Visualization of low Dimensional Structure in tonal pitch Space
In his 2001 monograph Tonal Pitch Space, Fred Lerdahl defined a distance function over tonal and post-tonal harmonies distilled from years of research on music cognition. Although this work references the toroidal structure commonly associated with harmonic space, it stops short of presenting an explicit embedding of this torus. It is possible to use statistical techniques to recreate such an embedding from the distance function, yielding a more complex structure than the standard toroidal model has heretofore assumed. Nonlinear techniques can reduce the dimensionality of this structure and be tuned to emphasize global or local anatomy. The resulting manifolds highlight the relationships inherent in the tonal system and offer a basis for future work in machine-assisted analysis and music theory. Comments Presented at the International Computer Music Conference (ICMC 2005 : free sound), Paper ID 1200, held in Barcelona, September 5-9, 2005. http://www.icmc2005.org/index.php?selectedPage=119 This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/cis_papers/193 VISUALIZATION OF LOW DIMENSIONAL STRUCTURE IN TONAL PITCH SPACE J. Ashley Burgoyne and Lawrence K. Saul Department of Computer and Information Science University of Pennsylvania {burgoyne,lsaul}@cis.upenn.edu