Marek Žabka

junior fellow
EURIAS cohort 2012/2013
discipline Mathematics and Musicology
Assistant Professor of Musical Theory at the Department of Musicology of the Comenius University, Bratislava

Research project

Generated Tone Systems - Mathematical Modeling in Music Theory


Interactions between music and mathematics are multifaceted and can be traced back into the ancient history of both disciplines. This project aims at contributing to a particular area of mathematical music theory. Recently, I have proposed and explored a special formal concept called «generated tone system» (GTS). Examples of GTS’s emerge in multiple musical contexts ranging from ancient music theories through Renaissance science of tuning to modern cognitive music psychology. As GTS’s are found in so many different and independent streams of musical scholarship, the concept seems to capture crucial structural and cognitive characteristics of music. The main objective of the proposed project is to expand existing work and to synthesize results into a monograph on generated tone systems.

The project will consist of two main parts: (i) historical survey of the concept, (ii) mathematical exploration. In the first part, belonging to the history of ideas, I intend to tell a story of the concept of GTS’s. I will try to refer to as diverse theoretical and historical contexts as possible. The second part, largely covered by my previous work, will provide a unified mathematical theory of generated tone systems. Both results of other scholars (such as Adriaan Fokker or Yves Hellegouarch) and my own will be presented in a single self-contained theoretical framework.

The connections between the historical and mathematical parts will be strongly emphasized. Historical examples will support and illustrate the formal framework, mathematical results will influence the historical interpretation. Finally, as a synthesis, the monograph will contain a comprehensive catalog of GTS’s. The catalog will be structured according to the mathematical formalism and will include references to the historical material. It will be a valuable source not only for historians of music theory and specialists in mathematical music theory but also for composers exploring alternative tone systems. As it will comprise interesting musical material, it may even inspire and enable composition of new music.



Marek Žabka is Assistant Professor of Musical Theory at the Department of Musicology of the Comenius University, Bratislava. He holds two Master degrees – in mathematics and in musicology – and a Ph.D. in music theory from Comenius University, Bratislava, Slovakia. In his research, he focuses on systematic musicology and music theory with focus on scale theories and neo-Riemannian theories. He serves on the Editorial Board of the Journal of Music Theory and is an Editor-in-Chief for the Journal of Mathematics and Music.

Selected publications


‘Introduction to Scale Theory over Words in Two Dimensions’, in C. Agon, E. Amiot, M. Andreatta, G. Assayag, J. Bresson and J. Mandereau (eds), Mathematics and Computation in Music, Springer, Berlin, 2011, pp. 311-325. 


‘Well-Formedness in Two Dimensions: A Generalization of Carey and Clampitt’s Theorem’, Journal of Mathematics and Music, vol. 4, no. 1, 2010, pp. 1-30.


‘Generalized Tonnetz and Well-Formed GTS: A Scale Theory Inspired by the Neo-Riemannians’, in E. Chew, A. Childs and C. H.C Chwan (eds), Mathematics and Computation in Music 2009, Springer, Berlin, 2009, pp. 286-298.


Štúdie z matematickej hudobnej teórie [Studies in Mathematical Music Theory], Stimul, Comenius University, Bratislava, 2009.


‘The Classification of Melodies with Finite Algebraic Fourier Transformation – Possibilities and Limitations’, Musicologica Istropolitana, vol. 6, 2007, pp. 123-133.


‘Mathematical Concepts in Musical Analysis – Exemplified on Analysis of Roman Berger’s Convergences I’, Musicologica Istropolitana, vol. 5, 2006, pp. 99-111.


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