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Sequential Machines and Affine Musical Contours

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Algebraic Modeling of Topological and Computational Structures and Applications (AlModTopCom 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 219))

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Abstract

Affine contours may be viewed as an abstraction of the notion of musical intervals and are closely related to sequential machines. We show that every commutative affine musical contour actually simulates the classical one \(c:\mathbb {Z}_{12} \times \mathbb {Z}_{12} \rightarrow \mathbb {Z}_{12}\), \(c(s,t)=t-s\).

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Author information

Authors and Affiliations

  1. Xifilinon 6, 55131, Thessaloniki, Greece

    Marianthi Bozapalidou

Authors
  1. Marianthi Bozapalidou
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Correspondence to Marianthi Bozapalidou .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, National Technical University of Athens, Athens, Greece

    Sofia Lambropoulou

  2. School of Chemical Engineering, National Technical University of Athens, Athens, Greece

    Doros Theodorou

  3. Department of Applied Mathematics, National Technical University of Athens, Athens, Greece

    Petros Stefaneas

  4. Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois, USA

    Louis H. Kauffman

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Bozapalidou, M. (2017). Sequential Machines and Affine Musical Contours. In: Lambropoulou, S., Theodorou, D., Stefaneas, P., Kauffman, L. (eds) Algebraic Modeling of Topological and Computational Structures and Applications. AlModTopCom 2015. Springer Proceedings in Mathematics & Statistics, vol 219. Springer, Cham. https://doi.org/10.1007/978-3-319-68103-0_21

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