Affinity spaces and their host set classes

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4 Citations (Scopus)

Abstract

This paper proposes the organization of pitch-class space according to the notion of affinities discussed in medieval scale theory and shows that the resultant arrangement of intervallic affinities establishes a privileged correspondence with certain symmetrical set classes. The paper is divided in three sections. The first section proposes a pitch-class cycle, the Dasian space, which generalizes the periodic pattern of the dasian scale discussed in the ninthcentury Enchiriadis treatises (Palisca 1995). The structure of this cycle is primarily derived from pitch relations that correspond to the medieval concepts of transpositio and transformatio.1 Further examination of the space's properties shows that the diatonic collection holds a privileged status (host set class) among the embedded segments in the cycle. The second section proposes a generalized construct (affinity spaces) by lifting some of the intervallic constraints to the structure of the Dasian space, while retaining the relations of transpositio and transformatio, and the privileged status of host set classes.2 The final section examines some of the properties of host set classes, and in turn proposes "rules" for constructing affinity spaces from their host sets. The study of affinity spaces will give us insights regarding scalar patterning, inter-scale continuity, the combination of interval cycles, voice leading, and harmonic distance.

Original languageEnglish
Title of host publicationMathematics and Computation in Music - First International Conference, MCM 2007, Revised Selected Papers
Pages499-511
Number of pages13
DOIs
Publication statusPublished - 2009
Externally publishedYes
Event1st International Conference on Mathematics and Computation in Music, MCM 2007 - Berlin, Germany
Duration: 18 May 200720 May 2007

Publication series

NameCommunications in Computer and Information Science
Volume37 CCIS
ISSN (Print)1865-0929

Conference

Conference1st International Conference on Mathematics and Computation in Music, MCM 2007
Country/TerritoryGermany
CityBerlin
Period18/05/0720/05/07

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