Iannis Xenakis proposed a psychologically relevant distinction between music as performed---which he called "inside-time"---and music as heard or felt, which he called "outside-time." In one interpretation, the apprehension of music is characterized by the fact that parts of the music can be voluntarily remembered, i.e., not bound by the order given in performance. Xenakis (4) presented this diachronic listening model in a "tentative axiomatization", roughly asserting that:
Xenakis made a further point which spoke of "linking" such steps together in a chain in one of two orientations, described as "accumulation or de-accumulation". He did not explain what he meant by these terms but we propose a new clarification based on three ideas.
1. What Xenakis calls "segment" or "landmark" we call "shape", an auditory analogy to the visual shape, which played a vital role in Xenakis' thinking. But there is a suggestion in the neuroscience literature (1) that the cortical processing machinery for both is homologous. Psychological parallels are manifest. As with visual shape, auditory shape can roughly be taxonomized in terms of simplicity: there are simplest auditory shapes, such as an even glissando. We argue that the simplest shapes are the perceptually most salient, and constitute a basic category of the "landmark." Hence the visuality of Xenakis' thought seems to lead back to the auditory (3).
2. The "perceptual step" is, roughly, a change in degree, or size, of a shape. The "step" from one loud and furious passage to another is the felt increase or decrease in loudness or furiousness (or whatever the defining features may be). In the Xenakian landmark step chain, shapes increase and decrease in size. There are clearly simplest ways to do this.
3. These changes result in the perception of motion, which we see as a low-level music perception substrate related to the listener's perception of motion in the physical world. (2) But how to construe the problem of motion in the criss-crossing of different landmark chains? We offer the concept of "motion asymmetries," the interlocking of chains with a view to imbalance or asymmetry, generating patterns of diachronic motion.
Asymmetries of the landmark/shape-linking/chaining "outside-time" can be shown in an enormous amount of music -- here, we will demonstrate the relevant ideas in folksong and in Xenakian compositions. As an appendix to the talk, I will indicate how these questions can be explored not only as problems in descriptive computational music theory, but in a generative music composition system in which an "outside-time" perspective is fundamental. The success of this reveals that the Xenakian "outside-time" concept offers a powerful theoretical perspective on musical perception and its relation to visuality, the organization of music, and on generative composition.