Knet Theory: A Reappraisal

Fortean pitch class set theory featured two major drawbacks: a limited methodology for relating different sets, and a lack of a rationale for the unfolding of set structure. Klumpenhouwer networks ("Knets") promised innovations in both areas: the ability to construct networks which would relate sets based on common partial content – two trichords that share an interval, for instance, or two tetrachords that share a trichord – and a recursive, network-of-network structure, one that could guide interpretation as well as provide a well-defined context motivating large-scale network structure. Unfortunately, the former innovation seemed to founder on the sheer number of possible Klumpenhouwer interpretations, the latter on the difficulty in connecting the recursive models to musical surfaces in convincing ways.

Lost in the mostly critical reception in recent years were the numerous advantages Knets had over pitch class sets as bearers of musical intuition and action; instead of the “black box” character of so many set theoretic analyses, where the internal relationships of the notes in an asserted set remain obscure, Knets provide a window into set constructability and experience, while suggesting paths of set modulation over time. 

This talk will be self-contained; the history and mechanics of Knet theory will be covered first before I explore a reevaluation that highlights its considerable strengths and potential contributions, focusing on extended passages from works by Karol Szymanowski, Maurice Ravel and other composers at the border of post-tonal practices.

BIOGRAPHY
Anton Vishio teaches music theory, musicianship, and global music analysis as an Associate Professor at the University of Toronto. His research focuses on late-twentieth-century music, exploring the development of a family of compositional strategies at different levels of surface organization. Other longstanding interests include polyrhythms, musical properties of the sestina permutation, and the songs of Rabindranath Tagore. A pianist and composer as well as music theorist, he has published or presented work on the music of Iannis Xenakis and Jo Kondo, on music and translation, on 'intercultural' variation in recent music, and on the compositional pathways developed by Ernst Krenek. He has taught subjects in composition as well as tonal and post-tonal theory at McGill, William Paterson, New York University, and other institutions in the United States. As pianist he has performed for many years, notably with the percussionist Peter Jarvis, and with the Neidhöfer-Vishio piano duo, which won the Kranichsteiner Musikpreis at the historic Darmstadt festival for new music.