Volume 112, Number 4, November 2015
|Number of page(s)||4|
|Published online||01 December 2015|
Non-Gaussian distributions of melodic intervals in music: The Lévy-stable approximation
1 Department of Engineering Sciences, Solid State Physics, The Ångström Laboratory, Uppsala University P.O. Box 534, SE-75121 Uppsala, Sweden
2 Betel Music Institute, Campus Bromma - Åkeshovsvägen 29, SE-16839 Bromma, Sweden
Received: 29 September 2015
Accepted: 12 November 2015
The analysis of structural patterns in music is of interest in order to increase our fundamental understanding of music, as well as for devising algorithms for computer-generated music, so called algorithmic composition. Musical melodies can be analyzed in terms of a “music walk” between the pitches of successive tones in a notescript, in analogy with the “random walk” model commonly used in physics. We find that the distribution of melodic intervals between tones can be approximated with a Lévy-stable distribution. Since music also exibits self-affine scaling, we propose that the “music walk” should be modelled as a Lévy motion. We find that the Lévy motion model captures basic structural patterns in classical as well as in folk music.
PACS: 05.40.Fb – Random walks and Levy flights / 05.45.Df – Fractals / 05.40.Ca – Noise
© EPLA, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.