Abstract
This chapter gives a prototypical example of mathematical methods that should play a role in musical composition of the future. Mazzola’s sonata is an explicit experiment to understand the mechanisms of mathematically shaped sonata construction and its creative limitations, starting from the analysis of Beethoven’s Hammerklavier Sonata Op. 106 to compose a new sonata. This is an example of Boulez’s creative analysis. We then critically review the Boulezian idea and the new composition.
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
Notes
- 1.
A transposition by n semitones is denoted by T n.
- 2.
For music theorists: The sharpened/flattened note names do not mean that we think in alterations, but simply denote the position of the note on the set of 12 pitch classes within an octave.
References
A. Boissière, Geste, interprétation, invention selon Pierre Boulez. Revue DEMéter, déc (2002), Univ. Lille-3
G. Mazzola, Gruppen und Kategorien in der Musik (Heldermann, Berlin, 1985)
G. Mazzola, Geometrie der Töne (Birkhäuser, Basel, 1990)
G. Mazzola, L’essence du bleu Acanthus (2002)
G. Mazzola, et al., The Topos of Music—Geometric Logic of Concepts, Theory, and Performance (Birkhäuser, Basel, 2002)
G. Mazzola, M. Mannone, Y. Pang, Cool Math for Hot Music (Springer, Heidelberg, 2016)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Mazzola, G. et al. (2020). Mazzola’s Sonata Construction: A Technical Approach and Its Limits. In: The Future of Music. Springer, Cham. https://doi.org/10.1007/978-3-030-39709-8_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-39709-8_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-39708-1
Online ISBN: 978-3-030-39709-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)