Scratching the Scale Labyrinth

  • Andrew J. Milne
  • Martin Carlé
  • William A. Sethares
  • Thomas Noll
  • Simon Holland
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6726)


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.


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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