John Cage
John Zorn
J-S Bach


Contrapunctus I

[1] Bach's The Art of Fugue consists of 18 contrapuncti. Zacher plays only the first one, 'Contrapunctus I'. Although many music theorists regard the first contrapunto as a fairly simple fugue that meets standard qualifications, the various analytical interpretations show strong differences. The object of investigation is invariably the score, the score as text, as writing. The same text allows for a series of different readings (and it is not merely a shift of focus - for example, paying attention to harmonic, melodic or rhythmic aspects - that leads to these varying results). The ineradicable heterogeneity of this text not only divides different discourses, but is at work within an individual discourse.

[2] Dieter de la Motte states that a common analysis of this fugue would lead to the following result (De la Motte, p.23-30) (cf. the score) :

  • Bars 01-16: Exposition. Subject respectively in D minor (alto), A minor (soprano), D minor (bass), and A minor (tenor)
  • Bars 17-22: Episode
  • Bars 23-35: Development. Subject in D minor (alto), A minor (soprano), and A/G minor (bass)
  • Bars 36-39: Episode
  • Bars 40-43: Development. Subject in D minor (tenor)
  • Bars 44-48: Episode
  • Bars 49-59: Development. Subject in D minor (soprano), and D minor (bass)
  • Bars 60-73: Episode
  • Bars 74-78: Development. Subject in G minor with close in D (tenor)

De la Motte presents this first, rough division as an obvious starting point. 'The initial form scheme specification is a necessary, but not a difficult task, a risk-free undertaking' (De la Motte, p.28, my translation). An exposition, 4 developments and 4 episodes. An easy traceable structure according to De la Motte. Panthaleon van Eck, however, makes quick work of this underestimation. He discerns two additional episodes, namely bars 27-8 and 53-5, bringing the total to 6. Gerd Zacher seems to share this view in his explanatory notes to Die Kunst einer Fuge. 'Bach carefully planned the length of episodes. They successively consist of 6, 2, 4, 5, 3 and finally 7 times 2 bars'. In other words, he discerns 6 episodes as well. 4 Episodes? 6 Episodes? It is not my intention to side with either party. It is extraordinary that at a first rough division, various experts already have different views on 'Contrapunctus I'. Would one of the readings be expressly erroneous, or is this where the musical text's openness would already present itself? Let's continue with De la Motte's analysis.

[3] To De la Motte, 'Contrapunctus I' seems an odd beginning for an art of writing fugues for several reasons. First, he perceives an unusually small tonal range. More often than not, the subject appears in the key of D minor (or on the dominant of D minor, A minor). Second, De la Motte acknowledges an exceptionally sloppy treatment of the subject. In only three out of the ten times that the subject appears it answers to the subject that was exposed in the beginning. (For convenience, I will pass on the question as to whether there can be a matter of a recurring motive at all. Is recurrence not something different every time? Wouldn't the subject adopt a different meaning every time because the context or intention changes? In 'At This Very Moment In This Work Here I Am', Derrida examines Levinas' frequent use of the phrase, 'at this very moment'. Derrida points out that 'the other' already manifests itself in the repetition of this phrase. Because the context constantly changes, the meaning of the phrase also changes. 'The 'same' 'very' of the 'at this very moment' has remarked upon its own alteration, one which will have ever since opened it up to the other' (At This Very Moment, p.22).) These comments from De la Motte should be viewed critically. It would indeed seem remarkable that the alto voice subject recurs in D minor (bars 23-27) since Bach usually modulates to another key. However, it is not especially remarkable that Bach rarely modulates in a given fugue (cf. the first fugue in C from Das wohltemperiertes Klavier).
As to De la Motte's second comment, Schlötterer-Traimer asserts that the subject may undergo several changes (Zacher, incidentally, seems to agree with this). The most important change is the so-called tonal, or plagal response. The interval D-A with which the dux (the voice introducing the theme) opens in the exposition becomes A-D in comes (the response, the second voice that exposes the same theme one fifth up after the dux has come to a close). The tonal response is opposed to the real response, the exact transposition that would lead to the A-E interval. In the exposition, the comes starts in D minor in bar 5, moves to the dominant A minor (leading note G sharp) in bars 6 and 7 to return again to D minor in bar 8. For a second time, De la Motte's comments, presented as obvious conclusions, are in need of differentiation.

