Abstract
Mathematical performance theory [1] uses a model of performative unfolding that is based on “sexual propagation” of successive performance refinements. It is formally described by a tree-shaped diagram, the performance stemma, starting at the primary “mother” performance that ramifies to a series of “daughter” performances. This propagation mechanism is induced by a series of performance operators stemming from the composition’s music analysis. In this paper we refine such networks to performance hypergestures whose curves represent continuous transitions from mother to daughter performances. This level of description uses the theory of Lie-type performance operators and enables a detailed analysis of different performative transition strategies. We then calculate the singular performance hypergesture homology H 1 and discuss its significance for the classification of transitional strategies.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Mazzola, G.: The Topos of Music. Birkhäuser, Basel (2002)
Mazzola, G., Zahorka, O.: The RUBATO performance workstation on NeXTSTEP. In: Proceedings of the International Computer Music Conference, San Francisco, CA (1994)
Mazzola, G.: Global networks in computer science? Invited talk at the Computer Science Department Colloquium, ETH Zürich, Switzerland (January 2006)
Mazzola, G.: Manifolds and singular homology of compositions, networks, and gestures: Classification, connecting functors, examples. Submitted for Publication to the Journal of Mathematics and Music
Widmer, G., Goebl, W.: Computational models of expressive music performance: The state of the art. Journal of New Music Research 33(3), 203–216 (2004)
Mazzola, G.: Categorical gestures, the diamond conjecture, Lewin’s question, and the Hammerklavier sonata. Journal of Mathematics and Music 3(1), 31–58 (2009)
Mazzola, G.: Singular homology on hypergestures. Journal of Mathematics and Music 6(1), 49–60 (2012)
Berg, A.: Die musikalische Impotenz der “Neuen Ästhetik” Hans Pfitzners. Musikblätter des Anbruch 2, 399–406 (1920)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mazzola, G. (2013). Hypergesture Homology for Performance Stemmata with Lie Operators. In: Yust, J., Wild, J., Burgoyne, J.A. (eds) Mathematics and Computation in Music. MCM 2013. Lecture Notes in Computer Science(), vol 7937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39357-0_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-39357-0_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39356-3
Online ISBN: 978-3-642-39357-0
eBook Packages: Computer ScienceComputer Science (R0)