Questions on Fugue No. 16
Well-Tempered Clavier, Book I
by Johann Sebastian Bach

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1. This fugue develops a small number of motives. How many?

one
two
three
four

2. Whereas the subject is made of m & n, the countersubject is made of u & w. Which of the following accurately describe how the countersubject is generated from the subject.

• Motive u is the retrograde of n.
• Motive u is the melodic inversion of n.
• Motive u is the retrograde inversion of n.
• The countersubject melodically inverts m & n.
• The countersubject reverses the order of m & n.

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

3. How is this fugue like a fractal?

• Its countersubject is generated from the subject.
• It contains nested layers of double counterpoint.
• It contains self-similar structures at various levels.
• It is the musical expression of (i x i) + c = i.

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

4. How many stretti are there in this fugue?

none
one
two
three
four

5. Fractals and fugues are both:

products of the imagination.
products of mathematical formulae.
processes that can produce music.
more than one of the above.
all of the above.

6. This is a difficult question, so careful framing of it is in order. At the heart of this question is the difference between motivic and textural variation. By "motivic" variation we refer to the production of new motives by the application of contrapuntal techniques to old motives. An example of motivic variation would be how motive u is generated from motive n by melodic inversion. By "textural" variation we refer to the production of new polyphonic textures without the production of new motives. With these definitions in mind, how many of the following statements are true of this fugue?

• When the subject and countersubject exchange registers, motivic variations are produced.
• When motives m & n (the subject) are melodically inverted to yield the countersubject, textural variations are produced.
• Double counterpoint always produces motivic variations.
• Melodic inversion always produces textural variations.

none of the above
one of the above
two of the above
all of the above

7. The countersubject of this fugue has a relationship to its subject like that of:

a lemon to iced tea.
a footprint to a foot.
the tooth fairy to a quarter.
a chameleon to a plaid shirt.

8. Which of the following is not true?

Fugues are like fractals.
Fractals can generate music.
Fugues can generate fractals.
Fractals can forecast the weather.

9. In Bach and the Patterns of Invention, Laurence Dreyfus theorizes that Bach began the composition of works like this fugue with the creation of a motivic complex -- a short segment containing the essential counterpoint and motivic variation of the work. The first statement of this fugue's motivic complex is in:

m. 1.
m. 2.
m. 3.
m. 4.

10. The motivic complex of this fugue is replicated, with slight variation: