Stockhausen and the serial shaping of space
In countless lectures, essays, and interviews, Karlheinz Stockhausen (1928-2007) emphasized the importance of spatial movement in his music. Throughout his over 50-year compositional career, Stockhausen developed sophisticated techniques for spatialization in both his electronic and instrumental music. From early works such as GESANG DER JÜNGLINGE (1955-56) to his last major piece, COSMIC PULSES (2007), one can find extensive sketch material relating to spatial movement, as well as detailed indications of spatial motion in his scores. Although scholars such as Harley (1994), Nauck (1997), Misch (1999), Overholt (2006) and Hofmann (2008) have investigated spatialization in contemporary music, none have developed an analytical methodology for quantifying and measuring the speeds, shapes, densities, and structure of spatial movement in Stockhausen's works, or any other music. Yet, in interviews with Jonathan Cott (1973) and others, Stockhausen suggested that such a methodology was necessary to understanding his achievements.
In the dissertation, I develop a method for precisely locating the pathway of movement in spatial music. Then, drawing from the music-theoretic tradition of set theory and transformation theory, and the mathematical field of graph theory, I developed techniques to identify spatial structures and relate them according to mathematical transformations. I then characterized the symmetries that might be present in physical musical space using mathematical groups. Thanks to several computer algorithms I developed, I was able to find ways to calculate the statistical distribution of sounds within a performance space, as well as the speed and density of musical material.
Applying this array of analytical tools to two major late works of Stockhausen, OKTOPHONIE (1991-2) and LICHTER-WASSER (1999), I uncovered spatial structures which were as subtle and intricate as Stockhausen's formal, rhythmic, timbral or pitch languages. Apart from providing a wealth of new data relating to Stockhausen's idiosyncratic compositional process, my analyses suggest new ways of hearing these works which Stockhausen himself might not have been aware of. These techniques were then extended further, to assist in analyzing and better understanding the "sonic storm" in Xenakis's Terretektorh (1965/66). Finally, I use the methodology to argue for a spatial structure that significantly enhances the sophisticated multi-choir texture in Thomas Tallis's (c. 1505–1585) famous 40-part motet Spem in alium.
My analyses provide a new and provocative glimpse into a musical domain which has figured greatly into contemporary musical practice, but has so far proved elusive to methods of quantitative analysis. The analytical techniques I developed are flexible enough to provide theorists and performers with tools for a wide range of music, not just Stockhausen's. Because of this, my work opens up many new paths of development in the fields of music cognition, music analysis, and musical spatialization.