The mathematical rules for creating musical harmony may be more malleable than thought. Western music theory traditionally holds that chords sound most pleasant when they contain notes separated by ...

Almost every song you hear has a chord progression. This forms the harmonic content of the song, and is often what gives a song its emotional impact. But what about the melody? The notes of the melody ...

A crucial link between mathematics and music is nicely illustrated by the Tonnetz, a geometric diagram representing the harmonic relationships between the notes of the musical scale. An early version ...