Math in Music

Ever wonder what the Golden Ratio sounds like? It’s hauntingly eerie and beautiful…

And this is a composer’s interpretation of fractal music (Gyorgy Ligeti):

It’s a really complicated piece that has so many different layers to it. Every time I listen to it, I hear something new.

“Fractals are patters which occur on many levels. This concept can be applied to any musical parameter. I make melodic fractals, where the pitches of a theme I dream up are used to determine a melodic shape on several levels, in space and time. I make rhythmic fractals, where a set of durations associated with a motive get stretched and compressed and maybe layered on top of each other. I make loudness fractals, where the characteristic loudness of a sound, its envelope shape, is found on several time scales. I even make fractals with the form of a piece, its instrumentation, density, range, and so on. Here I’ve separated the parameters of music, but in a real piece, all of these things are combined, so you might call it a fractal of fractals.”

-Gyorgy Ligeti, 1999 interview, The Discovery Channel