Rok Kršmanc (2009) Analysis of Homophony with Higher Order Markov Chains. EngD thesis.
The purpose of diploma paper is the development of application for the analysis of polyphonic musical pieces (especially from the view of vertical time progress of voices or homophony), together with the suitable theoretical study of the field in question. Beside the basic characteristics of sound simple harmonic motion and within the framework of consonance also aliquote tones and scales are described. All this is the source of motivation for the detailed study of consonance and more possible views of homophony. Music information retrieval is a strong tool for quantitative study of music. A few possible approaches are mentioned; however, mathematical tool of Markov chains which is a good starting point for the study of homophonic compositions is put out especially. The procedure which is concentrated on the use of higher order Markov chains and is used for the analysis is also described. This is what enables the consideration for history in musical progress and, consequently, a wider view. The elaborated application with the described method analyzes the composition written in MusicXML format. In this procedure the analysis takes suitable theoretical background into consideration. In this way the application is an effective resource in different musicological approaches to the study of homophony. Analysis, together with commented results, is made on the example of a concrete music piece. In the end some more possible starting points for further work are stated.
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