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Abstract
Music theory undertakes the audacious goal of understanding why music is pleasing to the ear and why it is effective at expressing emotions. Applying mathematical thinking to music analysis is nothing new; the field of mathematical music theory is well-established and dates back to Pythagoras. This said, there is little literature on understanding music through a holistic lens. Ecologists and economists are more familiar with analyses which address indirect, nonlinear, obscure relationships between component parts of networks, often using mathematical tools. Network Environ Analysis, one of these methods, views networks as transactional systems and uses hard mathematics to describe more fully the effects which arise as systems grow in size.In this document, we investigate how Network Environ Analysis can be applied to musical pieces to understand better their musical structures. We describe multiple ways of interpreting musical pieces as transactional networks and apply the corresponding mathematics in several cases. We attempt to draw links between mathematical indices which evaluate these networks' indirect structures and musical quality, and we use these measures to give rigorous meaning to subjective music theoretic judgements. Further, we develop statistical tools which use holistic information related to these transactional networks to define and demonstrate mathematical manifestations of the style and tonality of a piece of music.