[4] More pressing analytical problems with respect to the subject in the bass in bars 32-36, where the rhythmic pattern is maintained while the intervals have undergone great changes, come to light. According to Panthaleon van Eck, the listener is even confronted with the question as to whether he is still able to identify the melody presented here with the subject (cf. Panthaleon van Eck, p.41). This seems to be quite an exaggeration since the contour of the subject has been kept completely intact. Still, I would like to dwell upon this passage a bit longer. Following De la Motte's analysis, there are two possibilities here. The first holds that a comes in the A-key is suggested in bars 32-33. The second would be to regard the subject in bars 32-36 as a dux in G minor, where the first, third, and fourth notes are 'wrong'. (Alan Dickinson makes a slight connection between these two possibilities by stating that the bass entry, which is intended to appear in the dominant, drops halfway to the subdominant, thereby enhancing a sense of  development.) Going by the note material (the score), De la Motte hesitates between a comes and a dux.
Zacher, too, goes into the same issue, albeit, indirectly; I will partly join him on that course. In 'Der verdrehte Baß in Contrapunctus I aus der Kunst der Fuge', he states that between bars 29 and 44, Bach 'deconstructs' (actually, he uses the words, 'grundlich im Frage stellen', 'to question thoroughly') the concepts dux and comes. In bars 29-33,  Bach passes off the comes in the soprano as a dux. The passage opens with a dux signal - a fifth leap - however, it deviates from the comes in bar 5 by the second note only. In bars 40-44, Bach reverses this idea. The tenor is then a dux with an allusion to the comes (the fourth leap of E-A in bar 40); only the first note differs from the opening of 'Contrapunctus I'. But reading against Zacher, based on the notes in bars 29-33 it could just as well be stated that the theme actually does appear in the dux, with only the B flat in bar 32 denying a perfect modulation. It looks as though Bach wrote neither a dux nor a comes here. And at the same time he wrote both. Careful reading thus brings about an undecidability.
But let's continue with Zacher's reading. Like De la Motte, Zacher encounters problems analyzing the subject in bar 32-36. The theme opens in bar 32 as a comes (in A minor, similar to the first comes in bar 5) and turns via a broken F sharp minor triad into the subdominant G minor. Interesting, but incomprehensible to Zacher. Can there still be a matter of a dux or a comes here? Bach seems to disable any analysis that would graft itself onto either of these two notions. Still, Zacher looks for a solution. Based on the score, he finds that the bass in bars 32-36 (with the exception of bar 33) is identical to the tenor dux that appears as a comes in bars 40-44. He refers to a rhetorical trope (metalepsis) that holds that what precedes can only be understood through what follows. The past does not determine the future; it is the other way around. Time is out of joint. Derrida calls this a spectral moment. It is a moment that no longer belongs to time, if one understands by this the linking of modalized presents (past present, actual present: 'now', future present) (cf. Specters, p.xx). An analysis that ultimately allows Zacher to drag this bass theme into the domain of the dux. Nevertheless, additional problems remain here as well. The tones in the tenor that belong exclusively to the dux (bar 41) are transformed to tones in the bass that would seem appropriate to the comes (bar 33, where only C sharp makes up for a deviation from the comes in bars 5 and 6. Zacher believes that Bach replaces the C by a C sharp with attention to the F sharp in bar 34, in order to avoid the problematic interval, C-F sharp, the diabolus in musica). Time and again, the musical text refrains from a definitive determination. Both De la Motte and Zacher's interpretations miss out on a potential meaning of the text. The musical text escapes all attempts to pin it down in a final meaning, not by initiating another discourse, but on the basis of the same analytical notions.

[5] I will return once more to the passage between bars 29 and 44. According to Zacher's analysis, the comes in bars 29-33 is followed by a dux in bars 32-36 and by a dux in bars 40-44. This is peculiar, considering the meanings of both words. Dux may be translated as leader, predecessor, head, or chief, while comes represents follower, companion. In the present passage, the follower precedes the predecessor. In other words, the leader becomes the follower, the companion becomes a leader. No longer is the dux the cause producing a logical effect in the comes; it is the other way around. A comparable reversal of cause and effect occurs in Zacher's description of the relation between the dux in bars 32-36 and 40-44. In the terms of metalepsis, the 'explaining' fragment (bars 40-44) follows the effect (bars 32-36) and is projected a posteriori as its 'cause'. The cause is 'discovered' after the effect has occurred. Something strange is going on. In the conventional distinction between cause and effect, the cause is the origin, logically and temporally prior to the effect. But if the effect is what causes the cause to become a cause, then the effect may be treated as the origin (cf. Culler, p.86-8).
Zacher tracks down several significant displacements in his analysis. But even if we no longer follow Zacher, displacements still come to the forefront, for example, when we refrain from deciding between comes or dux in bars 29-33, and assume a fundamental undecidability instead. Dux and comes merge here. The leader is at once follower, the companion simultaneously is the predecessor.

[6] It is not my primary intention to compare the analytical comments of De la Motte, Zacher and myself to derive a ruling. I am primarily interested in the functioning of this strategy. Conflicts within a text seem to be reproduced as conflicts in and between readings of that text. Analytical readings transform the difference 'within' into a difference 'between' mutually exclusive positions. A deconstructive strategy is rather directed towards 'a careful teasing out of warring forces of signification within a text' (Barbara Johnson, cited in: Culler, p.213). My aim is to question some of the presuppositions and decisions by which a complex pattern of internal differences is translated into alternative positions or interpretations. I want to emphasize that the differences between interpretations are based on a repression of differences within a text, the way in which a text differs from itself. This becomes clear in the analysis of the subject in terms such as dux and comes. Which reading is the best?  The desire to come to a decision is precisely what is in question: our inclination to exclude possibilities that are manifestly raised by the musical text in order to arrive at clear and coherent positions, but that nonetheless pose a problem (cf. Culler, p.247). Deconstruction attends to structures within a text that resist the reduction of a text to a coherent scheme. This is also where the ethical implications of deconstruction arise. They consist in a concern for what must be suppressed in a text in order for the analysis to achieve some kind of 'validity'. Methods, such as the analytical duality dux-comes, have developed or evolved in ways that (systematically) obscure, deny or disavow the heterogeneity of the musical text. The result is that music comes to mean only what (privileged) methods allow it to mean (cf. Ferrara, p.xvi). Deconstruction, by contrast, allows the heterogeneity of a text to come to the forefront without again absorbing it in a coordinating, all-inclusive discourse.

