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

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

    Research output: Chapter in Book / Conference PaperConference Paperpeer-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 publicationProceedings: Mathematics and Computation in Music: 5th International Conference, MCM 2015, London, UK, June 22-25, 2015
    PublisherSpringer
    Pages97-108
    Number of pages12
    ISBN (Print)9783319206028
    DOIs
    Publication statusPublished - 2015
    EventMCM -
    Duration: 22 Jun 2015 → …

    Publication series

    Name
    ISSN (Print)0302-9743

    Conference

    ConferenceMCM
    Period22/06/15 → …

    Keywords

    • balance
    • microtones
    • music
    • musical intervals and scales

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