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POPSThe Shape of Music The shapes of the space of chords we have described also reveal deep connections between a wide range of musical genres. It turns out that superficially different styles--Renaissance music, classical and Romantic music, jazz, rock, and other popular forms--all make remarkably similar use of the geometry of chord space. Traditional techniques for manipulating musical scales turn out to be closely analogous to those used to connect individual chords. And some composers have displayed a profound understanding of the higher-dimensional geometry of musical chords. In fact, one can argue that Romantic composers such as Chopin had an intuitive feel for non-Euclidean higher-dimensional spaces that exceeded the explicit understanding of their mathematical contemporaries.
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