of opposites at this point or does it signal that this central process is not finished, drawing us into the continuation of the fugal cycle? Several aspects lead to an interpretation of Contrapunctus 5 as a formal conclusion to the previous three fugues. While there are expositions of the subject in more distant keys, the brief episodes which separate them give the effect of not modulating at all. Normally episodic material would move purposefully between keys by way of sequential structures, intensifying the level of opposition in the process. But here, suddenly the music is in a new key without having arrived by these conventional means. There are no strong cadences in the distant keys; rather they are approached indirectly from the third below (see, for example, the approaches to the F-major entry at mm. 32-33 and the B-flat entry at mm. 46-47). The episodes here are extremely short. They do not increase tension nor do they propel the music forward. A performer may find that this fugue presents two distinct affects in its two halves. Up to m. 53 the omnipresence of the subject renders the music quite lyrical, flowing, and gentle. There is a subtle yet steady increase of tension through opposition of harmony and the presentation of the subject in contrary motion that culminates at m. 53. However, the following music almost denies this moderation and delicacy. It obsessively reiterates the tonic key in the context of intense imitation. The fugue transcends simple conflict; the last thirty-seven measures seem excessively confirmative. This may well be because Bach conceives of this concluding segment of Contrapunctus 5 not only as a 44 conclusion to this fugue but as the finale to the four fugues with which the collection begins. Contrapunctus 5 thus marks the resolution of a large-scale opposition involving the preceding three fugues. 45 Tonal Opposition Between Contrapuncti 1, 3, 2, and 5 The earlier manuscript version of Die Kunst der Fuge prepared in 1742 follows a different plan than that in the original print of 1751. Contrapunctus 4 has been added while the ordering of Contrapuncti 2 and 3 is reversed. Contrapunctus 5 then was originally the fourth fugue in a group of four. The original print groups together similar kinds of fugues; the entries of the subject in Contrapuncti 1 and 2 are in recta motion exclusively while in Contrapuncti 3 and 4 they are in inversa motion. In the manuscript version the fugues are interconnected. This is most apparent in the close to Contrapunctus 3 (in second position in the manuscript version), a half cadence in D minor. This open-ended conclusion leads the listener to expect that something will follow immediately. An investigation of opposition as it manifests itself from one fugue to the next in the original ordering (Contrapuncti 1, 3, 2, 5) will reveal a deeper connection. Figure 1 shows the keys established in these four fugues. (The measure numbers appear along the x-axis while the keys that the fugue goes to appear along the y-axis.)1 0 The placement of the keys on the graph reflects the distance of each key from the tonic. D minor appears in the middle, with the subdominant (G minor) and its relative major (B-flat major) above and the dominant (A minor) and relative major (F major) below. (To complete the ambitus of the five most closely-related keys to the tonic, C major, the relative major of the dominant, would appear below F major but that key does not emerge in these four fugues.) The reasons for this ordering are self-explanatory; the dominant is often the initial key to which a fugue will modulate, the subdominant almost always plays an important role (particularly in minor-mode fugues), while the relative major of these 46 keys represent significant but more distant modulations. It should be noted that minor digressions or tonicizations do not appear on the graphs, and areas of uncertain keys are represented by dotted lines only when the music is quite chromatic for more than one measure. These graphs are intended to show the discernible movement away from, and return to the tonic. From Figure 1 opposition as a function of modulation to different keys over the course of each fugue can now be compared. It is immediately apparent that Contrapuncti 1 and 2 are similar. Both oscillate between the tonic and dominant before a short digression to other keys. But Contrapunctus 1 remains much closer to the tonic, while Contrapunctus 2 moves further away. The shape of the graphs bears out this similarity with Contrapunctus 2 appearing as an expansion of Contrapunctus 1. Contrapunctus 3, on the other hand, appears to be quite different. Its opening which strongly implies the dominant, A minor, and its moments of tonal uncertainty set it clearly apart from the two fugues which frame it. Furthermore, the return at the end to D minor is relatively short (in the early version it is even shorter and does not resolve properly in the tonic key). In fact, almost the entire fugue is