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The Future of Music pp 119–127Cite as

Mazzola’s Sonata Construction: A Technical Approach and Its Limits

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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.

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Notes

  1. 1.

    A transposition by n semitones is denoted by T n.

  2. 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

  1. A. Boissière, Geste, interprétation, invention selon Pierre Boulez. Revue DEMéter, déc (2002), Univ. Lille-3

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  2. G. Mazzola, Gruppen und Kategorien in der Musik (Heldermann, Berlin, 1985)

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  3. G. Mazzola, Geometrie der Töne (Birkhäuser, Basel, 1990)

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  4. G. Mazzola, L’essence du bleu Acanthus (2002)

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  5. G. Mazzola, et al., The Topos of Music—Geometric Logic of Concepts, Theory, and Performance (Birkhäuser, Basel, 2002)

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  6. G. Mazzola, M. Mannone, Y. Pang, Cool Math for Hot Music (Springer, Heidelberg, 2016)

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Authors and Affiliations

  1. University of Minnesota, School of Music, Minneapolis, USA

    Guerino Mazzola, Shuhui Yao, Jay Afrisando, Christopher Rochester & William Neace

  2. Department of Theatre Arts & Dance, University of Minnesota, Minneapolis, USA

    Jason Noer & Yan Pang

Authors
  1. Guerino Mazzola
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  2. Jason Noer
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  3. Yan Pang
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  4. Shuhui Yao
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  5. Jay Afrisando
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  6. Christopher Rochester
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  7. William Neace
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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

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