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The flow of harmony as a dynamical system
When analysing the evolution of harmony within a composition, one can distinguish between two parts: on the one hand a dynamical system and on the other hand the composer. The dynamical system summarises the rules of harmony, whereas the composer intervenes at certain points, e.g. by choosing new initial values. This viewpoint is helpful for the musical analysis of a composition and will be exemplified by analysing the first movement of Beethoven's first symphony. Note that some difficulties occur when considering a discrete phase space with a metric in the definitions of stability. However, we will not go into further detail since we are only interested in the general concept.
History
Publication status
- Published
ISSN
1865-0929Publisher
SPRINGER-VERLAG BERLIN, HEIDELBERGER PLATZ 3, D-14197 BERLIN, GERMANYExternal DOI
Issue
1Volume
37Page range
117-123Pages
7.0Presentation Type
- paper
Event name
1st International Conference on Mathematics and Computation in MusicEvent location
Berlin, GermanyEvent type
conferenceEvent date
18-20 May, 2007ISBN
978-3-642-04578-3Department affiliated with
- Mathematics Publications
Notes
Source: Mathematics and Computation in Music. Series: Communications in Computer and Information ScienceFull text available
- No
Peer reviewed?
- Yes