Questions on Fugue No. 24
Well-Tempered Clavier, Book I
by Johann Sebastian Bach

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Listen to the fugue while studying the timeline animation. Watch for the letter Chi χ as it materializes 61 times. Each instance represents a “chiastic” (also called “cruciform”) musical relationship, with some appearances of χ coinciding with a complex of more than one method. These methods are of three types:

Questions 1-4 refer to the preceding methods. In each, the comparison is between measures heard at the beginning of the animation and those heard at its end. Each of these four questions begins by identifying a group of measures. Click the timeline in that group, watch the animation, then answer the question about it.
  1. Mm. 9-11 demonstrate which methods?

    all three
    cruciform motifs and melodic inversion
    cruciform motifs and contrapuntal inversion
    melodic inversion and contrapuntal inversion

  2. Mm. 13-15 demonstrate which methods?

    all three
    cruciform motifs and melodic inversion
    cruciform motifs and contrapuntal inversion
    melodic inversion and contrapuntal inversion

  3. Mm. 47-50 demonstrate which methods? (Click m. 47 to begin the animation.)

    all three
    cruciform motifs and melodic inversion
    cruciform motifs and contrapuntal inversion
    melodic inversion and contrapuntal inversion

  4. It is possible that the author made arbitrary choices in comparing segments with each other. In question 2, for example, the animation began with mm. 4-6 going to mm. mm13-15. But for the present question, please compare mm. 13-15 with mm. 9-11. There is no animation for this, so you’ll need to study the score. Here’s the question. Measures 13-15 employ which methods when compared with mm. 9-11?

    all three
    cruciform motifs and melodic inversion
    cruciform motifs and contrapuntal inversion
    melodic inversion and contrapuntal inversion

  5. Was the author’s pairing of segments arbitrary? Definitely not! Rather, they were chosen to demonstrate that Bach had a contrapuntal plan, which he grounded in the exposition.


    • Mm. 1-3 present the subject.
    • Mm. 4-6 add counterpoint to the subject. This new melody is the countersubject, which has two parts that are identified on the timeline in turquoise (the countersubject’s head motif) and in tan (its tail motif).
    • Mm. 9-11 provide variation to the fugal complex of mm. 4-6 by melodic inversion of the countersubject’s head motif.
    • Mm. 13-15 transform mm. 9-11 still further by double counterpoint.

    Each subsequent animation of the fugal complex (after the exposition) suggests that it was derived either from the third or fourth step (above). Let’s begin with complete statements of the subject, by which we mean all of those red segments, after the exposition, that are three measures long (12 beats). Notice that all of them have been animated as originating from the mm. 13-15. In each: (1) the cruciform motif is heard three times, (2) there is melodic inversion of the “turquoise” motif, and (3) there is contrapuntal inversion in the voices. This is to say that Bach used all three cruciform methods outlined at the beginning of this quiz. Which of the following represents the best answer to the question, “How else did Bach develop the fugal complex?”

    Most of the “false subjects” (incomplete statements of the subject) are animated as originating in mm. 9-11.
    All of the false subjects are counterpointed only with the countersubject’s head motif and not its tail (with m. 74 being exceptional).
    All of the complete statements of the subject could have been animated as having originated in mm. 9-11, but this comparison would have demonstrated no melodic inversion and only a miniscule instance of contrapuntal inversion (in m. 21).
    All of the above are true.
    Two of the above are true.

  6. The sequential episodes of mm. 17-20, mm. 26-29, and mm. 65-68 offer four more χ ’s, all made by contrapuntal inversion. “Double counterpoint” involves the contrapuntal inversion of two voices, and “triple counterpoint” involves three voices. Follow the animations, then choose the best answer.

    Mm. 17-20 employ triple counterpoint as do mm. 26-29.
    Mm. 65-68 employ double counterpoint.
    A comparison of mm. 26-29 with mm. 17-20 reveals double counterpoint at work. (Click m. 24 to initiate this animation).
    All of the above are true.
    Two of the above are true.

  7. In 2009 the Hungarian composer, György Kurtág said: “A Bach fugue has the Crucifixion in it – as the nails are being driven in. In music, I am always looking for the hammering of the nails . . . . [1] It is not clear to which fugue Kurtág refers, but the present one seems to qualify. Related to it, in Bach’s handwritten score of the St. Matthew Passion, there is one place where he used χ in place of the German word “Kreuz” (cross). This is in the aria for bass (NBA 23), “Gladly I will submit myself to carry the cross and drink of the cup as my Savior did”). Significantly, Bach also composed the musical symbol for his name into that aria, six times. Finally, Bach wrote SDG (“Soli Deo Gloria”) on the reverse side of the last page of the present fugue.