[7] According to De la Motte, Bach frustrates attempts to establish whether we are dealing with a dux or a comes in various places. That decision often needs to be postponed. For example, three dux entries are written one major second too high. They begin with a fourth leap, on account of which they could be considered a comes, until it shows later on that they are actually a dux. Their tonal position thus becomes clear only in the second bar (cf., for example, bar 40 ff). Besides, two comes entries and one dux entry modulate (in bars 5, 13, and 39 respectively) in the last quavers, for which reason they would be 'incorrect'. Finally, the appearance of the subject in bars 32-36 is more or less undecidable (cf. De la Motte, 24-5). However, neither De la Motte nor Zacher mention a similar undecidability towards the end of 'Contrapunctus I' (bars 74-78) where the theme in the tenor at first seems to start in the dominant A minor (bar 74; compare bar 5), then shifts to the subdominant G minor (bars 75-77), to finally conclude in D (bars 77-78). Although the resolution of the subdominant to the tonic recurs in more contrapuncti of The Art of Fugue, Dickinson nonetheless speaks of a 'reluctant surrender', as the resolution of IV to I remains problematic. Again, it is unclear as to whether this is a comes or a dux. Bar 74 seems to verge on a comes (cf. bar 5). However, this premise needs to be adjusted in the following bars where the subject continues as in bars 40-44 and 49-53. Zacher opted for a dux that only deviates in the first note. The quavers in bar 77, however, deviate from the operative subject (they appear one major second too high). They make the decision for a dux difficult once again, unless we settle for five deviating notes (the first, and last four) out of a total of thirteen.
In summary, only three out of ten entries correspond with the theme that was introduced in the exposition. De la Motte finds it remarkable that these difficulties occur in the opening piece of Die Kunst der Fuge, after all, a work with a strong pedagogical commitment, a thesaurus for the writing of  fugues (cf. Heinrich. cf. Die Kunst der Fuge [The Art of the Fugue] ).
He adds another argument. 'It is striking that the counterpoint loses significance in the course of the fugue (the theme also appears less and less). What is started in bars 5-8 plays a role in bars 10-11, 14-16, 24-26, and 50-51 and therefore determines the beginning; it appears briefly once more in the middle section and is completely absent in the remaining part' (De la Motte, p.25, my translation). De la Motte concludes that the art of writing fugues is somewhat postponed in the first counterpoint. Incidentally, Carl Dahlhaus, in response to this analysis, comments that the lenient melodic treatment of the theme and the counterpoint is compensated by stricter rhythmic connections that interweave the individual voices, keeping them together. The rhythmic patterns thus seem to function as motives. Dahlhaus believes the problem to be in the subordinate position of rhythmic figures in relation to interval structures in many analyses. Many theoreticians disregard the development of rhythmic patterns. In addition, Dahlhaus wonders whether a consistently executed (he uses the term 'obligatory') counterpoint should belong to the art of writing fugues. Would that not rather be a stereotypical mannerism that should perhaps be avoided? Both music theoreticians, therefore, observe a certain 'non-identity' in 'Contrapunctus I' (that is possibly or partly counterbalanced in the rhythmic course), but they value this differently. De la Motte experiences it as a deficiency and an inadequacy, while Dahlhaus leaves the possibility open that Bach's superiority would gain additional stature through this. Dickinson, however, begins his modest analysis of 'Contrapunctus I' with the comment that Bach 'relies on the variable harmony of free counterpoint to color the flow of entries in tonic and dominant' (Dickinson, p.120). No counterpoint or free counterpoint? Again, it is not the decision that matters to me here. The textuality of the text installs the absence of an ultimate meaning. With that, the infinite play of interpretations may commence. Of course, this does not mean that every interpretation is equally convincing or adequate (cf. the amount of episodes in 'Contrapunctus I'). Within a certain context, within certain conventions, one interpretation may be preferred to another. And some interpretations are more powerful than others. However, the co-existence of different interpretations (be they analytical readings or performances) is only possible by the grace of the undecidability of the text itself.

[8] One small remark to close with. In Silence and/in Music, I state that the attention for silences is a peripheral moment in music analysis. In my discussion of the analyses of 'Contrapunctus I', it appears that I am confirming the idea that no attention is given to the (toccata-like) breakdown in bars 71 and 72; indeed, a very noteworthy moment. However, I compensate for this in No (-) Music - D. Schnebel where I elaborate upon Zacher's tenth version of 'Contrapunctus I', which is based entirely on the rests in bars 71 and 72.