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Scratching the scale labyrinth

Milne, Andrew; Carle, Martin; Sethares, William A; Noll, Thomas and Holland, Simon (2011). Scratching the scale labyrinth. In: Agon, C.; Amiot, E.; Andreatta, M.; Assayag, G.; Bresson, J. and Mandereau, J. eds. Mathematics and Computation in Music. Lecture Notes in Artificial Intelligence (6726). Berlin Heidelberg: Springer-Verlag, pp. 180–195.

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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.

Item Type: Book Chapter
Copyright Holders: 2011 Springer-Verlag
ISBN: 3-642-21589-0, 978-3-642-21589-6
Extra Information: The original publication is available at

Third International Conference, MCM 2011, Paris, France, June 15-17, 2011
Keywords: MOS Scales; Well-Formed Scales; Diatonic; Chromatic; Stern- Brocot Tree; Farey Sequence; Fourier Scratching
Academic Unit/Department: Mathematics, Computing and Technology
Mathematics, Computing and Technology > Computing & Communications
Interdisciplinary Research Centre: Centre for Research in Computing (CRC)
Related URLs:
Item ID: 28690
Depositing User: Andrew Milne
Date Deposited: 06 May 2011 08:51
Last Modified: 11 Feb 2016 11:27
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