A Concept for Exploring Western Music Tonality in Physical Space

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Behringer, R ; Elliott, J (2009)

Musical theory about the structure and morphology of Western tonality is quite difficult to teach to young children, due to the relatively complex mathematical concepts behind tonality. Children usually grasp the concepts of musical harmony intuitively through listening to music examples. Placing the 12 notes of the well-tempered scale into a spatial arrangement, in which the proximity of these notes represents their mutual harmonic relationship, would allow to link physical motion through a spatial area with the exploration of music tonality. Music theorists have postulated the Circle of Fifth, the “Spiral Array”, and the “Tonnetz” as paradigms for spatial arrangements of music notes which allow mapping the distance between notes onto their “mutual consonance”. These approaches mostly have been of qualitative nature, leaving the actual numeric parameters of the spatial description undetermined. In this paper, these parameters have been determined, leading to a concrete numerical description of the planar Tonnetz. This allows the design of a physical space in which the music notes are distributed in space according to their musical consonance. Set up in an outdoor area, handheld devices (e.g. PDA) with integrated Global Positioning System can be used to play these notes at their actual physical location. This makes it possible for children to explore this musical space by moving through the real spatial area and experience the relationships of the notes through their proximity. Defining a range for each note as a circular area around each note location, consonant chords can be produced in those areas where those circles overlap. Using this concept, games can be developed in which the listeners have to perform certain tasks related to this musical space. This appears to be a promising approach for the music education of young children who can intuitively learn about music morphology without being explicitly taught about the complex theoretical mathematical background.
  • References (10)

    [1] White, R., and Stoecklin, V.L. Children's Outdoor Play & Learning Environments: Returning to Nature. Early Childhood New. March/April 1998.

    [2] Costa-Giomi, E. Young Children's Harmonic Perception. Annals of the NY Acad.Sci. 2003 Nov, 999. 477-84.

    [3] Chew, E. Towards a Mathematical Model of Tonality. PhD thesis, MIT, Cambridge (2000)

    [4] Euler, L. Tentamen Novae Theoria Musicae. P. 147(1739)

    [5] Riemann, H. Skizze einer Neuen Methode Harmonielehre. Leipzig: Breitkopf und Härtel (1880).

    [6] Lewin, D. Generalized Musical Intervals and Transformations. New Haven: Yale University Press (1987).

    [7] Kelley, R. Mod-7 Transformations in Post-Functional Music. PhD thesis, Florida State College of Music, Tallahassee (2003)

    [8] Krumhansl, C. Perceived Triad Distance: Evidence supporting the Psychological Reality of Neo-Riemannian Transformations. Journal of Music Theory 42/2: 265-281 (1998).

    [9] Cohn, R. Neo Riemannian Operations, Parsimonious Trichords, and Their "Tonnetz" representations. Journal of Music Theory, 41.1: 1-66 (1997).

    [10] Hewlett Packard. Mscape. Get out and http://www.mscapers.com/ (accessed 7.April 2009)

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