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 ...

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 ...

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 ...

Many musical cultures choose scales that establish simple frequency ratios (2:1, 3:2, 4:3) between notes. It is commonly believed that this choice is solely explained by the intention to maximize the ...