Project Title:
Mathematical analysis of self-similarity and other fractal features in musical
forms.
Advisor: John Konvalina
Description: What distinguishes the music of Mozart from the music of Beethoven? What
distinguishes the various musical genres such as pop music, classical music and
folk music? In this project we will apply mathematical techniques, such as
spectral analysis and fractal analysis, to shed some light on these questions.
To quantify the differences we will consider the pitch and the duration of
various musical scores and convert them to time series. Using statistical and
mathematical software packages the time series will be analyzed for degrees of
regularity using various measures such as spectral analysis and fractal
measures of self-similarity.
The
student will perform the following tasks:
A.
Become familiar with research in the literature involving the application of
mathematical techniques to the study of music.
References
1. J. Fauvel (ed.), Music and Mathematics,
2. G. Gunduz and U. Gunduz, The mathematical analysis of the structure of some songs, Physica A 357 (2005), 565-592
3. C. Madden, Fractals in music, High Art Press, 1999
B.
Become familiar with statistical and
mathematical software (for example, Minitab and Matlab)
in order to be able to write and run several programs related to time series
analysis, spectral analysis, and fractal analysis.
C.
Analyze and interpret the resulting time series data from various musical
scores including several composers and various musical genres.
D.
Create a final research report to be presented at
the MAM Symposium.
OTHER
REQUIREMENTS: The students interested in the project
above are expected to have had some computer programming experience.
NOTE: The results of this research will represent the core of a
research paper that later will be sent for publication to a suitable journal.