Facilitating access to atonal music: Ligeti's second string quartet

Atonal music is generally perceived as opaque and difficult to understand because it rarely makes aural sense to the uninitiated listener. A method is proposed to assist teaching and learning in this field. It links up with the mathematical Fibonacci series that has the relationship of the golden section in its upper range. As the golden section can also be identified in the plastic arts and architecture, it enables one to make interdisciplinary connections. This essay also establishes a connection with the modulor, a harmonic measure which Le Corbusier proposed and applied in the design of buildings. Firstly, it is shown that the order of the numbers in the Fibonacci series creates the opportunity to label trichords that appear frequently in atonal music. Secondly, prominent trichords in György Ligeti's second string quartet are linked to Fibonacci relationships. To balance this synchronic understanding of micro structures, it is shown how, thirdly, the relationship of the golden section facilitates a diachronic understanding of macro structure, making sense of the quartet as a whole. Journal of Musical Arts in Africa Vol. 2 2005: pp. 55-6