Abstract
Two approaches for characterising scales are presented and compared in this paper. The first one was proposed three years ago by the musician and composer Pierre Audétat, who developed a numerical and graphical representation of the 66 heptatonic scales and their 462 modes, a new cartography called the Diatonic Bell. It allows sorting and classifying the scales according to their similarity to the diatonic scale.
The second approach uses the Discrete Fourier Transform (DFT) to investigate the geometry of scales in the chromatic circle. The study of its coefficients brings to light some scales, not necessarily the diatonic one, showing remarkable configurations. However, it does not lead to an evident classification, or linear ordering of scales.
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© 2009 Springer-Verlag Berlin Heidelberg
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Junod, J., Audétat, P., Agon, C., Andreatta, M. (2009). A Generalisation of Diatonicism and the Discrete Fourier Transform as a Mean for Classifying and Characterising Musical Scales. In: Chew, E., Childs, A., Chuan, CH. (eds) Mathematics and Computation in Music. MCM 2009. Communications in Computer and Information Science, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02394-1_16
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DOI: https://doi.org/10.1007/978-3-642-02394-1_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02393-4
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