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Counterexamples in Music Theory

In 2003, as a sophomore in college, I was happily sinking more and more deeply into both music theory and mathematics. As befits my personal brand, I wrote a 12-tone serial setting of one statement of the fundamental theorem of calculus for an assignment in a 20th century music class. 

Twelve-tone serialism, as Vi Hart explains in an excellent video below, was proposed in the early 20th century to encourage composers to break free of traditional tonality and write music in which no note is more important than any other notes.

A serial composer starts with a tone row, which is an ordering of the twelve half steps (or 12 piano keys: C-C#-D-D#-E-F-F#-G-G#-A-A#) in an octave.

A sketch of a keyboard showing the 12 pitches that make up the notes in a 12-tone row. Credit: Evelyn Lamb, based on Spindoktoren~commonswiki Wikimedia (CC BY-SA 3.0)

The tone row I used in my composition was F#-A-E-D-C#-F-B-G-G#-A#-D#-C.

My tone row, notated on a staff. Credit: Evelyn Lamb

That row and certain modifications of it, such as transposing the row so it starts on a different note or playing it backwards, provide the allowable material in the piece. The composer must use the pitches from one of these rows, in any octave, in order before reusing the earlier pitches. (Some composers interpret the rules slightly differently, but that’s the gist.) This is the first line in the vocal part of my song.

A line of music with the lyrics If f is continuous on the interval from a to b
Credit: Evelyn Lamb

My composition was by no means a work of genius (to listen to a 12-tone serial work of genius, check out Alban Berg’s Lyric Suite), but my tone row

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