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Reinterpreting and Extending Anatol Vieru’s Periodic Sequences Through the Cellular Automata Formalisms

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Mathematics and Computation in Music (MCM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11502))

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Abstract

In this paper we focus on Anatol Vieru’s periodic sequences that we approach with the formalism of the theory of cellular automata. After extending previous results about the action (in the image direction) of one particular cellular automaton on periodic sequences we show the existence of a second one which is its complementary (or dual). The main idea of the paper is that the study of preimages of one of those two automata is the study of the images of the other one and vice versa. By using the duality, we have been able to show explicitly the evolution of the period and the form of the preimages for both automata. In order to illustrate the theoretical constructions, a musical composition is presented using the two automata both in the image and preimage directions.

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Notes

  1. 1.

    This is slightly contrasting with conventional terminology in which saying a sequence is \(\tau \)-periodic does not imply minimality.

  2. 2.

    http://repmus.ircam.fr/_media/moreno/score_lanthier_duality.pdf.

  3. 3.

    http://repmus.ircam.fr/_media/moreno/audio_lanthier_duality.mp3.

References

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Author information

Authors and Affiliations

  1. Université de Rouen, LMRS (UMR 6085), Mont-Saint-Aignan, France

    Paul Lanthier

  2. Université Strasbourg, USIAS/IRMA (UMR 7501), Strasbourg, France

    Corentin Guichaoua & Moreno Andreatta

  3. IRCAM/CNRS/Sorbonne Université, Paris, France

    Moreno Andreatta

Authors
  1. Paul Lanthier
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  2. Corentin Guichaoua
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  3. Moreno Andreatta
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Corresponding authors

Correspondence to Paul Lanthier , Corentin Guichaoua or Moreno Andreatta .

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Editors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Mariana Montiel

  2. Technical University of Madrid, Madrid, Spain

    Francisco Gomez-Martin

  3. Technological University of the Mixteca, Oaxaca, Mexico

    Octavio A. Agustín-Aquino

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Lanthier, P., Guichaoua, C., Andreatta, M. (2019). Reinterpreting and Extending Anatol Vieru’s Periodic Sequences Through the Cellular Automata Formalisms. In: Montiel, M., Gomez-Martin, F., Agustín-Aquino, O.A. (eds) Mathematics and Computation in Music. MCM 2019. Lecture Notes in Computer Science(), vol 11502. Springer, Cham. https://doi.org/10.1007/978-3-030-21392-3_21

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  • DOI: https://doi.org/10.1007/978-3-030-21392-3_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-21391-6

  • Online ISBN: 978-3-030-21392-3

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