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Lukas Yanni Prof. Porter Calculus III 11/30/2012 Mathematics and Atonal Music This talk was about the relation of mathematics and music, and the mathematical theory behind the mixture of different tones and musical notes. It was explained as to what atonal music was and the keys that comprise them. There are a few basic minor keys such as the natural, harmonic, and melodic. The presenter proved that music and musical patterns are deeply rooted in mathematics and set theory. One can discover such patterns through inverting and transposing. Isometrics are a commonly used practice on the mathematical nature of the music as it preserves the intervals between musical tones in a set. I really enjoyed the analysis she did, it was very interesting and quite clear, especially when she looked at Schoenberg’s Suite for Piano op. 25, Prelude. She exposed his use of transpositions, retrograding, and permutations of tone rows throughout different parts of the piece. She refers to sub rows, or sub groups within the tone rows. There are seven contrasting sections in the Prelude, and she analyzed each section in not only mathematical dialect, but also in good metaphors such as “train wreck” and acceleration of the piece. Though, the primary ideas she touched on were dissonance. By putting the notes into set, mathematically they can be manipulated into different combinations and create music based in and shaped by mathematics. The degree of inversion controls the degree of dissonance in the music. The creation of atonal music relies heavily on combinatorics, group theory, and mathematical patterns in general. Atonal music was not widely accepted at the time of its creation, but slowly became more welcomed into the musical style arena. What I found quite interesting regarding the presentation is that as a demonstration she allowed us to make whatever noise we wanted for roughly four minutes, and it would be classified as atonal music. This drove the point home as to what atonal music was in practice and how broad the spectrum of atonal music was. She also played on the piano for a while to demonstrate the atonal notes and answer many of the question that the audience had. Though, she did state that atonal music is not entirely modeled by mathematics, it does boil down to the creativity of the composer. Overall she was a very interesting talk, and she did quite well.