Questions on Fugue No. 8
Well-Tempered Clavier, Book I
by Johann Sebastian Bach
©2014 Timothy A. Smith

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  1. The subject of this fugue is remarkably similar to one of Bach’s last compositional cycles, the great Art of Fugue. This is a series of fourteen contrapuncti (fugues) plus four canons. In the present fugue from the Well-Tempered Clavier, Bach developed the subject right side up (rectus), upside-down (inversus, which is the same thing as “melodic inversion”), and also in rhythmic augmentation (doubling each note’s duration). Listen to these five from the Art of Fugue then select the true statement.

    All are true.
    Three are true.
    Two are true.
    One is true.

  2. The subject of this fugue is also similar to that of the bbm fugue of the Well-Tempered Clavier, book 1. What is the primary difference in voice leading between these two subjects?

    The bbm leaps up a 9th where the ebm steps up a 2nd.
    The bbm fugue is played alla breve, but the ebm is in common time.
    The bbm fugue has two more voices than the ebm fugue.
    Bach actually wrote ebm fugue in d#m.

  3. The exposition concludes with a Phrygian half cadence, which is nearly always harmonized as iv6-V. The cadence chord, the V chord, is what makes it a “half” cadence. What makes it “Phrygian” is “le-sol” (b6-5) in the bass, which is made by the iv6 chord. Which of the following would also yield “le-sol” (moveable “do”) in the bass?

    • viio42 - V
    • viio6/V - V
    • iiø43 - V
    • Fr+6 - V

    all of the above
    three of the above
    two of the above
    one of the above

  4. The Phrygian half cadence is heard three times in this fugue. How many times is it preceded by a lament (also called a lamento bass)?

    three times

  5. Evaluate the following statements then select the best answer.

    • A canon is a stretto.
    • Stretto involves a motif, like a fugal subject, in counterpoint with itself.
    • There are 13 stretti in this fugue, some involving two voices and others three.
    • The subject of the present fugue, augmented, is heard once in stretto with its non-augmented inversion.
    • The subject of the present fugue, augmented, is heard once in stretto with its non-augmented self.

    All are true.
    Four are true.
    Three are true.
    Two are true.
    One is true.

  6. A fugue, like a novel, can involve contradiction and conflict resolution. This can exist on many levels: in rhythm, melody, harmony, counterpoint, or form. In this fugue the conflict begins with the subject’s inversion in the second development, and achieves its most compressed enactment in which measures?

    mm. 52-55
    mm. 62-66
    mm. 67-72
    mm. 77-82
    mm. 84-86

  7. Dostoevsky’s “Legend of the Grand Inquisitor” and “Life of the Hieromonk and Elder Zosima” are subplots that the author nested within the larger narrative. The fugal analog to this is:

    the exposition
    rhythmic augmentation of the subject
    melodic inversion of the subject
    modulation to related keys
    sequential episodes like mm. 84-86

  8. Polyphonic music, like a polyphonic novel, achieves its effect by:

    rhythmic deviations
    deliberately unresolved gaps
    implied intersections
    radical transformation of the subject
    independent voices

  9. Bach composed the odd interval of a diminished third twice in this fugue – both involving F-flat to D. The author notes that elsewhere Bach set the word “crucified” to diminished thirds. Which work was suggested as an example?

    St. John Passion
    St. Matthew Passion
    Mass in B Minor
    Cantata 4

  10. The author concludes by quoting Søren Kierkegaard on the significance of paradox as a passion of thought. “The ultimate paradox,” wrote Kierkegaard, is “to want to discover something that thought itself cannot think.”

    At the core of how we think as modern people is a method developed by another philosopher, René Descartes [1]. His empirical method is the basis for how science works today. Descartes is best remembered for the phrase, “Cogito, ergo sum,” which means, “I think, therefore I am.” But few people know the paradoxical thought that caused Descartes to know that he existed. It goes like this:

    • We shouldn’t place confidence in anything that has an element of doubt.
    • All things, all logic, math, science, history, etc. have elements of doubt.

    It is at this point that Descartes wrote (beginning of his Second Meditation): “I have convinced myself that there is absolutely nothing in the world, no sky, no earth, no minds, no bodies. Does it now follow that I too do not exist?” But then he thought this:

    • I have no doubt that I cannot prove that God does not exist.

    And in this paradoxical thought, Descartes found something certain, of which he had no doubt. He could not prove that God didn’t exist. And in thinking this paradox, he knew without doubt that he existed, for he had thought something of which he had no element of doubt. He himself was therefore the source of certainty, and from his own thought he could move, with equal certainty, to a philosophy of rationalism rooted in the self. In short, much of what modernity deems to be certain and beyond doubt is predicated upon the certainty that we can’t prove that God doesn’t exist.

    This fugue also contains a paradox. The second development presents the subject as the inversion of the first development, which presents the subject as the inversion of the second development. They are inversions of each other. Now pretend that there is no such thing as time. Without time, the inversional relationship of these two melodies exists for sure, but one can’t determine which is the inversion of the other. For the purpose of answering this question, let us think of the subject in its rectus and inversus forms as motifs x and y. Which of the following statements is analogous to Descartes’ primal thought (in red above).

    Motif x cannot be without y as the implied necessity of its being.
    Motif y cannot be without x as the implied necessity of its being.
    Motifs x and y can come into being only in simultaneity, not as each other’s cause, but implicit in the being of the other.
    Motifs x and y are distinct melodies that are of one being.
    Where the one exists, I have no doubt that I cannot prove that the other does not also.

Does this mean that for every melody there is an “anti-melody” (its melodic inversion) that necessarily coexists? Yes it does! But few inversions are able to sound in harmony with themselves as per norms of tonal counterpoint. By the word “invention,” Bach meant the very discovery of these preternaturally harmonious relationships.

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1. This synopsis of Descartes is based on Michael Allen Gillespie's chapter, “Descartes' Path to Truth,” in The Theological Origins of Modernity (University of Chicago Press, 2008), pp. 170-206. [Return]