unstable. Following the earlier ordering, one might consider Contrapunctus 1 as a statement (simple and undeveloped), Contrapunctus 3 as a departure (more complex and unstable), and Contrapunctus 2 as a return (simple but more developed). In Contrapunctus 5, which follows as a sort of conclusion, the dominant (A minor) is conspicuous for its absence. This fugue leaves D minor for a longer period of time, but instead of modulating to and prolonging the dominant, this key plays virtually no part in the modulatory scheme. The main harmonic conflict has already been thoroughly worked out in the previous three fugues and it remains for Contrapunctus 5 to 47 state and restate the subject in the tonic key. Thus, the group of fugues is given a fitting tonal conclusion. 48 Contrapunctus 1: G minor D minor A minor 0 Contrapunctus 2: B-flat major G minor D minor A minor F major 10 20 30 40 50 60 70 80 90 Tn_n_rui 10 20 30 40 50 60 70 80 90 Contrapunctus 3: G minor D minor A minor F major 0 10 20 30 40 50 60 70 80 90 Contrapunctus 5 B-flat major G minor D minor A minor F major 0 10 20 30 40 50 60 Figure 1. Comparison of tonal remove over time (in measures). 70 80 90 49 Conclusion Analyses of fugues should focus on continuous, dynamic, organic processes that evolve over time, rather than on the static and discontinuous dismemberment into strictly delineated sections. Evolution is the very nature of fugal process and understanding the transformative processes at work is of the utmost importance. As a point of departure, opposition has been used to define the dynamic shape and growth of the four fugues which open the early version of Die Kunst der Fuge. Opposition is a basic tenet of music; one that is readily identifiable and clearly audible. Conflict through opposition takes various forms; melody (contrary motion), polyphony (contrapuntal inversion), harmony (dissonance), density (texture), rhythm (syncopation), and tonality (modulation) to name the most important parameters. Taken in combination, these create a complex fabric lending each fugue its unique nature. Melodic opposition, the vertical juxtaposition of two parts in contrary motion, creates tension. This is friction on a small scale of a purely local kind requiring the performer to link the parts mentally while maintaining the same articulation and intensity in each voice. The clash between dissonant harmonies can be underlined through clear articulation and dynamic contrast, as can textural opposition. Rhythmic opposition manifests itself both vertically as the clash between a syncopated countersubject and the subject it opposes and horizontally in the contrast between an unsyncopated statement of the subject which subsequently appears syncopated. The affect of syncopation is to destabilize the regular pulse, and instability creates tension. Any syncopated note, even down to its resolution in a suspension, must be articulated clearly to show it as a 50 departure from, and in opposition to the normal rhythm. Tonal opposition is a conflict that occurs both on the macro and micro levels. Everything from a sudden diminished harmony, to a delayed resolution of a harmonic progression, to a long departure from the tonic leads to tonal instability and tension with the home key, the eventual goal of resolution. The relative distance from the tonic with each tonal shift and its placement in the overall structure can be highlighted by means of tone colour, tempo flux or a particular kind of stress. Conflict is of paramount importance in these fugues and great care must be taken in projecting them. Analysis of the level of conflict provides minute clues for the interpretation of certain passages and add to the overall mental picture of the fugue. In choosing articulation, tempi, phrasing, dynamics, and style the performer should keep in mind the point at which he/she is in the argument, the degree of intensification present in the various oppositional parameters in effect without losing sight of the goal and the resolution of the conflict. If the opposition in a certain passage highlights one kind of conflict, then that must appear in the performance. The climaxes and resolutions related to each element of conflict, whether or not they coincide (most often they do not), should be rendered audible. The first should strike the listener as the point of greatest distance between two parties engaged in an argument, a point of crisis, while the second should have the affect of a settlement of all differences of opinion. Turning to large-scale elements, the calm serenity of Contrapunctus 1 is manifest in its limited tonal conflict. The intensity which, unusually in this case, occurs after the return of the tonic key is evident in the textural and rhythmic climax at this point. In Contrapunctus 3, chromaticism and syncopation build instability and tension throughout 51 the fugue not resolved until after the final statement of the subject. At the same time, other factors such as changes in texture