Diffusion-based music analysis : a non-linear approach for visualization and interpretation of the geometry of music
- Diffusion mapping is a non-linear data analysis method based off a model of the data as a states in a random walk. Through this approach, the global structure of the data is built up from local connectivity rather than pure distance. This diffusion-based approach is advantageous because, by using only local connectivity, it is still robust and meaningful in high dimensional spaces, unlike Euclidean distance, without requiring any assumptions about the structure of the data. Also, the diffusion mapping format leads directly into meaningful low-dimensional spaces for visualization of the data's structure. I will examine the effectiveness of diffusion mapping as a tool for analysis and visualization of music theory and, through these demonstrations, make an argument for its vast potential in the field. Diffusion has never been applied to music at this level before, nor has it been used at any other field for an analysis on a comparable level to music theory, but it will be shown that the approach is not only capable of organizing and visualizing music, but also, through those organizations and visualizations, communicating the underlying music theory used in creating the data sets. Example applications include demonstrations in the geometric representations of intervals, organizing data sets based on key and meter, and visualization of musical excerpts as trajectories in a diffusion-derived space.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|2010, c2011; 2010
|Sell, Gregory Kennedy
|Stanford University, Department of Music
|Wang, Ge, 1977-
|Wang, Ge, 1977-
|Statement of responsibility
|Gregory Kennedy Sell.
|Submitted to the Department of Music.
|Thesis (Ph.D.)--Stanford University, 2011.
- © 2011 by Gregory Kennedy Sell
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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