Puzzling News / Sep 2000


	SCOTT KIM’S PUZZLING NEWS / SEPTEMBER 2000 J. S. Bach

In 1975, as an undergraduate at Stanford University, I first met Douglas Hofstadter. He was teaching a seminar called Gödel's Theorem and the Human Brain, based on his then partially written book Gödel, Escher, Bach. The poster for the seminar showed an Escher print, and mentioned Bach's music.
     It all sounded too good to be true. I had just read Nagel & Newman's thrilling "Gödel's Proof," I admired Escher's art, and as a music major specializing in piano I was deeply drawn to Bach's music. I was particularly interested in canons and fugues -- compositions in which several interwoven melody lines all expound on a single theme.
     I loved playing fugues with many voices. Bach's Well-Tempered Clavier features a couple five-voice fugues — at any one time half your fingers may be occupied. I had recently learned the monumental six-part fugue from The Musical Offering, the only six-voice keyboard fugue that I know of. And I was working my way through Bach's final work, the Art of Fugue.
     Doug was interested in all these things, and having a grand old time weaving them together into a literary work that would become a classic. We found that we shared other passions -- writing names so they read upside down, carving a block of wood so it casts shadows of three different letters, writing canons and fugues. Soul mate!
     A year later I helped Doug teach the next installment of his course. We began by acting out the story of the Musical Offering. In 1747 Bach visited King Frederich the Great of Prussia at his court in Potsdam. The king, an accomplished musician, played a long sinuous theme he had written.
     In his time Bach was renowned as an improviser. The king asked Bach to improvise a 3-voice on the royal theme. Bach obliged. Then the king asked for a 6-voice fugue on the same theme. Bach declined -- he substituted a simpler theme of his own instead -- but several months later he sent the king a Musical Offering, which included the 3-voice fugue he had improvised, ten canons, a trio sonata, and a 6-voice fugue, all on the royal theme. (Here are a MIDI file you can listen to online, the printed score, and a CD of the Musical Offering.)
     Acting the part of Bach, I performed the 3-voice fugue, then the 6-voice fugue. To top it off I surprised Doug with a new canon on the Musical Offering theme I had written for the occasion. In this canon two voices start at the same time an octave apart. The high voice plays twice as fast as the low voice, completing two
repetitions in the time it takes the low voice to complete one. I chose to write a two-voice "canon by augmentation" because it is a particularly challenging form, and there isn't already one in the Musical Offering.
     Bach continues to play a major role in my life. My book Inversions includes several designs on Bach's name, including the mirror symmetrical design featured as the current inversion of the month. I am fond of Norman McLaren's animation Spheres, which choreographs spheres in space to Bach fugues, and Canon.
     More recently I've talked about Bach with Seattle singer/songwriter Linda Waterfall, friend of my wife Amy, whose intricately contrapuntal arrangements owe a debt to Bach, and violinist/conductor Karen Bentley, who is thinking about including Bach-like compositions by other composers in her annual local Bach festival.

WHAT’S NEW SEPTEMBER 2000

Inversion of the Month: J. S. Bach. Mirror symmetrical tribute to the master of musical symmetry.

NewMedia Puzzler. True Colors — identify the companies by their corporate colors.

Discover Magazine Boggler. September: Digital Dexterity (tie your fingers in knots), Scrambled Geometry (anagrams), Base Impulses (base 12 and beyond)

Math Dance web site. Just launched! Classroom activities for teachers.

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