Scholarly
    Communications Project


Document Type:Master's Thesis
Name:David Matthew Franz
Email address:dfranz@vt.edu
URN:1998/00793
Title:Markov Chains as Tools for Jazz Improvisation Analysis
Degree:Master of Science
Department:Industrial and Systems Engineering
Committee Chair: Joel A. Nachlas
Chair's email:nachlas@vt.edu
Committee Members:Brian M. Kleiner
Chip McNeill
Keywords:Markov Chain, Jazz Improvisation, Creativity, Musical Analysis
Date of defense:April 23, 1998
Availability:Release the entire work immediately worldwide.

Abstract:

This thesis describes an exploratory application of a statistical analysis and modeling technique (Markov chains) for the modeling of jazz improvisation with the intended subobjective of providing increased insight into an improviserís style and creativity through the postulation of quantitative measures of style and creativity based on the constructed Markovian analysis techniques. Using Visual Basic programming language, Markov chains of orders one to three are created using transcriptions of improvised solos by John Coltrane in his song Giant Steps. Still considered as statistical data, the Markov chains are examined and information is extracted from them through the development of several statistical tools for musical analysis. Two general categories of tools for analysis are developed: Subtraction matrices and graphical comparisons of distributions. Using these tools and the raw Markov chain data for musical analysis, quantitative measures for creativity and style are postulated. These measures are based on previously developed models and definitions of creativity and style taken from the literature. The information acquired from the implementation of the analysis tools is applied to the models in order to provide a theoretical basis for the development of the quantitative measures and a framework for the interpretation of the information. Guilford's Structure of Intellect model is used for developing creativity measures and Heen's model of the constructs of style analysis is used for determining measures of style. Overall, this research found that Markov chains provide distinct and useful information for musical analysis in the domain of jazz improvisation. Many examples of Markov chains are enumerated and tools for analysis are developed that implement the Markov chains. It is then explained how Markov chains and the tools for their analysis can be interpreted to determine quantitative measures of creativity and style. Finally, this thesis presents conclusions on Markov chain portrayals, new analysis tools and procedures, quantitative measures of creativity and style, and, in sum, that Markovian modeling is in fact a reasonable and useful modeling approach for this application.

List of Attached Files

dmfetd.pdf dmfetd2.pdf dmfetd3.pdf


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