The Open UniversitySkip to content

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.

Full text available as:
PDF (Accepted Manuscript) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (3975Kb)
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


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: Faculty of Science, Technology, Engineering and Mathematics (STEM)
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Computing and Communications
Interdisciplinary Research Centre: Centre for Research in Computing (CRC)
Item ID: 28690
Depositing User: Andrew Milne
Date Deposited: 06 May 2011 08:51
Last Modified: 25 Oct 2016 04:53
Share this page:


Scopus Citations

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

▼ Automated document suggestions from open access sources

Actions (login may be required)

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340