Questions on Fugue No. 4
Well-Tempered Clavier, Book II
by Johann Sebastian Bach
©2009 Timothy A. Smith

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Before answering anything, click the following buttons to familiarize yourself  with some terms and concepts of Schenkerian graphic analysis as applied to the "butterfly" subject.

Foreground: While every pitch is important, each derives its existence from the c-sharp with
       which the fugue begins.  Every pitch's importance derives from relationships with others.

1st Middleground : Our immediate impression is of neighbor notes (N).  M. 1 begins with
       two neighbor clusters, and m. 2 with another.  I've represented the neighbors in gray, and the
       neighbor groups with broken-line ties, indicating prolongation of the main notes.  In the
       2nd Middleground we will drop the neighbors and represent their main notes with stems.

2nd Middleground: In this view passing tones (P) connect main notes by step.  The diagonal
       line is the unfolding symbol, which can be used to connect consonant skips, sometimes
       involving "gap fill" (passing notes between).  In the 3rd Middleground we'll drop the passing
       notes and represent the low g# as a prefixed consonant skip in relation to the c# that follows it.

3rd Middleground: The pitches in gray are now heard as neighbors and consonant skips
       (CS) in relation to the stemmed pitches (main notes). Notice how the first  d#, now represented
       as a suffixed upper neighbor, had been heard in the 2nd Middleground as a main note.  Thus, a
       pitch with high functionality at one level, derives its existence from something greater than it.
       In the language of computer programming, the "parent object" (main note) of any diminution
       may itself be the child object (diminution) of a more fundamental pitch.
Alternate View of the 3rd Middleground : The dotted ties indicate prolongation of c#
       and f#.  Each prolongation involves one neighbor (N) and one consonant skip (CS), but in the
       reverse order: MN-N-CS-MN becomes MN-CS-N-MN.  Each contour retrogrades the other.

Background: At the highest level, the final E is the subject's goal. Although it is the goal,
       E is nevertheless a consonant skip from the initial C#. The E is "prolonged" by a prefixed
       incomplete upper neighbor.


  1. C-sharp is heard four times.  In order, what roles does the c-sharp play? (Study the 1st & 2nd Middlegrounds.)

    N - P - N - MN
    MN - P - N - MN
    N - MN - N - CS
    MN - MN - N - MN

  2. In the 2nd Middleground, the low g-sharp is stemless . . . mistake.  It should have a stem.
    ...because in the 3rd Middleground it is shown to be a prefixed CS to the c# that follows.
    ...because in the 3rd Middleground it is shown to be a suffixed CS to the d# that precedes it.
    ...for no particular reason.  Schenkerian analysis is arbitrary in its use of stems.

  3. The 2nd Middleground has two pairs of diminutions represented in gray.  The diagonal
    "unfolding" symbol indicates a consonant skip from C-sharp to E.  Which of the following
    contradicts the interpretation offered in the 2nd Middleground?  

    The 1st pair of diminutions passes from G# to C#.
    The 2nd pair of diminutions passes from C# to F#.
    The 1st pair is less complex than the 2nd.
    The 2nd pair implies the diminution of a diminution.

  4. The 3rd Middleground and its alternate represent pretty much the same thing, but with
    a nuanced difference.
      Which radio-button option represents the whole case?

    (1) The 3rd Middleground emphasizes the prolongation of main notes.
    (2) The Alternate emphasizes the relationship of diminutions to their main notes.

    The first statement is true.
    The second statement is false.
    Both statements are true.
    Both statements are false.

  5. The following express Schenkerian ideas in the language of computer programming (which also admits double negatives). How many are FALSE?
    The F#, a "child object" in the Background, was a "parent object" in the Middlegrounds.
    The C# of the Background is the root parent that generates all others.
    The E is represented in the Background as both a child (of C#) and parent (of F#).
    The F# of the Background derives its function from the C# by way of the E.

    none of the above
    fewer than three
    more than two
    all of the above

  6. Bach has given the subject three expositions, two right side up, and one upside down (melodic inversion).  After this he has introduced a fourth exposition, with a lamentable subject that seems ill suited for this happy fugue.  He has has concluded the work in stunning double counterpoint of the lament against both the "butterfly" subject and its inversion.  The following represents the first two of these, where the original subject is represented in pink, and the lament in green.  The example on the right is generated from the left by double counterpoint at which of the following options? (To find the answer, hunt for the "fugue" card in the movie's overlayed hypertext.)



  7. The butterfly metaphor has been applied because (best answer please):

    The subject is frolicsome and gay.
    Psyche was the Greek word for "butterfly."
    Both Nabokov and Bach liked butterflies.
    All fugues involve contrapuntal metamorphosis.

  8. Of Borges's root metaphors, which one best applies to this fugue?

    fire and war
    flowers and women
    stars and eyes
    sleep and death

    time and the river

  9. The author makes the case that the fugue and Nabokov's Pale Fire are most alike in:

    their self-reflexive point of view.
    the inversion of their respective subjects.
    their use of puns and wordplay.
    their concept of counterpoint.    

  10. The philosopher Derrida, although a self-described atheist, advanced a philosophy that allowed metaphysics.  He understood that to deny metaphysics is to admit having taken a metaphysical position.  A good way to articulate this dilemma is to ask you to tell me one thing that you don't know that you don't know.  See the problem?  Can you appreciate the rationality, then, of a metaphysical assumption?  To deny what may exist outside the realm of what one can know to exist (the mind) is solipsism, which, in its extreme form, denies the existence of any "other" mind.

    The author takes the position that Bach's melodic inversion of the subject, and their combination with a lament, was his method of reconciling a metaphysical ontology (spirit, death, God, and the universe of what may not be fully knowable) with a physical epistemology (science, body, life, and the speck of the universe that can be known). The dualism between John Shade and Charles Kinbote also addresses the disconnect between what is, and what may not be, knowable.  If all that you knew of John Shade and Charles Kinbote was the following, in which character might Bach have found a kindred mind or spirit.

    With no Providence the soul must rely on the dust of its husk, on the experience gathered in the course of corporeal confinement, and cling childishly to small-town principles, local by-laws and a personality consisting mainly of the shadows of its own prison bars.  Such an idea is not to be entertained one instant by the religious mind.   How much more intelligent it is--even from a proud infidel's point of view!--to accept God's presence--a faint phosphorescence at first, a pale light in the dimness of bodily life, and a dazzling radiance after it? 
                        from Charles Kinbote's comment on Shade
                        line 549: "While snubbing gods including the big G"

    My God died young. Theolatry I found
    Degrading, and its premises, unsound.
    No free man needs a God; but was I free?
    How fully I felt nature glued to me.
                       John Shade, lines 99-102, Pale Fire

    Bach would have found in Kinbote a kindred spirit.
    Bach would have found in Shade a kindred mind.

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