Thesis (MMus (Music))--University of Stellenbosch, 2009. / The relationship between music and mathematics has been subjected to debate for
centuries. There are two schools of thought with the one viewpoint holding that the
relationship between mathematics, which is conceived as an abstract and cold
discipline, compared to music, which is rich with emotion, must be very limited.
Arguments for this view draws, for example, on recent research which indicates that
musical talent is not inherently linked to mathematical capability. On the other pole
of the debate is the belief that although music and mathematics contribute to different
parts of society, there is a very important inter-relationship between the two fields. Of
great interest to the latter is the Greek composer Iannis Xenakis whose musical
aesthetics incorporates this philosophy.
As composer, Xenakis used mathematical theories as basis for his musical works. He
not only incorporated well known mathematical principles such as the Golden Section
into his compositions but went further and, for instance, utilized Boolean Algebra,
Probability theory and Stochastic processes in his music. His composition method
based on these mathematical principles became known under the term Stochastic
music and forms the focus of this thesis.
The research project concentrates on the early part of Xenakis’ life in order to provide
insight into the development of his composition methods. The mathematical
principles at the centre of his stochastic compositions receive specific rationalisation.
In doing so, the most significant probability distributions (Linear, Exponential,
Poisson and Normal distribution) are defined in terms of their properties and Xenakis’
use of them. The application of these distributions is considered by looking at the
early works Metastaseis (in which Xenakis confronted most of his musical problems
and which formed the basis for his musical style) and Achorripsis (where he fully
developed their implementation).
An in-depth examination of the construction of Achorripsis is performed while
scrutinizing Xenakis’ calculations. Specific attention is drawn to alterations and
adjustments made to the calculations. His implementation of them into the final score
is furthermore examined and it is shown where he deviated between the calculations
and score. The thesis concludes by considering the extent and significance of the
adjustments made by the composer in the name of artistic freedom.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/1645 |
| Date | 03 1900 |
| Creators | Du Toit, Pierre Johannes |
| Contributors | Herbst, T., Vermeulen, J., University of Stellenbosch. Faculty of Arts and Social Sciences. Dept. of Music. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | University of Stellenbosch |
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