ï~~THE CYCLOTRON: A TOOL FOR PLAYING WITH TIME Daniel Trueman Princeton University Music Department ABSTRACT The Cyclotron is a graphical tool and associated software engine for creating and manipulating meters. The history and motivations for creating the Cyclotron are described, and recent work in metric theory is highlighted to provide a theoretical context for considering ways of conceiving of time digitally. Several examples are explored, in particular the Norwegian telespringar, a dance meter that poses particular challenges to metric theory. Finally, the use of the Cyclotron in recent and in-progress compositions is described. 1. INTRODUCTION AND PRE-HISTORY The Cyclotron is a circular graphical metaphor for representing and playing with timed events. By "playing with," I mean both in the sense of experimenting, "toying around with," as a way to discover and create musical ideas, and also literally, as one might play with a metronome or drum-machine. I built the first Cyclotron in 1996 and then abandoned it until 2007 when recent developments in metric theory and real-time music systems inspired me to revisit and redesign it. (http://music.princeton.edu/-dan/cyclotronPage/cyclotron.html is an online paper about the original). The original Cyclotron consisted of a series of moveable spokes, each representing the timing of an event in an abstract phase space (Figure 1). The length of the spokes was defined to represent the probability of that event actually occurring. Through the use of scriptable "playcycle" commands, these "wheels" would be virtually spun to generate "playnote" commands for Paul Lansky's real-time mixing program rt: (http://music.princeton.edu/winham/PPSK/rt.html). I used this version of the Cyclotron in the composition of Waltz (programmed at ICMC Ann Arbor); my colleague Nick Brooke also used it in the composition of Pemangku (also programmed at ICMC Ann Arbor). 2. MOTIVATIONS AND THEORETICAL BACKGROUND My experiences as a Hardanger fiddler in the Norwegian Telemark style and also a general frustration with typical timeline-based sequencer interfaces were the original motivations for creating the Cyclotron. The telespringar is a dance in three beats, however the three beats are of noticeably different lengths and are impossible to subdivide evenly in any meaningful way. In some measurements, these beats subdivide the measure in percentages like 39:33:28 and 38:33:29 depending on the particular fiddler [1][2][3]. One clear way to hear these variations is in the many tunes that feature sequences of triplets which will generally stretch and compress as the beats do (though often with other stylistic variations within the warped structure of the meter). Rather than being thought of as some kind of rubato, or subtly adjusted even beats, these beats are inherently uneven, reflecting physical aspects of the dance, and, as David Code argues, "They don't feel like the beats are coming in early or late or are somehow syncopated: the beats just are." This kind of meter is impossible to elegantly represent in typical timeline-based sequencers, which assume meters are built up from small, completely even subdivisions. My original motivation for building the Cyclotron was to provide an alternate visual metaphor for representing and manipulating meter that was built from the top down (the cycle, or the bar), rather than the bottom up (the subdivision). Ironically, Justin London, in his book Hearing in Time [4], also assumes meters are built on even subdivisions (or N-cycles, as he calls) while also representing them as circles, not unlike the Cyclotron. London posits a collection of "wellformedness" constraints that "delimits the range of musically possible meters," [4, p77] the first of which specifies that the distance "between time points on the N-cycle must be categorically equivalent. That is, they must be nominally isochronous and must be at least 100ms." Telespringar is, then, mal-formed, and should not even be possible. My primary interest is not, however, theoretical, and I take no offense at the implication that somehow the music I play is illegitimate. David Code has argued
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