Date Presented

Spring 4-1-2007

Document Type


Degree Name

Bachelor of Arts



First Advisor

Kevin Peterson

Second Advisor

Nancy Cowden

Third Advisor

Chris Gassler


This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals with the relationship between music and math. Contrary to previous investigations, the purpose of this thesis is to take something purely mathematical and make music from it. From the methods used, the music created from formulas for fractal music and chaotic unimodal quadratic maps created the most musically interesting melodies.