    This question has two parts. First, do you think it is plausible that this wordless fugue, the bm from WTC 1, has a Christological connotation whether or not the present analysis is correct in all of its details? Second, do you think that Kurtág’s “dual vision” (see footnote #1) is a reasonable approach for people who don’t subscribe to Bach’s faith?

    yes and yes
    yes and no
    no and yes
    no and no

  8. In your opinion, what is meant when the Cranachs, both father and son, paint themselves into the picture, and Bach composes his signature melody into this fugue?

    The artists are signing their works for posterity.
    The artists are being pompous.
    The artists are identifying themselves with belief signifiers that permeate the work of art.
    Two of the above.

  9. John Eliot Gardiner writes of Bach’s extensive library of Luther’s works: “What it does reveal, beyond his personal piety, his lifelong reverence for Luther and the central importance of Luther’s writings in both his personal and professional capacities, is that ‘Bach was evidently deeply – and apparently uncritically – immersed in a mindset that was at least two hundred years old.’” [2] Read the foregoing again, carefully, and notice that Gardiner has quoted somebody else [John Butt], with whom he apparently agrees that Bach was “uncritical” in his approach to Luther. Now hold that thought! Bach was uncritical of Luther. In the American vernacular, let’s exaggerate the position by imagining that Bach swallowed Luther “hook line and sinker.”

    Challenging such a view, Laurence Dreyfus posits that Bach subverted the conventions of his day, particularly that of the Word (of which Luther was a thundering defender). Dreyfus’s position is that Bach challenged his contemporaries in their conceptions of musical correctness, devotion to God, creativity, and especially of words. Music taps into a higher power and is therefore of higher authority than these [3]. John Butt seems to reconcile the problem by suggesting that Bach was orderly in his subversion of the existing order, with his purpose being to establish a new and higher order – that of music [4]. In his beautiful Music in the Castle of Heaven Gardiner cites both Dreyfus and Butt approvingly.

    Now for the question. Do you think it possible for Bach to have been uncritical of Luther while at the same time subversive?


  10. There is no question that Bach absorbed Luther voraciously, incorporating the Reformer’s ideas both into his texts and music. This absorption began as an infant really, when Bach was baptized within feet of the pulpit where Luther once had preached, and continuing in the Latin School that both attended as boys in the little town of Eisenach. But as an adult, it seems equally plausible that Bach’s appropriation of Luther was attended by a good deal of critical reflection, and that this deep thinking expressed itself not just in his liturgical texted music, but also in non-liturgical works too, of which this fugue represents a fine example.

    Think about it. How would a composer, as opposed to a philosopher or poet, critique a body of literature and thought like Luther's? A composer would write music, would he not? If it is true that the compositional choices of this fugue posit, in some sense, Bach's appraisal of Luther, then what could be more apparently critical than the counterpoint of this fugue? Remember this! Just because a person does not repudiate a belief system does not mean that this person has not thought critically about it. It is often exactly the other way around! Thoughtful people frequently affirm and adhere more strongly to their beliefs only after critical inquiry that is frequently initiated by a high degree of skepticism and doubt.

    Without Luther, there may never have been a Bach as we know him. If that were true, then it would be important to understand not just Luther’s view of music (he had a very high view), but also of life itself. One cannot read far in the literature about Bach without finding reference to Luther’s “theology of the cross.” It is the purpose of this reading and final question to explore, briefly, that theology and to consider how it is enacted in Bach’s music. Read the following synopsis, from pp. 114-115 of Michael Allen Gillespie’s Theological Origins of Modernity (University of Chicago Press, 2008), then answer the last question.

    Luther’s understanding of God rests on the recognition of God’s absolute sovereignty, that is, upon the nominalist notion of divine omnipotence. What follows from this? In Luther’s view literally everything, that is to say, everything that occurs happens as a result of God’s willing it to be so. The purposes of such an all-overpowering God, in Luther’s view, are necessarily unfathomable. [Now quoting Luther] “For as in His own nature God is immense, incomprehensible, and infinite, so to man’s nature He is intolerable [meaning that our finite minds fail us in trying to comprehend the infinity of God].” He argues that we thus must abstain even from a search into God’s majesty, for as the Scriptures make clear, “No man may see me and live.” God’s power is so profound and inexplicable that it would destroy the man who sought to comprehend it. God thus conceals his majesty—he is a hidden God, a deus absconditus.

