23 March 2025 marks the 10-year anniversary of “Imagining a Non-Geometrical Rhythm,” my inaugural professorial lecture at the University of Huddersfield, where I worked from 2007–22. These lectures are a lovely part of the British academic tradition. They are open, public lectures, advertised fairly widely across the community, and they’re an opportunity to formally mark and celebrate the appointment to the rank of full Professor through the presentation of some element of one’s research. Often these events are done in full academic regalia—thankfully for mine it was just a suit and tie—and they’re followed by a round of questions and discussion, and then of course by celebratory food and drinks.
The talk that I delivered was highly speculative. These were issues that I had been mulling over, problems that I had been grappling with, but the handful of proposed solutions (presented fairly briefly at the end of the talk) were very much in a nascent state. Indeed the graphical examples of the notational models I was developing were made specifically for the lecture itself; all of the actual compositional sketches were just rough pen and paper scribbles at that point (one of them literally on the back of an envelope, as shown about an hour into the lecture video).
In the intervening 10 years, these notational and compositional models have become a central element of my practice, and while I’ve talked about them in various guest lectures scattered around the globe, I haven’t written or published anything about the evolution of those models, nor have I written about the rather significant evolution of my implementation of the tools and techniques that I’ve developed to work with rhythm given the alternatives presented by this new notational system. What follows is a series of updates and insights, an attempt to put into writing some of the things I’ve learned—including as a conductor—in the decade of tweaking and refining my approach.
When I presented “Imagining a Non-Geometrical Rhythm” in March 2015, I was at a musical crossroads. A careful scan of my Works List will show a pretty significant gap between February 2012, when I finished A painter of figures in rooms, and July 2016, when I finished The wreck of former boundaries. Only APOFIR-REDUX (2013), my first, tentative effort at making electronic music, appears in that gap. At the time of the lecture, The wreck of former boundaries was still only really in its infancy. The extractable work for 5.1-channel electronics was finished, and I’d been working on some of the general issues, ideas, and materials of the piece, but of all the instrumental material that would eventually form the piece, only the contrabass solo that opens the work existed in even the roughest of sketches.
The two notational models presented towards the end of the lecture ended up playing a significant role in The wreck of former boundaries, though even already in that piece one can see fairly clear differences between those early notational prototypes introduced in the lecture and the notation that ends up being used in the piece … and in the 10 years that have followed, the materials first presented in Wreck have undergone significant further evolution.
Notation model 1: force vs. resistance
The first of the two rhythmic prototype models underwent a few important changes before it was first implemented in an actual piece. The gradated scale of three degrees of force and resistance (the downward arrows and lines on the stems, respectively) was replaced with a more continuous depiction using widths of lines and colors/hues. The colors of the original prototype, which were simply a carryover from the coloring used in my Second String Quartet (2010), were changed to something a bit more intuitive (green means go, red means stop), and I got rid of the stepped bow subdivisions as well (originally in green boxes), replacing these with a more fluid and graphical notation (in blue).
This modified version of this first rhythmic approach, which appears in slightly different forms in the Wreck solos for contrabass and electric lap steel guitar, has been a bit of a compositional dead end, however. Although the force vs. resistance models that appear in that notation were absolutely fundamental to the content of the lecture—particularly in the central thematic strand around curves—and although the visual character of the lap steel solo, in particular, feels like a fairly iconic aspect of the ‘notational image’ of my work of that era, over the years I have found these materials more difficult to work with, or at least more difficult to develop into more sophisticated or multilayered compositional structures.
On the one hand, this model seems to be largely limited to instruments with physical gestural palettes that are fairly broad, wide, dramatic, and visibly traceable. I haven’t yet found a way to transfer it into instruments with more delicate or ‘microscopic’ movement profiles (buttons, keys, shifts of embouchure, etc.), and the model itself seems to encourage somewhat exaggerated choreographic materials, which then has a very clear impact on the concomitant pitch materials of these works. The model was ideal for what I was trying to do in Wreck, but in recent years I have been looking for something a bit more nuanced and subtle in both its gestural language and its approach to harmony, and the force/resistance model becomes a bit too hypothetical in those circumstances.
