Exploration of Music Theory Using Mathematical Modeling Techniques
Location
CSU 238
Start Date
16-4-2013 10:05 AM
End Date
16-4-2013 11:05 AM
Student's Major
Mathematics and Statistics
Student's College
Science, Engineering and Technology
Mentor's Name
Jeffrey Ford
Mentor's Department
Mathematics and Statistics
Mentor's College
Science, Engineering and Technology
Description
There is a deep connection between mathematics and music. The music was created first, however, and the math behind it is still being discovered – from counting beats to abstract algebraic models. We are looking for mathematical representations for two specific aspects of the relationship. One aspect relates multiple musical notes. All of the current research on this topic uses the frequency of the notes in the equal temperament method of tuning. This is the tuning like that of a piano. Bands and orchestras do not use the equal temperament method of tuning, when tuning chords, however. They use a method of tuning called just intonation. We hypothesize that using just intonation creates less sporadic sound waves, causing our ears to perceive them as less dissonant. We can look at the sound wave graphs of chords using the two tuning methods to compare and contrast. Another aspect of the relationship considers not just the sounds but the compositions. We will be using a specific type of music, change- ringing, the art of ringing a set of tuned bells in mathematical patterns without attempting to produce a melody. We will attempt to create models of the change-ringing composition process. Our exploration will use previously developed modeling techniques, as well as, their application to our key topics of tuning methods and change-ringing composition.
Exploration of Music Theory Using Mathematical Modeling Techniques
CSU 238
There is a deep connection between mathematics and music. The music was created first, however, and the math behind it is still being discovered – from counting beats to abstract algebraic models. We are looking for mathematical representations for two specific aspects of the relationship. One aspect relates multiple musical notes. All of the current research on this topic uses the frequency of the notes in the equal temperament method of tuning. This is the tuning like that of a piano. Bands and orchestras do not use the equal temperament method of tuning, when tuning chords, however. They use a method of tuning called just intonation. We hypothesize that using just intonation creates less sporadic sound waves, causing our ears to perceive them as less dissonant. We can look at the sound wave graphs of chords using the two tuning methods to compare and contrast. Another aspect of the relationship considers not just the sounds but the compositions. We will be using a specific type of music, change- ringing, the art of ringing a set of tuned bells in mathematical patterns without attempting to produce a melody. We will attempt to create models of the change-ringing composition process. Our exploration will use previously developed modeling techniques, as well as, their application to our key topics of tuning methods and change-ringing composition.
Recommended Citation
Painter, Sarah and Leah Lumley. "Exploration of Music Theory Using Mathematical Modeling Techniques." Undergraduate Research Symposium, Mankato, MN, April 16, 2013.
https://cornerstone.lib.mnsu.edu/urs/2013/oral-session-05/1
