Symmetry In The Structure Of Musical Nodes

We investigate, if any symmetry that lies ubiquitously in most of the structures of nature is also present in music and how it presents itself within music. We try to quantify symmetry and patterns by constructing the statistical and visual directed graphs of pitch frequencies and their temporal alignment (time duration) in a composition. We draw these graphs for 1,409 tracks. This paper realizes the structure in between the pitch and time duration sequences via the underlying probability distributions and graph theory. It reduces the analysis of pitch frequencies in a given composition to 20 % out of 128 and the time durations of in the composition to only 53 out of the range of 0 to 2400 (approximately). Furthermore, we observe symmetric patterns for temporal graphs and their degree distribution indicates a self-organizing behaviour. To model pitch prediction in our brain while listening to a musical composition via Upper Confidence Bound Reinforcement Learning (UCB-RL) algorithm and analyze the learning curves per the composition of the Beethoven, Mozart, and Bach. We observe the highest smallest learning curve for Beethoven and the largest for Bach. This work may find its potential applications in music therapy, music synthesis, and cognitive science.