March 23, 2020 Journal of Mathematics and Music 0’00” Submitted exclusively to the Journal of Mathematics and Music Last compiled on March 23, 2020 From actantial model to conceptual graph: thematized action in John Cage’s 0 ′ 00 ′′ (4 ′ 33 ′′ No. 2) Michael D. Fowler a∗ a Japan-Zentrum, Ludwig-Maximilians-Universit¨at M¨ unchen, Germany () In this article I build an actantial model (Greimas 1983), M, of John Cage’s 1962 indeter- minate work 0 ′ 00 ′′ (4 ′ 33 ′′ No. 2). To further investigate Greimas’ actantial axes of desire, knowledge and power, I generate an ontology, O, that records the facts of the model through hierarchies of relations and concepts. This allows for a conceptual graph (CG) (Sowa 1984), C, that describes the score’s instructions and its actants. Extracting subgraphs of C then allows for reasoned arguments about the implications of Cage’s instructions in the score, and in particular, the composer’s reference to “an obligation to others.” Through a conceptual graph rule R, I offer a framework for generating the structure of a score-informed interpre- tation of 0 ′ 00 ′′ (4 ′ 33 ′′ No. 2) that is based on a number of key conditionals that map the actants of the piece, and their relation to the unfolding of the work’s narrative. Keywords: John Cage; indeterminacy; 0 ′ 00 ′′ (4 ′ 33 ′′ No. 2); conceptual graphs; predicate logic; actantial model; semiotics; A. J. Greimas 2010 Mathematics Subject Classification : 03B10, 68T30 2012 Computing Classification Scheme : applied computing 1. Introduction In the years following David Tudor’s premiere of John Cage’s notorious 4 ′ 33 ′′ at Wood- stock, NY in 1952, Cage had returned to traditional notation in the Music for Piano se- ries, worked extensively in the electronic music studio to develop the tape works Fontana Mix and Williams Mix as well as began experimenting with new indeterminate notations and materials in the Variations series. Some ten years after the premiere of 4 ′ 33 ′′ , Cage conducted a tour of Japan with Tudor, Yoko Ono and Toshi Ichiyanagi in 1962. One of the works premiered in Tokyo was 0 ′ 00 ′′ (4 ′ 33 ′′ No. 2). 1 The work’s official designation as a second “version” of 4 ′ 33 ′′ is notable for its inverse relation to its predecessor in terms of the generation of sound events. If 4 ′ 33 ′′ is concerned with ambient sound, per- formance through “non-performance,” and the subtle limits of perceiving the acoustic horizon, then 0 ′ 00 ′′ is very much a forced interrogation into the qualities of everyday sounds delivered under conditions of maximum amplification. Like its predecessor, 4 ′ 33 ′′ , the score of 0 ′ 00 ′′ (Cage 1962) is comprised entirely of natural language, though seems to present a more obvious functional narrative. The score is dedicated to Yoko Ono and Toshi Ichiyanagi, and is dated October 24, 1962, Tokyo. Cage specifically indicates that the work is a “solo to be performed in any way ∗ Corresponding author. Email: synthifou@gmail.com 1 In this article, I use throughout the shortened name 0 ′ 00 ′′ .