    This was the God that so terrified the young Luther, the omnipotent and transrational God of nominalism. In Luther’s later thought this God is superseded although he is never truly eliminated. Indeed, this hidden God remains the controlling if incomprehensible force behind all things, and in his unpredictable omnipotence generates a vast and irremediable unease that is strengthened by Luther’s insistence that it not be considered. Only this God is truly free, and the grounds of his actions are totally beyond human ken. For us, he is thus not a personal God at all but resembles the Greek concept of fate governing and determining all things.

    The difficulty with such a notion of divine omnipotence is that it makes God responsible not only for all of the good in the world but for all of the evil as well. Augustine sought to solve this problem by attributing freedom to the human will in order to free God from the imputation of doing or causing evil. Luther’s denial of human freedom removes this as a possible explanation for him. The source of evil for Luther is neither man nor God, but the devil. Indeed, for Luther, existence is a continual and unceasing war between God and the devil for possession of man. Satan is pictured as the ruler of this world and God the ruler of heaven. While on the surface this notion seems quasi-Manichean, at the heart of things this cannot be the case, since Satan for Luther must ultimately also be in God’s service. Behind Satan lies the hidden mystery of absolute divine sovereignty. The question of demonic forces for Luther is thus only the obverse of the question of God. If God is omnipotent, how can he not be the source of evil? How can he also not be the devil?

    Luther’s solution to this problem is to insist that we focus not on a theology of glory but on a theology of the cross, not on a hidden and inexplicable God who wills all things but on God as he reveals himself to us in Scripture. We must see, in other words, the incarnate God. In Christ, the hidden God conceals his majesty and transforms it into its opposite, weakness on the cross. This revealed God in Luther’s view is more familiar to us and we can love him for the suffering he underwent on our behalf. . . .

    Christ is God and Christ is man, but it is this connection to man that is decisive. He is not a distant and unfeeling being, as nominalism at times imagined him. Indeed, according to Luther, he understood to the bitter end what it meant to be human. Christ crucified thus becomes the basis of the Reformation. Luther believes that in our pain and suffering, and in the midst of our doubts, we can be comforted by the fact that Christ himself suffered and doubted. Thus, [quoting Marius’s book on Luther] “to contemplate Jesus is to be reminded in the midst of the most radical kind of doubt and fear that God is with us.”

    Select the option that best completes the following sentence.

    Bach enacts Luther’s theology of the cross in . . .

    his making of chiastic musical relationships.
    counterpoint, which is one method whereby (a) can be achieved musically.
    words that he associates, in his liturgical music, with (a) and (b).
    his Christocentric focus, which manifests itself in (a), (b), and (c).

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1. György Kurtág, Three Interviews and Ligeti Homages, Bálint Andras Varga, editor (2009), as quoted in John Eliot Gardiner, Bach: Music in the Castle of Heaven (Alfred A. Knopf, 2013), p. 154.  The Gardiner quotation, in context, reads as follows: “One of the most widely revered figures among contemporary European composers, György Kurtág, recently confessed, ‘Consciously, I am certainly an atheist, but I do not say it out loud, because if I look at Bach, I cannot be an atheist. Then I have to accept the way he believed. His music never stops praying. And how can I get closer if I look at him from the outside? I do not believe in the Gospels in a literal fashion, but a Bach fugue has the Crucifixion in it – as the nails are being driven in. In music, I am always looking for the hammering of the nails . . . That is a dual vision. My brain rejects it all. But my brain isn’t worth much..’” [Return]

2. The quotation is from John Eliot Gardiner, Bach: Music in the Castle of Heaven (Alfred A. Knopf, 2013), p. 155.  In the sub quotation (the “apparently uncritically” clause) Gardiner quotes John Butt, Bach’s Dialogue with Modernity: Perspectives on the Passions (2010), p. 53. [Return]

3. Dreyfus, 2011 Lufthansa Lecture, London. Dreyfus suggests that Bach undermined the logos by his, “cavalier treatment of poetic texts [that] borders on the reckless,” defining logos as, “the notion which asserts the supremacy of the Word.” [Return]

4. On pp 438-439 of Music in the Castle of Heaven, Gardiner writes: “Theology is traditionally expressed in words, while music, Bach’s habitual form of expression, obeys rules that override word-driven considerations – in procedures that Dreyfus shows to be quite anti-literary at times. In the interplay – even friction – between words and music in his church cantatas, a strong sense emerges of Bach reaching for the definitive summative formulation of meaning. In the process he seems constantly to be challenging his listeners to consider what it means to be a Christian (freighted with obligations as well as joys). He uses music both to draw new meanings out of the Gospel texts and to hint at others that occur to him, perhaps subconsciously, in the process of composing and performing.” [Return]