Non-interactive Media

Thue-Morse Music

Brian Bowers and Dr. Neil Calkin

It is often useful to view mathematical sequences in nonstandard ways to improve our understanding of them. This project is an attempt to present a well-known mathematical sequence, the Thue-Morse sequence, in a musical format. The values of the sequence are reflected in the melody, chords, and rhythms of the piece. The piece is generated entirely from a portion of the sequence.

Thue-Morse Music by Brian Bowers and Dr. Neil Calkin It is often useful to view mathematical sequences in nonstandard ways to improve our understanding of them. This project is an attempt to present a well-known mathematical sequence, the Thue-Morse sequence, in a musical format. Information on the sequence can be found at http://en.wikipedia.org/wiki/Thue%E2%80%93Morse_sequence. I have created a program that generates values from the sequence and then uses a cipher I made to convert the values into a musical representation. The values of the sequence are reflected in the melody, chords, and rhythms of the piece. The piece is generated entirely from a portion of the sequence. I have also included a pictorial representation of the sequence. Both presentations draw attention to the so-called "self-similarity" of the sequence; this means that we can find copies of the sequence within itself, much like we can find copies of a fractal within itself. My hope is that this musical representation can bring to light previously-unseen patterns and properties of the sequence.
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