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 ...

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 ...