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Page 1 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 . 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 , 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
Page 2 ï~~eloquently about the strengths and limitations of London's theory, in particular with regard to the telespringar and related dance meters . London's theory and his many examples, however, renewed my interest in the Cyclotron and suggested both a crucial design addition and some deep questions about how musical time works. 3. DESIGN AND EXAMPLES The design of the new Cyclotron combines both the original Cyclotron's "phasor"-like representation with the London N-cycle even subdivisions as markers within the cycle. These markers help orient the user and make the creation of well-formed metric structures trivial. The positions of the spokes are not limited to subdivision positions, as they are in a traditional sequencer, and can be placed to subdivide the cycle in any way, including the telespringar beat lengths. However, spoke positions (spokes are initially evenly divided across the cycle when created) can be quantized to N-cycle positions, if desired. In Figure 2, for instance, 4 beats (initially evenly dividing the cycle) are quantized to the nearest positions of a 9-cycle; this yields the familiar 2+2+2+3 pattern that London illustrates with Dave Brubeck's "Blue Rondo al a Turk." are maximally even, another of London's well-formedness constraints. Spoke lengths can be adjusted and also quantized to a set of subdividing circles, while the "cap" of each spoke can be variably sized to create, for instance, accent patterns. The new Cyclotron interface was written with Processing  (a provisional web version of the interface can be found here: http://music.princeton.edu/-dan/Cyclotron/index.html). However, it is purely a graphic interface for manipulating data and has no internal sense of time, nor do any of the visual parameters-spoke position, length, or capsize-have any predefined meaning. In order to actually use the interface, it must be connected to some kind of audio environment. I use it in conjunction (communicating via Open Sound Control ) with a set of classes written in ChucK . ChucK's strongly timed nature suits the Cyclotron particularly well, though it could certainly be used with Max/MSP, Supercollider, or other audio programming environments. In any case, it is within these ChucK classes that the Cyclotron comes to life-time passes, events occur-and its parameters become defined-the spoke length comes to mean, for instance, pitch, while the cap size controls, perhaps, gain. ChucK sends information back to the interface so the user can see how time is passing and when spokes are activated. To return to one of my original motivations for making the Cyclotron, how might we represent the uneven telespringar? Figure 3 illustrates the obvious tact: three spokes placed at the appropriate (uneven) points within the cycle. In Figure 4, we see this same meter but with even triplet subdivisions. Neither of these captures everything about the telespringar or reflects the range of variation that exists from fiddler to fiddler, but they are at least possible and reasonably elegant, relative to any representation within a conventional bottom-up time-line metaphor. In all of these examples, time has been assumed to move at a constant rate, so the uneven feel of the telespringar results from beats of different lengths, rather than any sense that time itself seems to move faster or slower within the meter. This, however, is an intriguing assumption, and doesn't necessarily match with my experience dancing and playing this dance. The basic steps for the dance are: beat 1, step slightly up, light, hanging; beat 2, step down, heavy; step 3, fairly quick step, to reach beat 1. Associated with these stems is the svikt, a characteristic rise and fall most easily apparent in the way the tops of the heads of a group of dancers will rise slightly (on beat 1) and fall quickly (on beat 2). The physical effort required to execute these steps varies, and another way to think about this dance is in three steps that are actually even, but that our sense of how time passes is affected by the physicality of the steps; rather than time moving at a constant rate, it ebbs and flows. rfigure: ine oasic yclotron ilnteriace, Win '4 oeats, quantized to the nearest positions of a 9-subdivision Ncycle (9-cycle). The lengths of the N-cycle is user-controllable, allowing experimentation with many different combinations of beat numbers quantized to particular N-cycles. For instance, quantizing 5 beats to a 12-cycle yields the common West African bell pattern 2+2+3+2+3, while quantizing 4 spokes to a 10-cycle yields the North Indian jhaptal tala (2+3+2+3). All meters generated this way
