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  • Book
  • May 2023

Classification of Musical Objects for Analysis and Composition

  • The book is a basis for software development for creative composition

  • Provides a first easily accessible account on classification topics in music

  • Accessible to mathematically non-trained readers

Part of the book series: Computational Music Science (CMS)

About this book

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 Beethoven’s sonatas, and some of the author’s 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.


  • classification
  • global composition
  • gesture
  • denotator
  • chord classes
  • local composition
  • motif classes
  • analysis
  • composition
  • creativity

Authors and Affiliations

  • School of Music, University of Minnesota, Minneapolis, USA

    Linshujie Zheng, Guerino Mazzola

About the authors

Linshujie Zheng is a soprano. She has a master’s 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 David’s 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 Society for 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.

Bibliographic Information

  • Book Title: Classification of Musical Objects for Analysis and Composition

  • Authors: Linshujie Zheng, Guerino Mazzola

  • Series Title: Computational Music Science

  • Publisher: Springer Cham

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-30182-7Due: 19 May 2023

  • Softcover ISBN: 978-3-031-30185-8Due: 19 May 2024

  • eBook ISBN: 978-3-031-30183-4Due: 19 May 2023

  • Series ISSN: 1868-0305

  • Series E-ISSN: 1868-0313

  • Edition Number: 1

  • Number of Illustrations: 50 b/w illustrations

  • Topics: Computational Mathematics and Numerical Analysis, Applications of Mathematics, Music