K. Mpizas, Stochastics in music: Analysis of melodies using the Hurst-Kolmogorov model, Diploma thesis, Department of Water Resources and Environmental Engineering – National Technical University of Athens, November 2023.
The current thesis discusses the study of musical melodies from a mathematical perspective. A methodical study regarding the finding of mathematical motif behavior of monophonic melodies will be attempted. Said motifs will be examined on a statistical and stochastic basis with an accentuation on the stochastic parameters of the Hurst Kolmogorov model. To achieve this, a thorough python code will be developed, in order to process MIDI (Musical Instrument Digital Interface) song files from five genres. These genres consist of baroque, classical and romantic periods as well as soul and rock & roll as two separate types of contemporary music.The central axis of the processing is the comparison of statistical properties, moments, distributions and climacogramms. The study utilizes the tracks’ notes as the time series’ random variable. However the study of musical intervals or distances from the tonic note in certain points of the analysis also serves a purpose. The application of the Hurst-Kolmogorov (HK) & Generalized H-K model aims to deduce conclusions about the persistence in musical arts and attempts to categorize harmonic rules and techniques. In addition, an attempt to apply the model on a non-natural phenomenon, which consists of actual rules, is being made, considering that music is characterized by human creation.
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