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Systematic Musicology: Empirical and Theoretical Studies

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Edited By Albrecht Schneider and Arne von Ruschkowski

This volume contains articles most of which present empirical studies in the field of systematic musicology. Contributions in particular deal with aspects of melody including modeling and computer-assisted analysis as well as with various issues in sound and music perception, musical acoustics and psychoacoustics. Topics range from loudness perception in ‘Techno’ music to sound radiation in classical singing styles, and from timbre research to wave field synthesis and room acoustics. One focus of this volume is on pop and rock music, another is on ethno and folk music. In addition to empirical investigations, theoretical and methodological issues are addressed including some fundamental concepts in ethnomusicology and folk music scholarship.

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Daniel Müllensiefen, Geraint Wiggins: Polynomial Functions as a Representation of Melodic Phrase Contour

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63 Daniel Müllensiefen Geraint Wiggins Polynomial Functions as a Representation of Melodic Phrase Contour Abstract The present paper explores a novel way of characterising the contour of melodic phrases. Melodic contour is represented by a curve that can be derived from fitting a polynomial equation to the pitch values given the note onsets. To represent contour numerically, we consider the coefficients of the polynomial equation as well as the time limits of the melodic phrase. After a brief review of different theoretical, didactic, analytic, and computational approaches to melodic contour, a detailed step-by-step description is provided of how polynomials can be fitted to melodic phrases. In two application examples, it is demonstrated how polynomial contour can be used as a basis for the computational processing of melodic information. The first application estimates the frequency of occurrence or prevalence of a phrase contour: a probabilistic model is constructed based on a large sample of phrases from popular melodies using a standard density estimation procedure to obtain an indicator of contour occurrence frequency. The second application is a similarity measure that exploits polynomial curves graph- ically and is based on Tversky’s (1977) ratio model of similarity. Further applications of the approach as well as quantitative tests of the existing ones are discussed as options for future work. 1 Introduction 1.1 Background Melodic contour is often regarded as one of the most important features in the analysis and composition of melodic music, i.e. music that is mainly conceived as consisting of one...

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