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The Mystery of Anatol Vieru’s Periodic Sequences Unveiled

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Mathematics and Computation in Music (MCM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13267))

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Abstract

In [10], Anatol Vieru proposed a compositional technique based on an algorithmic manipulation of periodic sequences in \( \mathbb Z_{12} \). This technique was translated in mathematical terms in ([3, 4, 8]). Two mathematical problems arose starting from the so called Vieru’s sequence V: period of primitives and proliferation of values. In this paper we announce, providing only the sketch of the proofs, the solution of these questions in a purely algebraic way.

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Authors and Affiliations

  1. Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Padua, Italy

    Luisa Fiorot, Alberto Tonolo & Riccardo Gilblas

Authors
  1. Luisa Fiorot
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  2. Alberto Tonolo
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  3. Riccardo Gilblas
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Corresponding author

Correspondence to Riccardo Gilblas .

Editor information

Editors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Mariana Montiel

  2. Technological University of the Mixteca, Huajuapan de León, Mexico

    Octavio A. Agustín-Aquino

  3. Universidad Politécnica de Madrid, Madrid, Spain

    Francisco Gómez

  4. Life University, Marietta, GA, USA

    Jeremy Kastine

  5. National Autonomous University of Mexico, Mexico City, Distrito Federal, Mexico

    Emilio Lluis-Puebla

  6. Georgia State University, Atlanta, GA, USA

    Brent Milam

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Fiorot, L., Tonolo, A., Gilblas, R. (2022). The Mystery of Anatol Vieru’s Periodic Sequences Unveiled. In: Montiel, M., Agustín-Aquino, O.A., Gómez, F., Kastine, J., Lluis-Puebla, E., Milam, B. (eds) Mathematics and Computation in Music. MCM 2022. Lecture Notes in Computer Science(), vol 13267. Springer, Cham. https://doi.org/10.1007/978-3-031-07015-0_33

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  • DOI: https://doi.org/10.1007/978-3-031-07015-0_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-07014-3

  • Online ISBN: 978-3-031-07015-0

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