Page 3 ï~~instance, with the Cyclotron we could represent the telespringar as three even beats, perhaps with even triplet subdivisions, and then have time move more slowly towards the beginning of the cycle and faster towards the end. In my ChucK classes for the Cyclotron, I have embedded a "warp" parameter which allows the entire cycle to be warped (a warp value of 1 indicates "linear" even time, whereas warp values greater than 1 lengthen the beginning of the cycle, and warp values less than 1 lengthen the end of the cycle). For the telespringar, a warp value of 1.5 applied to three even beats with triplet subdivisions yields a remarkably convincing telespringar feel (Figure 5). gure i: a representation of ine tnree uneven oeats of Ine telespringar. r igure 5: even Deats ana witn warped time to represent telespringar One benefit of this conceptual inversion is that it simplifies the data we are considering; we can use simple subdivisions and quantizations (as in Figure 5) without having replicate idiosyncratic measurements (as in Figure 4) and then we can warp these subdivisions consistently and in highly controllable ways. In a future version of the Cyclotron, I hope to integrate more generalized time warping functions, building on the work of Honing , Dannenberg , and others. 4. IN PERFORMANCE While I initially created the Cyclotron to be used as a compositional tool, I quickly found it of use in performance. It can be used as a highly malleable metronome or click-track, providing a tool for performers to explore unusual meters together; this is especially useful in cases like the telespringar, where time seems to move at an uneven rate. In Lasso and Corral.: Variations on an Ill-Formed Meter (presented at ICMC r igure:; V eventplut suouivisitons or teL wIelngar I don't mean to make some metaphysical suggestion where somehow the laws of nature are called into question, but I do wonder whether our cognitive sense of time and how we represent it should be overly constrained by quantitative notions about time. For
Page 4 ï~~Copenhagen), the Cyclotron played a central role, changing in specific and learnable ways over the course of the piece and even carrying pitch material (Figure 6), all the while taking advantage of the Cyclotron's ability to warp time......... w: cv 4t 6. REFERENCES  Blom, Jan-Petter. "The Dancing Fiddle: On the Expression of Rhythm in Hardingfele Slittar", in Norsk Folke Musikk: Hardingfele Sldttar, Norsk Folkemusikksamling, Oslo, Norway, 1981.  Code, D. "Measure for Measure: Re-forming Metric Wellness," Music Theory Midwest meeting, Oberlin, 2005.  Code, D. "The AsymMetronome," http://www.wmich.edu/mustheo/AsymMetronome/    London, J. Hearing in Time. Oxford, 2004. Processing: processing.org Wright, M., A. Freed, A. Momeni, "OpenSound Control: State of the Art 2003" New Interfaces for Musical Expression, Montreal, Canada 2003. \ \~jV  Wang, G. and P. Cook. "On-the-fly Programming: Using Code as an Expressive Musical Instrument," Proceedings of the International Conference on New Interfaces for Musical Expression, Hamamatsu, Japan, June 2004.  Honing, H. "From Time to Time: The Representation of Timing and Tempo," Computer Music Journal 25:3, 2001.  Dannenberg, R. "Abstract Time Warping of Compound Events and Signals," Computer Music Journal 21:3, 1997. Figure 6: example from Lasso and Corral: Variations on an Ill-Formed Meter. The top curving line indicates how the speed of time varies over the course of each bar. Each player has their own click-track, notated above their part. I am currently composing a work for the American Composers Orchestra and the Princeton Laptop Orchestra that will similarly use the Cyclotron to provide a kind of time roller-coaster for the conventional orchestra to ride, warping the bars in consistent ways that would be impossible otherwise. Similarly, an upcoming commission from So Percussion, a New York-based percussion quartet, will make heavy use of the Cyclotron, both driving and being driven by the ensemble. 5. CONCLUSIONS The computer offers an unusual opportunity to play with our sense of time, and the metaphors we use to represent time play a crucial role in both inspiring and limiting our ability to conceive of various time structures. The Cyclotron is a provisional tool suggesting alternative ways of creating and manipulating time structures. The Cyclotron: