Scratching the Scale Labyrinth

  • Andrew J. Milne
  • Martin Carlé
  • William A. Sethares
  • Thomas Noll
  • Simon Holland
Conference paper

DOI: 10.1007/978-3-642-21590-2_14

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6726)
Cite this paper as:
Milne A.J., Carlé M., Sethares W.A., Noll T., Holland S. (2011) Scratching the Scale Labyrinth. In: Agon C., Andreatta M., Assayag G., Amiot E., Bresson J., Mandereau J. (eds) Mathematics and Computation in Music. MCM 2011. Lecture Notes in Computer Science, vol 6726. Springer, Berlin, Heidelberg

Abstract

In this paper, we introduce a new approach to computer-aided microtonal improvisation by combining methods for (1) interactive scale navigation, (2) real-time manipulation of musical patterns and (3) dynamical timbre adaption in solidarity with the respective scales. On the basis of the theory of well-formed scales we offer a visualization of the underlying combinatorial ramifications in terms of a scale labyrinth. This involves the selection of generic well-formed scales on a binary tree (based on the Stern-Brocot tree) as well as the choice of specific tunings through the specification of the sizes of a period (pseudo-octave) and a generator (pseudo-fifth), whose limits are constrained by the actual position on the tree. We also introduce a method to enable transformations among the modes of a chosen scale (generalized and refined “diatonic” and “chromatic” transpositions). To actually explore the scales and modes through the shaping and transformation of rhythmically and melodically interesting tone patterns, we propose a playing technique called Fourier Scratching. It is based on the manipulation of the “spectra” (DFT) of playing gestures on a sphere. The coordinates of these gestures affect score and performance parameters such as scale degree, loudness, and timbre. Finally, we discuss a technique to dynamically match the timbre to the selected scale tuning.

Keywords

MOS Scales Well-Formed Scales Diatonic Chromatic Stern-Brocot Tree Farey Sequence Fourier Scratching 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andrew J. Milne
    • 1
  • Martin Carlé
    • 2
  • William A. Sethares
    • 3
  • Thomas Noll
    • 4
  • Simon Holland
    • 1
  1. 1.The Open UniversityMilton KeynesUK
  2. 2.Humboldt-Universität zu BerlinGermany
  3. 3.University of Wisconsin-MadisonUSA
  4. 4.Escola Superior de Música de CatalunyaBarcelonaSpain

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