RECURRING HARMONIC WALKS AND NETWORK MOTIFS IN WESTERN MUSIC

Shalev Itzkovitz, Ron Milo, Nadav Kashtan, Reuven Levitt, Amir Lahav and Uri Alon
Additional contact information
Shalev Itzkovitz: Departments of Molecular Cell Biology and Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
Ron Milo: Departments of Molecular Cell Biology and Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
Nadav Kashtan: Departments of Molecular Cell Biology and Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
Reuven Levitt: Departments of Molecular Cell Biology and Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
Amir Lahav: The Music Mind and Motion Lab, Sargent College of Health and Rehabilitation Sciences, Boston University, Boston, MA 02215, USA;
Uri Alon: Departments of Molecular Cell Biology and Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel

Advances in Complex Systems (ACS), 2006, vol. 09, issue 01n02, 121-132

Abstract: Western harmony is comprised of sequences of chords, which obey grammatical rules. It is of interest to develop a compact representation of the harmonic movement of chord sequences. Here, we apply an approach from analysis of complex networks, known as "network motifs" to define repeating dynamical patterns in musical harmony. We describe each piece as a graph, where the nodes are chords and the directed edges connect chords which occur consecutively in the piece. We detect several patterns, each of which is a walk on this graph, which recur in diverse musical pieces from the Baroque to modern-day popular music. These patterns include cycles of three or four nodes, with up to two mutual edges (edges that point in both directions). Cliques and patterns with more than two mutual edges are rare. Some of these universal patterns of harmony are well known and correspond to basic principles of music theory such as hierarchy and directionality. This approach can be extended to search for recurring patterns in other musical components and to study other dynamical systems that can be represented as walks on graphs.

Keywords: Network motifs; music complexity; music perception; complex networks; design principles; graph theory (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S021952590600063X
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:acsxxx:v:09:y:2006:i:01n02:n:s021952590600063x

Ordering information: This journal article can be ordered from

DOI: 10.1142/S021952590600063X

Access Statistics for this article

Advances in Complex Systems (ACS) is currently edited by Frank Schweitzer

More articles in Advances in Complex Systems (ACS) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().