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Distant Neighbors and Interscalar Contiguities

  • Daniel HarasimEmail author
  • Thomas Noll
  • Martin Rohrmeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11502)

Abstract

This paper studies the “integration” problem of nineteenth-century harmony—the question whether the novel chromatic chord transitions in this time are a radical break from or a natural extension of the conventional diatonic system. We examine the connections between the local behavior of voice leading among diatonic triads and their generalizations on one hand, and the global properties of voice-leading spaces on the other. In particular, we aim to identify those neo-Riemannian chord connections which can be integrated into the diatonic system and those which cannot. Starting from Jack Douthett’s approach of filtered point symmetries, we generalize diatonic triads as second-order Clough-Myerson scales and compare the resulting Douthett graph to the respective Betweenness graph. This paper generally strengthens the integrationist position, for example by presenting a construction of the hexatonic and octatonic cycles that uses the principle of minimal voice leading in the diatonic system. At the same time it provides a method to detect chromatic wormholes, i.e. parsimonious connections between diatonic chords, which are not contiguous in the system of second order Clough-Myerson scales.

Keywords

Diatonic theory Hexatonic cycles Neo-Riemannian transformations Maximally even scales Voice-leading parsimony 

Notes

Acknowledgement

The authors would like to thank Fabian C. Moss, Christoph Finkensiep, and the two anonymous reviewers for their constructive, and helpful comments.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Digital and Cognitive Musicology LabÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Departament de Teoria, Composició i DireccióEscola Superior de Música de CatalunyaBarcelonaSpain

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