Math & Music Theory

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Ellyn McCall
Term Report

Mathematics and Music Theory

In the study of mathematics, at first glance it seems clear that mathematics is cut and dry, black and white, completely numerical. But in many ways, mathematics extends into other areas of life. While some people may think of mathematics and art as being two separate entities, Math is very present in many artistic endeavors. Music, commonly referred to as an art, would not be possible without the relationship it shares with mathematics. In many different ways, math is an important part of music theory.

One way that math and music theory are intertwined is within a theory of mathematics called Geometrical Music Theory. Clifton Callender, Ian Quinn, and Dmitri Tymoczko, who attended Florida State, Yale, and Princeton Universities respectively, created this method of music analyzing. Geometrical music theory is based on the mathematics locked within the structure of music. Their theory is based on their research that shows that “musical operations, such as transpositions, can be expressed as symmetries of n-dimensional space (Geometrical Music Theory, par. 3).” Scales, chords, and rhythms can all be categorized into mathematical ‘families’. Different geometrical spaces are created by different types of categorization. Using this method, researchers can analyze more types of music more effectively and show the changes in music over time in a straightforward manner.

In it’s simplest iteration, geometrical music theory provides a unified framework to decode musical events that are presented differently but are similar in nature. The creators believe that this theory can be used to compare different types of music to find underlying mathematic similarities or differences. In this way, those viewing the geometric sequences can see the visual difference between different genres and eras of music. It could one day also be possible to eventually show visual representations of music at...
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