and the rhythmic and melodic form of the subject are concentrated in the middle of the fugue. Contrapunctus 2 marks a return to the overall structure of the first fugue in terms of stasis, although its tonal horizons are expanded. Contrapunctus 5 depends almost entirely upon perhaps the most fundamental means of opposition, namely the conflict between the normal and inverted forms of the subject juxtaposed in various ways. Following the manifestation of opposition throughout the cycle reveals that each of these four fugues projects on the micro scale a basic tripartite musical scheme of statement, departure, and return. On a macro scale, the same three-part disposition occurs. Contrapuncti 1, 3, and 2 each represent one element while Contrapunctus 5 serves as a clear conclusion, summing up all that has taken place before. Above all, it should never be forgotten that every fugue is dynamic, organic, continuous, constantly in flux and that the processes at work are evolving at different rates over time. This requires analytic flexibility. As an ideal approach, opposition is simple enough that it can be applied to any facet of composition but also flexible enough to be applied to complex situations. A perceptive performance will mirror the inherent conflict with intensity and focus, and reveal the dynamic nature of fugue. 52 Notes Introduction 1. Daniel Harrison, "Rhetoric and Fugue: An Analytic Application," Music Theory Spectrum 12 (1990): 5. 2. Hans Heinrich Eggebrecht, J. S. Bach's "The Art of Fugue ": The Work and its Interpretation, trans. Jeffery L. Prater (Ames, Iowa: Iowa University Press, 1993), 9. 3. Ralph Kirkpatrick, Interpreting Bach's "Well-Tempered Clavier": A Performer's Discourse of Method, (New Haven: Yale University Press, 1984). 4. For example, see Gregory Butler, "Fugue and Rhetoric," Journal of Music Theory 21 (1977): 49-110. 5. These are dealt with at length in Butler, "Fugue and Rhetoric," 84-92 upon which my list is based. 6. Marpurg is a Berlin theorist from the circle of C. P. E. Bach. Intensely interested in the fugues of J. S. Bach he was chosen by C. P. E. Bach to write the foreword to the second edition of Die Kunst der Fugue (1752). Since Marpurg may have consulted with the elder Bach in Leipzig at the end of the composer's life, he was in a particularly good position to undertake analyses of the master's fugues. 7. Friedrich Wilhelm Marpurg, Die Abhandlung von der Fuge, I (Berlin, 1753), facs ed. (Georg Olms: Hildesheim, 1970), 143, TAB. XLII. 8. For a discussion of disposition as it relates to fugue and of the close links between opposition and refutation, see Butler, "Fugue and Rhetoric," 68-71, 84-86. Contrapunctus 1 9. Johann Sebastian Bach, Die Kunst der Fuge BWV1080 (Munich: G. Henle Verlag, 1980), 2. A l l following musical excerpts reproduced here are taken from this source. Tonal Opposition Between Contrapuncti 1, 3, 2, and 5 10. These graphs are based on an idea appearing in Daniel Werts, "The Musical Circle of Johannes Mattheson," Theoria 1 (1985): 97-131. 53 Bibliography Primary Sources Bach, Johann Sebastian. Die Kunst der Fuge, Band I: Fruhere fassung der autographen partitur. Frankfurt: C. F. Peters, 1987. Bach, Johann Sebastian. Die Kunst der Fuge BWV1080. Munich: G. Henle Verlag, 1980. Secondary Sources Bach, Carl Philipp Emanuel. Versuch iiber die wahre Art das Clavier zu spielen, vol. 1. Berlin: C. F. Henning, 1753; vol. 2, G. L. Winter, 1762; trans. William J. Mitchell. Essay on the True Art of Playing Keyboard Instruments. New York: W. W. Norton & Company, 1949. Butler, Gregory. "Fugue and Rhetoric." Journal of Music Theory 21 (1977), 49-110. Eggebrecht, Hans Heinrich. J. S. Bach's "The Art of Fugue": The Work and its Interpretation. Translated by Jeffery L. Prater. Ames, Iowa: Iowa University Press, 1993. Gollin, Edward. "Representations of Space and Conceptions of Distance in Transformational Music Theories." Ph.D. diss., Harvard University, 2000. Harrison, Daniel. "Rhetoric and Fugue: An Analytic Application." Music Theory Spectrum 12.1 (1990), 1-42. Lenneberg, Hans. "Johann Mattheson on Affect and Rhetoric in Music." Journal of Music Theory 2.1-2 (1958), 47-84, 193-286. Lester, Joel. Compositional Theory in the Eighteenth Century. Cambridge, Massachusetts: Harvard University Press, 1992. Kirkpatrick, Ralph. Interpreting Bach's "Well-Tempered Clavier "': A Performer's Discourse of Method. New Haven: Yale University Press, 1984. Mann, Alfred. The Study of Fugue. New York: W. W. Norton & Company, 1958. Mattheson, Johann. Der vollkommene Capellmeister. Hamburg: Christian Herold, 1739; trans. Ernest C. Harriss. Johann Mattheson's "Der vollkommene Capellmeister": A Translation and Commentary. Ann Arbor, UMI Research Press, 1981. 54 Tovey, Donald Francis. A Companion to "The Art of Fugue ". London: Oxford University Press, 1931. Werts, Daniel. "The Musical Circle of Johannes Mattheson." Theoria 1 (1985): 97-131. 55 

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