Diffusion mapping is a non-linear analysis method that builds the structure of a data set though local connectivity rather than pure distance. This approach is advantageous because, by only using local connectivity, it is still robust and meaningful in high dimensional spaces without requiring any assumptions about the distribution of the data. Also, the diffusion mapping format leads directly into low-dimensional spaces for visualization. In this talk, I will examine the effectiveness of diffusion mapping as a tool for analysis and visualization of music theory. It will be shown that the approach is not only capable of organizing and visualizing musical data, but also, through these organizations and visualizations, communicating the underlying music theory. Examples will include demonstrations in the geometric representation of intervals, organizing data sets based on key and meter, and mathematically recreating historical visualizations of music theory.
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