Download Mathematics and Atonal Music

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.