Eine Kleine Nachtfractal
Friday, October 12, 2007 
Listen to Mozart by Renata SpiazziThe melodic recursiveness of most music, especially as manifested in the crystalline, almost-mathematical purity of Mozart compositions, suggests the presence of fractal-like structures that exist both in time and the frequency domain - structures that are both solid and ephemeral, logical and otherworldly.
Some may hear (even if they don't articulate) a richness that is reminiscent of fractal construction. Marin Alsop, Music Director of the Baltimore Symphony Orchestra, describes Mozart's popularity as the result of "the depth of the music and ... the fact that Mozart makes contact with our inner selves. Maybe it's because of his organic approach to composition - taking a small, cellular idea and developing it into something beautiful, he takes you by surprise but also comforts you."
The starting musical "cell ", feeding back on itself through multiple recursions/variations, grows into an exquisitely beautiful musical "structure", with layer-upon layer of filigreed nuance present in every measure.
If mathematics and music can't be separated, what then of art, which despite all efforts of artists to break free of figurative representation, still must be beholden to the mathematics of the 2-D plane? The infinite richness of fractals can break this canvas constraint, impelling creativity. Digital artist Renata Spiazzi writes in Why Fractals of the power of fractals to inspire her work: it was not the mathematics of the science that was interesting, but the fascination of the shapes, the colors and the illusion of space that was achieved in the images.
Spiazzi proclaims a fascinating mission that seems eminently achievable: to continue working towards a fractal that because of its beauty will bring tears to your eyes.
And no one should be surprised that Spiazzi is aided in her work by listening to music - none other than the Mozart whose cellular ideas spring forth into artistic creation ... in time, frequency, and the 2-D palette: When creating fractals I like to have the music playing. I think it puts me in a high feeling mood, and it allows me to see things in the fractals I would not see with different sounds surrounding me.
See Spiazzi's website for some beautiful images. Her Listening to Mozart is included at the top of this post.
Reader Comments (2)
If I may toss forward my own additive to this already exceptional post - one of "dimensionality".
Among others, Mozart has been a composer who influenced many facets of my own life, from my early school days to my present musical compositions. The number of dimensions in which I have felt the grandeur of Mozart's compositions is daunting when I investigate myself in retrospect. Most of all, I must make mention to K626, the great Requeim Mass in D minor. In your post you make mention to the "2-D" aspect of music. Certainly, on paper, the leggers and notes are no more than this. However, if there were a way to quantify the number of dimensions present within the intricate four part harmonies as they are sung and heard live, say at Lincoln Center in NYC, I would wager that the number certainly exceeds two. Perhaps, even, some unique "musical dimension" is brought forth at such moments.
Stepping aside from the chaos for a moment and to a biological phenomenon, I must confess, as I read this post I felt a warm chill (if there is such a thing) run up my spine. It is that feeling many artists or appreciators or art expereince upon the conclusion of a great sonata, or on the reading or viewing of a magnificent and personally favored masterpiece. This sort of triggered mental response is very sensitive and for myself, reacts strongly when the music of Mozart (most especially the Requiem) is heard, and seen, as it can be in concert or via some of the wonderful fractal images of Spiazzi. Bravissimo!
Even though I was referring to the 2-D plane of the painter's canvas, I acknowledge your intuition that the intricacy of the Requiem demands an extra-dimensionality to be "captured" in some numerical scheme. I wonder, though, what is lost when this program is carried out. The search for a dimension that somehow characterizes a piece of music appears to be the ultimate reductionist exercise - analagous to measuring the fractal dimension of Jackson Pollock's drip paintings. In the end, does the dimension correlate with your rhapsodic response to Mozart? Were Salieri's compositions of "lesser" dimension?
Unlike Spiazzi, who listens to Mozart as she creates, I prefer listening to some good jazz piano, Marian McPartland, say, or Bill Evans. That's when I get that "warm chill" to which you refer.