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Canon by Intervallic Augmentation

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Overview Edit

Achilles and the Tortoise try to resolve the question, "Which contains more information -- a record, or the phonograph that plays it?" This odd question arises when the Tortoise describes a single record which, when played on a set of different phonographs, produces two quite different melodies: B-A-C-H and C-A-G-E. It turns out, however, that these melodies are "the same", in a peculiar sense.

While you read Edit

Questions Edit

  1. How many haiku can you find in the dialogue?
  2. How does Mr. Tortoise’s fortune cookie relate to the previous dialogue? Who’s the eater and who’s the cookie? What are the possible interpretations?
  3. Do you think the jukebox is physically realizable?
  4. Who is John Cage?
  5. The three musical pieces are apparently just variations on a common theme. What would happen if three other pieces had been randomly played from Mr. Crab’s jukebox?

Music Edit

Unlike some other dialogues, this title does not refer to a real Bach piece.

Bach wrote many canons where one part is some functional transformation of another part -- within the Musical Offering, you'll find parts that are other parts upside down, backwards, or played twice as slowly. But he never wrote a canon that involved multiplying the intervals by a common factor.

In fact, doing math on the number of semitones in an interval is a 20th century idea that Bach would find deeply weird. (John Cage would have been fine with it, of course, unless he decided it wasn't weird enough.)

The only work of John Cage's that most people are familiar with is 4'33", which is completely silent. Here's another piece to illustrate what John Cage is about: Imaginary Landscape No. 4 for 12 Radios.

You might well ask "is this even music?". John Cage's goal was to make you ask that.

Topics Edit

Steganography Edit

A modern analogue to the Tortoise's jukebox full of record players may be the practice of ➟ steganography -- where a file looks innocuous when opened with the expected computer program, but hides a secret message when opened with a different program.

Commentary Edit

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