ES.258 | Spring 2007 | Undergraduate
Gödel, Escher, Bach


The text for this course is:

Hofstadter, Douglas. Gödel, Escher, Bach: An Eternal Golden Braid. New York, NY: Basic Books, 1999. ISBN: 9780465026562.

In this list, each chapter of the book is associated with a musical piece that the instructor chose to accompany it. The pieces by J. S. Bach are labelled with their BWV catalog number.

Introduction - Brandenburg Concerto No. 5 in D major (BWV 1050), for no particular reason except that it’s a good Bach piece to start things off.

1. Three-Part Invention - The Three-Part Ricercar, from the Musical Offering (BWV 1079), introduces the King’s theme (which appears in nearly every piece of the Musical Offering) and the fugue style in general.

2. Two-Part Invention - Two-Part Invention in C major (BWV 772)

3. Sonata for Unaccompanied Achilles - Sonata No. 1 for solo violin: Adagio (BWV 1001). If an accompanied version of this exists somewhere, I don’t know where to find it.

4. Contracrostipunctus - Contrapunctus 19 from the Art of Fugue (BWV 1050). This performance abruptly ends in the same place that the score ended due to Bach’s death. Bach left his name in the music, as the German notes B-A-C-H, a few measures before the end.

5. Little Harmonic Labyrinth - The Little Harmonic Labyrinth turns out not to be by Bach at all! It was written instead by his much lesser-known contemporary, Johann David Heinichen. Disappointingly, it doesn’t even have a fake resolution near the end, as the dialogue implies. Also, it’s boring.

A completely unrelated piece, however, does have a clear “pushing and popping” structure to it, and a fake resolution: Waltz #2 by Billy Joel. Yes, that Billy Joel, retired from pop and writing classical music. Allow Achilles and the Tortoise one more anachronism and pretend this is what they’re listening to.

6. Canon by Intervallic Augmentation - Bach never multiplied the intervals of a theme by 3 1/3. He did multiply them by -1 in this canon by exact inversion, the Canon Perpetuus from the Musical Offering. An effect of the exact inversion is that the piece has to oscillate constantly between major and minor chords, and technically it can’t end.

7. Chromatic Fantasy, and Feud - The title is a pun on the Chromatic Fantasia and Fugue (BWV 903). Hofstadter acknowledges that the dialogue “bears hardly any resemblance, except in title” to the music.

8. Crab Canon - Hofstadter’s entire dialogue structure emerged from writing a dialogue based on the Musical Offering’s Crab Canon (Canon Cancrizans).

9. A Mu Offering - If I can pick any piece of the Musical Offering I want to listen to, it’s the Allegro from the Trio Sonata at its center. It’s mostly a free composition, but listen closely for where the King is hiding.

10. Prelude…

11. …Ant Fugue - The Prelude and Fugue in C Major (BWV 846) open the first book of the Well-Tempered Clavier. “ATTACCA” is notated in between them in the score, meaning you should progress immediately from the prelude to the fugue.

12. English French German Suite - English Suite No. 2 in A Major, Prelude (BWV 807). You won’t hear any Jabberwocky here, just a lively Bach keyboard piece.

13. Aria with Diverse Variations - This chapter refers extensively to the Goldberg Variations (BWV 988), an extensive set of variations on an aria. The 30th and final variation is a straightforward statement of the theme called the Quodlibet, after which the variations continue on with a “post-ending ending”, the Finale.

You can find this piece among the famous recordings by eccentric pianist Glenn Gould. If you listen
closely, you can in fact hear him singing along under his breath.

14. Air on G’s String - Bach’s Air on the G String (BWV 1068) is a soothing string piece, much unlike Gödel’s unsettling mathematical string.

15. Birthday Cantatatata… - The characters refer to a cantata Bach wrote for the birthday of the King of Poland. When you track it down (Wikipedia reveals that this person was in fact better known as the King of Saxony), it leads to Cantata 206 (BWV 206), an obscure but wonderfully joyful cantata.

16. Edifying Thoughts of a Tobacco Smoker - The poem really is by Bach, and he even supposedly set it to music, but I would have no idea where to find it.

17. The Magnificrab, Indeed - The title is a pun on the Magnificat in D Major (BWV 243), whose translation begins “My soul doth magnify the Lord”. (“My soul! How you magnify the Crab!”)

18. SHRDLU, Toy of Man’s Designing - A pun on Jesu, Joy of Man’s Desiring, a well-known movement from Cantata 147 (BWV 147).

19. Contrafactus - Contrapunctus 12 from the Art of Fugue can be played either in its standard form (“rectus”) or inverted on the scale (“inversus”). They are usually performed back-to-back in that order, but clearly they would be performed in the other order if up were down. Or would they?

20. Sloth Canon - This is the name Hofstadter gave to the Canon by Augmentation in the Musical Offering. Like in the dialogue, one part is twice as slow and inverted with respect to another part, while the third part is free.

Synthesized recordings of the Endlessly Rising Canon on the Shepard scale can be found on the Web.

21. Six-Part Ricercar - A dialogue full of deep structure and subtle tricks, based on a fugue that could be described the same way: the Six-Part Ricercar that ends the Musical Offering.

Additional Readings from the Class

Hofstadter, Douglas R., and Clément Marot. Le Ton Beau De Marot: In Praise of the Music of Language. New York, NY: Basic Books 1998, chapter 5. ISBN: 9780465086450.

Chapters from: Hofstadter, Douglas. Metamagical Themas. New York, NY: Basic Books, 1996. ISBN: 9780465045662. (Toward the end of the class): A Coffeehouse Conversation on the Turing Test and Who Shoves Whom Around Inside the Careenium?