Perfect balance: a novel principle for the construction of musical scales and meters

Andrew J. Milne*, David Bulger, Steffen A. Herff, William A. Sethares

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

    19 Citations (Scopus)

    Abstract

    We identify a class of periodic patterns in musical scales or meters that are perfectly balanced. Such patterns have elements that are distributed around the periodic circle such that their ‘centre of gravity’ is precisely at the circle’s centre. Perfect balance is implied by the well established concept of perfect evenness (e.g., equal step scales or isochronous meters). However, we identify a less trivial class of perfectly balanced patterns that have no repetitions within the period. Such patterns can be distinctly uneven. We explore some heuristics for generating and parameterizing these patterns. We also introduce a theorem that any perfectly balanced pattern in a discrete universe can be expressed as a combination of regular polygons. We hope this framework may be useful for understanding our perception and production of aesthetically interesting and novel (microtonal) scales and meters, and help to disambiguate between balance and evenness; two properties that are easily confused.

    Original languageEnglish
    Title of host publicationMathematics and Computation in Music
    Subtitle of host publication5th International Conference, MCM 2015, London, UK, June 22-25, 2015, Proceedings
    EditorsTom Collins, David Meredith, Anja Volk
    Place of PublicationCham
    PublisherSpringer, Springer Nature
    Pages97-108
    Number of pages12
    ISBN (Electronic)9783319206035
    ISBN (Print)9783319206028
    DOIs
    Publication statusPublished - 2015
    Event5th International Conference on Mathematics and Computation in Music, MCM 2015 - London, United Kingdom
    Duration: 22 Jun 201525 Jun 2015

    Publication series

    NameLecture Notes in Computer Science
    PublisherSpringer International Publishing
    Volume9110
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other5th International Conference on Mathematics and Computation in Music, MCM 2015
    Country/TerritoryUnited Kingdom
    CityLondon
    Period22/06/1525/06/15

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