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.

A fascinating article exploring the mathematical foundations of music. What came to my mind while reading it, is that our aesthetic pleasure from listening to music, arises from the fact that music allows us to explore and navigate higher dimensional spaces, while our immediate perception is confined to 3 dimensional space. Music if so is experienced as a kind of very profound freedom.

music allows us to explore and navigate higher dimensional spaces, while our immediate perception is confined to 3 dimensional space. Music if so is experienced as a kind of very profound freedom.

While the audio is a bit over-modulated, this recording of John Coltrane's My Favorite Things is perhaps the greatest expression of that notion ever achieved. Every time I listen to his recordings of this, I find places and emotions I had not yet found prior. EVERY TIME.

Thanks, A great piece.

great clip Silkweaver.10x.

great piece BartendingBear. your chosen tune tempted me to chose one immediately (just one among so many..-)) it is recorded in Montreux Festival 2006 featuring Erik Truffaz Murcof and Talvin Singh.
hope you enjoy it

Interesting article thanks. But I can't help thinking of the Frank Zappa quote: "Writing about music is like dancing about architecture."