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Tropical Generalized Interval Systems

  • Giovanni AlbiniEmail author
  • Marco Paolo Bernardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11502)

Abstract

This paper aims to refine the formalization of David Lewin’s Generalized Interval System (GIS) by the means of tropical semirings. Such a new framework allows to broaden the GIS model introducing a new operation and consequently new musical and conceptual insights and applications, formalizing consistent relations between musical elements in an original unified structure. Some distinctive examples of extensions of well-known infinite GIS for lattices are then offered and the impossibility to build tropical GIS in the finite case is finally proven and discussed.

Keywords

Tropical semiring Ordering Generalized Interval System 

Notes

Acknowledgments

We thank Claudio Bernardi (Università di Roma “La Sapienza”, Department of Mathematics) and the reviewers for their useful suggestions and remarks.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Conservatorio “Jacopo Tomadini”UdineItaly
  2. 2.Eesti Muusika- ja TeatriakadeemiaTallinnEstonia
  3. 3.ISSM “Franco Vittadini”PaviaItaly
  4. 4.Università degli Studi di PaviaPaviaItaly

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