Contour modeling by multiple linear regression of the nineteen piano sonatas by Mozart.

摘要

Theories of musical contour can be described as the study of the change in one musical parameter as a function of another. In my dissertation, contour theories proposed by Robert Morris, Michael Friedmann, Elizabeth Marvin, Paul Laprade, Ian Quinn, Robert John Clifford, Larry Polansky and Richard Bassein are reviewed. In general, these authors approach changes in pitch as a function of time. A commonality between these theories was shown to be the use of a system of pitch level identification based on the relative highness or lowness of the pitches, not based on actual pitch frequencies or pitch intervals in the melody. Additionally, these theories did not account for rhythmic or durational elements of the pitches as they are articulated in time. Music perception studies were cited that indicated that contour can play an important role in the recognition and memory of a melody, and that pitch interval and rhythmic components are vital elements in music understanding. Because these contour theories lacked the important musical elements of pitch and rhythm, an analytical method for the study of musical contour that incorporates both of these in its model of a melody is developed. This analytical method uses the mathematical technique of multiple linear regression to develop a model of the melody that can be graphed as representative of the contour of the actual melody. This method was used to analyze the first themes from the first movements of the nineteen piano sonatas composed by Mozart. Using regression modeling, the sonata melodies were categorized into two melody types: Type MD and Type LB. Analytical methods proposed by other theorists were then used to analyze selected melodies, and a comparison between the multiple linear regression model and these results was made.