David Smith on Math and Music
February 27, 2013David Smith is an associate professor of mathematics at Virginia Highlands Community College, a pianist and formerly taught piano.
"Music may be the most abstract of the arts, mathematics the most abstract of the sciences. Both give accessible form to deep perceptions; both can offer unique beautiful and creative solutions to problems; both work within and expand a set of existing structures.
"The tools used in constructing and interpreting music are to an extent mathematical in nature. The harmonics on which music is based can be analyzed and represented mathematically. There are mathematical symmetries in overall structure, in melodic and harmonic development, etc. At deeper levels, it might have to do with both music and mathematics giving form to the abstract.
"The common process might be the representation of abstract perceptions. In the end the result is formulated using the tools and structures of the discipline, and there is certainly a thought process at this level. The process originates, though, at a level deeper than thought.
"There is a problem solving aspect to both, in which a problem arises, you immerse yourself in it, look at it from a variety of perspectives, experiment with it, hope for inspiration, hope that thoughts and perceptions and images crystallize into a beautiful solution.
"Good mathematical structures are complex and beautiful in ways that are less apparent to the layman than those of music, which at the level of our sense is more immediately accessible. Music is perceived through our senses but can be appreciated at deeper levels as well. Deep problems emerge in both mathematics and music. Often such problems can only be solved by an act of creation.
" I doubt that most composers are consciously aware of the connections between Fibonacci numbers and golden ratio. These connections may be coincidental, or they might be the result of some underlying phenomenon.
"I do not compose, but algorithmically-generated music (music created by a process that includes some degree of randomization within a set of rules) can be executed by a computer. It is largely mathematical in its execution. Algorithms have been developed that result in pleasing and sometimes critically-acclaimed music. There is no reason to believe that algorithmically-generated music won't continue to get better, and it isn't inconceivable that it could eventually exceed the quality of the best human compositions."
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