Looking beyond the staff lines and listening behind the sound: Novel applications of two old-fashioned paradigms to the analysis of musical harmony - Talk by Dr. Thomas Noll, Escola Superior de Musica de Catalunya


Event details

Date and time 13.01.2020 16:0017:00  
Place and room
Speaker Dr. Thomas Noll (Germany, Spain) is a leading researcher in mathematical music theory, on the faculty of Escola Superior de Musica de Catalunya in Barcelona. In addition to his PhD from Technische Universität Berlin, he holds degrees in mathematics and semiotics. His 1995 dissertation, Morphologische Grundlagen der abendländlischen Harmonik, was subsequently published, followed by over 50 journal articles and book chapters. Co-editor of the Journal of Mathematics and Music from 2006–2012, and founding member of the Society for Mathematics and Computation in Music, he co-authored several articles with David Clampitt, including one that received the Society for Music Theory 2013  Outstanding Publication Award. 
Category Conferences - Seminars
Two traditional accounts to the analysis of chord progressions – Roman Numeral Analysis and Functional Harmony – have recently been joined by two paradigms which by themselves are timehonored domains of music-theoretical reasoning and conceptualization. But their application to musical harmony is a more recent development. One productive idea is to view chords and chord inversions as if they where scales or modes. This allows a productive transfer from a mathematical discipline called algebraic combinatorics on words to the combinatorics of modes (including chords and their inversions). The meanwhile ramified body of knowledge includes contributions by Eric Regener, John Clough, Jack Douthett, Norman Carey, David Clampitt, Karst de Jong and others (including Daniel Harasim and myself :-). Thereby it turns out that some of the mathematical findings are by no means alien to traditional music-theoretical knowledge. They rather turn out to be natural consequences of insights which underly the invention of traditional musical pitch notation. The applications to chord progressions include aspects of voice leading as well as the patterns underlying typical fundament progressions. Another productive idea is a quite unorthodox application of Fourier analysis, which in connection with music is usually admired as the ultimative tool for the study and experimental manipulation of musical sounds. It turns out, however, that it can also suitably be applied to the study of pitch class sets (subsets of the chromatic 12-tone-system) and pitch class profiles (fuzzy subsets). The contributions to this direction are due to David Lewin, Ian Quinn, Emmanuel Amiot and Jason Yust. Also here it turns out that the incorruptible mathematical results are not alien to traditional musictheoretical knowledge. The „partials“ of the Fourier decompositions are closely related to prominent pitch class collections. For given chord progressions in musical pieces they lend themselves to be interpreted as events in „analytical voices“. After brief informal introductions to these different mathematical approaches I will dedicate the last part of my talk to the comparison of associated analytical results in selected musical pieces and to the detection of instances of solidarity between these results. It is a challenging open task at the borderline between theory and analysis to disentangle systematic dependencies from ideosyncratic piece-specific correspondences.