Dimitris Exarchos
In the early 1960s Xenakis developed a compositional theory based on the observation that certain musical structures are independent of time. His approach to this matter was, among others, a critique of those traditional conceptions that emphasize the temporal dimension of music. He insisted that all music has an aspect outside of time and that a progressive “degradation of outside-time structures” has been Western music’s most typical shortfall for centuries (Xenakis 1992, 193). Such a bold claim was not unusual for the early Xenakis. Having said that, we should note that for Xenakis time is a linear structure that exhibits a certain kind of causality (in the simple sense of cause and effect). This means that the temporal dimension of an entity lies not so much in its duration, but on the fact that its elements are placed in a certain succession, forming a sequence. A melody, for example, is a temporal entity not because it “takes time” to complete its course, but because its tones are heard in a particular succession and thus can only be described by a discourse that includes terms such as before and after. On the contrary, a structure that is equipped with its own internal hierarchy, such as a set of numbers arranged from the smaller to the larger, lies outside of time. Thus, whereas a melody exists inside time, the scale on which that melody may be based lies outside of time. Between 1962 and 1969 Xenakis presented his theory in various ways and occasionally he included a third category, that of the temporal. However, as elaborated in Solomos 2004 and Exarchos 2008, this theory boils down to two categories only: (a) outside-time and (b) inside-time (I am not following Xenakis’s own terminology, but the one suggested by Flint 1993 and Squibbs 1996). Structures that belong to the former category, those with their own inherent ordering, are also called totally ordered structures. The following is perhaps Xenakis’s simplest description of this:
[Totally ordered structure] means that given three elements of one set, you are able to put one of them in between the other two. […] Whenever you can do this with all the elements of the set, then this set, you can say, is an ordered set. It has a totally ordered structure because you can arrange all the elements into a room full of the other elements. You can say that the set is higher in pitch, or later in time, or use some comparative adjective: bigger, larger, smaller (Zaplitny 1975, 97).
A renewed interest on the topic led to further publications in the 1980s, which led to chapter X of Formalized Music (1992), “Concerning Time, Space and Music.” There Xenakis departs from the above categorization, in favor of a more philosophical approach.
Further to the observation above, a melody has an outside-time aspect, not only in relation to pitch, but also in relation to its rhythmic elements, that is, the time-values attached to its pitches. We may abstract these time-values and form a rhythmic sequence, free of pitch. Due to time’s linearity, a rhythmic sequence can be “expressed with real numbers, and shown as points on a straight line” (Varga 1996, 82-3). This means that time has an abstract image that allows it to be measured: we might call this abstract image, metric time. “There is the temporal flow, which is an immediate given, and then there is metrics, which is a construction man makes upon time” (Xenakis 1985, 97). Thanks to the metrical aspect of time, one can compare two temporal intervals as one would compare any two quantities. This means that, as with pitches, time-values can be expressed with simple mathematical relations that exist outside of time (that is, time-values can be compared to one another regardless of their order of appearance). Therefore, a rhythmic sequence has an outside-time aspect, to the extent that its time-intervals may be thought of as magnitudes to be compared, aggregated, rearranged, etc. It could be said that outside-time structures are essentially spatial, as their elements are arranged in a “room.”
In order for this metric aspect of time to be possible, there need to be at least three events which “divide time into two sections [that] may be compared and then expressed in multiples of a unit” (Xenakis 1992, 160). Elsewhere, Xenakis draws on an observation Bertrand Russell made in relation to the axiomatics of numbers: there exists “no unitary displacement that is either predetermined or related to an absolute size” (Xenakis 1992, 195). Thus, we can make a conceptual distinction between succession and temporal configuration (such as in a rhythmic sequence): saying that one event follows another, regards the structure from a temporal perspective (inside time); but saying that an event takes place that much later than another (as one would say a pitch is that much higher than another) concerns its outside-time aspect.
Considering the relevance of outside-time structures to both pitch and rhythm, we can rephrase the aforementioned remark: whereas a melody exists inside time, both the pitch scale that it is based on, and the set of durations (time-values) attached to its pitches, lie outside of time. Xenakis responded to the “degradation of outside-time structures” with his sieve theory, designed for the construction of musical scales. These scales concerned primarily pitch, but Xenakis also used sieve theory to construct rhythmic sequences; he called these structures sieves . Alongside sieve theory Xenakis experimented also with group theory to this purpose. Group theory is rather complicated, as groups can differ greatly in quality between one another; some groups lie in Xenakis’s outside-time category and hence his research of these in the construction of scales; others are clearly inside time and have been employed in the construction of sequences (of pitch, durations, sounds, etc.). The discovery of outside-time structures informed most, if not all, of Xenakis’s subsequent work.
References
Exarchos, Dimitris. 2008. “Iannis Xenakis and Sieve Theory: An Analysis of the Late Music (1984-1993).” Doctoral thesis, Goldsmiths, University of London.
Flint, Ellen Rennie. 1993. “Metabolae, Arborescences and the Reconstruction of Time in Iannis Xenakis’ Psappha.” Contemporary Music Review 7 (2): 221–48. https://doi.org/10.1080/07494469300640131.
Solomos, Makis. 2004. “Xenakis’ Thought through His Writings.” Journal of New Music Research 33 (2): 125–36. https://doi.org/10.1080/0929821042000310603.
Squibbs, Ron. 1996. “An Analytical Approach to the Music of Iannis Xenakis: Studies of Recent Works.” Doctoral thesis, Yale University.
Xenakis, Iannis. 1985. Arts/Sciences: Alloys: The Thesis Defence of Iannis Xenakis before Olivier Messiaen, Michel Ragon, Olivier Revault d’Allones, Michel Serres and Bernard Teyssèdre. New York: Pendragon Press.
Xenakis, Iannis. 1992. Formalized Music: Thought and Mathematics in Composition. Rev. ed. Stuyvesant, NY: Pendragon Press.
Zaplitny, Michael, and Iannis Xenakis. 1975. “Conversation with Iannis Xenakis.” Perspectives of New Music 14 (1): 86–103. https://doi.org/10.2307/832544.
How to cite
EXARCHOS, Dimitris. 2023. “Outside of Time.” In A Xenakis Dictionary, edited by Dimitris Exarchos. Association Les Amis de Xenakis. https://www.iannis-xenakis.org/en/outside-of-time