Mathematical and architectural concepts manifested in Iannis Xenakis's piano music
This treatise explores the principles of a figure who was equally versed in several disciplines: music, architecture, and mathematics. Such combination has permitted the possibility of a great expansion of aesthetic principles, techniques, and general concepts of musical coherence beyond those of an ordinary composer. During the twentieth century, interest in new musical sources flourished. Composers explored music in combination with other disciplines; composers developed serialism, used electronic devices, and researched other fields such as mathematics and architecture. Iannis Xenakis (1922 – 2001) is such a figure. A Greek composer, who resided in France, he keenly sought a way to approach the creation of music from a different field in order to expand the possibilities of composition, and used computer and other electronic devices as part of his overall techniques. Being a civil engineer and an architect himself, Xenakis related music to architecture and mathematics. The probability theory forms the macrostructure and the distribution of notes in Xenakis’s music. From the structure to such distribution, the probability/stochastic laws take the main role in making decisions. Other factors, such as mathematical set theory, are also used, for example in his solo piano piece, Herma. Xenakis’s architectural constructions also influenced the main concepts and structures of his compositions. Projects such as the Couvent de la Tourette and the Phillips Pavilion show keen relationship with the composition of Metastaseis and Concret P.H. Golden proportion, one of the main considerations in architecture and a proportional phenomenon in nature, has served as a formulaic source for many composers of the twentieth century. In Xenakis’s Herma and Evryali, golden mean underlies the macro- and the microstructure. The mathematical set theory in Herma and the arborescence method in Evryali are joined with golden section to determine the actual deployment of notes, the occurrence of phrases, and durations. Despite the difficulties and the discussions on the performance of Xenakis’s music, it seems that many performers find Xenakis’s pieces challenging, yet interesting. The mathematical and symbolic pre-compositional principles do not seem directly relevant to music. However, they intellectually underlie the construction of the pieces and show inevitable associations with music.