This book presents and discusses the fundamental topic of classification of musical objects, such as chords, motifs, and gestures. Their classification deals with the exhibition of isomorphism classes. Our structure types include local and global constructions, the latter being similar to global structures in geometry, such as differentiable manifolds.
The discussion extends to the role, which classification plays for the creative construction of musical compositions. Our examples include references to classical compositions, such as Beethovens sonatas, and some of the authors own compositions of classical and jazz styles.
We also discuss software that enables the application of classification to musical creativity.
The volume is addressed to an audience that would apply classification to programming and creative musical construction.
Part I Initial Orientation.- 1 The Basic Problem of Classification.-
Part II General Formal Concepts.- 2 Ontology, Oniontology, and Creativity.-
3 Formal Representation of Musical Structures.- 4 Denotators over General
Categories.- 5 Composition Denotators and Classification.- 6 Gestural
Denotators: A First Overview.- 7 The Escher Theorem for Compositions and
Gestures.- Part III Local Classification.- 8 Local Composition and Gesture
Classification.- 9 Classification of Chords.- 10 Motif Classes.- 11 Third
Chain Classes.- 12 Harmony through Third Chains.- 13 Counterpoint Worlds.- 14
Strong Interval Dichotomies.- 15 Microtonal Contrapuntal Theories.-
16 Dodecaphonic Rows.- Part IV Global Classification.- 17 Global Composition
and Gesture Classification.- 18 The Classification Theorem for Global
Compositions.- 19 The Classification Problem of Global Gestures.- 20 Singular
Homology of Hypergestures.- 21 Local Gestures, Structures of Knots, and Local
Gestures as Local Compositions.- Part V Classification and Creativity.-
22 Gestural Interpretation and Future Developments.- Part VI References,
Index.- 23 Classification Lists.
Linshujie Zheng is a soprano. She has a masters degree with distinction at Cardiff University. Currently she pursues a doctoral degree in voice at the University of Minnesota. Zheng has received awards and scholarships in China, the UK, and the US. She has performed at the Royal Albert Hall, Wales Millennium centre, and St Davids Hall. She also sung principal roles, including Zerlina in Don Giovanni, Genovieve in Suor Angelica, Susanna in Le nozze di Figaro. Zheng not only focuses on the performing arts, she also has a passion for Gesture and reception theory.
Guerino Mazzola qualified as a professor in mathematics and in computational science at the University of Zürich. Visiting professor at the ENS in Paris in 2005. Since 2007 professor at the School of Music, University of Minnesota. He developed a Mathematical Music Theory and music software presto and Rubato. 2007-2021 he was the president of the Societyfor Mathematics and Computation in Music. He has published 33 books and 150 papers, 27 jazz CDs, two DVDs, and a classical sonata. His most important book is The Topos of Music, about mathematical music, performance, and gesture theory.