I also somehow found the rhythmic character that this notational model engendered to be a bit too loose and flexible. The graphical, spatial element of the notation seems to mostly take over, in ways that were never my intention. (It’s notable that the original prototype intentionally avoided any visual representation of duration—each event was equidistant, with the idea that its actual duration would only emerge organically through the interaction between the force/resistance structures. I would have liked to have been able to stick to that plan, but this became impossible once this notational approach was combined with the second rhythmic model (discussed below), which happens already by the third page of the score to the full ensemble version of Wreck, in which there is a direct link between duration and notational widths/space. Indeed the difficulties to scale this first notational model to chamber/ensemble settings is one of the primary reasons why I haven’t returned to it in the last decade.)
Notation model 2: ‘fluid’ tempo staff, and some practical things
The second prototype model introduced in the lecture—at that point developed only through some test attempts to transcribe the rhythms present in some free improvisation examples—on the other hand has been absolutely central to everything I’ve written in the last decade, and it’s that model I’d mostly like to focus on in this text.
Like the first model, there are some obvious differences between the original prototype and the system I’ve actually used in the end for pieces. For starters, I abandoned the lower portion of the rhythm staff—the portion that represented proportional subdivisions of the beat, and, within those proportions, further rhythmic, proportional representations of duration and articulation. These were replaced with a much looser graphical representation of the proportional placement of individual events within each flexible tempo/beat unit, as demonstrated in the two examples below.
I simply found this lower ‘staff’ of rhythmic information difficult to read, and a bit unintuitive. And I disliked the fact that the y-axes of these two rhythmic staves meant two different things (one speed, the other percentage), and worse, that the lower of these would almost certainly cause reading/perception challenges once combined with any situation in which pitch was also represented on the y-axis. (As a general rule in my work I try to avoid—or at least minimize as much as is possible—situations in which a single axis represents multiple, contradictory things.)
This however raises the first of two simple, practical notational things that I’d like to address here:
I’ve been asked a few times why the tempo staff, which has now been present in every work I’ve written since 2015, is represented in both the x and y axes. It’s a rare bit of redundancy in my notational practice (I also try to be extremely disciplined about avoiding notational redundancy), since both axes in effect give the same information—how fast the beat is (fast is high, slow is low) is the same information as how long the beat lasts (fast is short, slow is long). The answer is fairly simple: I find it much easier to differentiate similar beat durations/speeds with this ‘duplication’ of the data. It’s quite challenging to see small deviations in duration/speed if only the horizontal time domain is represented without the additional information carried by the vertical speed domain, as demonstrated below.
But I suppose this is also a more fundamental question of what is being represented here. For me, what’s important is that I tend to think about this material really as ‘speed’—which, in my way of thinking makes more sense as up/down—more than as ‘duration’. In a sense, it’s the horizontal element that is actually secondary; the horizontal depiction is, in effect, the result of the changes in the speed of the beats. The material is speed/velocity; the result of that material is how long the beat lasts.
The second practical notational issue is really just to publicly admit a not-so-small error that I made in the earliest versions of this ‘tempo staff’ notation.
When I first deployed this tempo staff model, I treated the vertical space of the tempo staff as though the depiction of speed/time was linear rather than logarithmic. I calculated the correct widths for the given tempo for the upper and lower limits (the fastest and slowest options on the tempo staff), but then connected these with a straight line in order to calculate the widths of the intervening speeds/durations, rather than the correct curved line. This means that, in truth, the relationship between the vertical locations and their horizontal widths for the given tempo indications in the score for The wreck of former boundaries are … wrong, really. It’s not an enormous problem—at least it’s not so considerable to require going back and fixing every tempo staff line in the score—but it was a problem that definitely needed a proper longterm solution. I redesigned the tempo staff templates for each metronome mark speed (there are 81 of them, from 30 BPM to 110 BPM, which is the tempo span that has sort of stabilized as the most useful ambit so far), and those redesigned templates have been used in the pieces completed after A republic of spaces (2018, rev. 2019).
(In the case of Wreck, as I’ll explain in more detail below, it’s really the horizontal ‘width’ element that’s correct; its vertical location along the tempo/speed staff is wrong. In general, all of the medium and longer lines should really clump more towards the bottom of the staff—because of the logarithmic nature of tempo, there should be considerably more variation in the width of these lines towards the bottom of the staff, whereas there’s fairly minimal variation in the widths towards the top of the staff, when depicted properly.)
“So, what ever happened to the curves, then?”
There’s one further practical thing which probably deserves a special mention:
Ideas around curves were obviously central to the original lecture. Curves are the central thread of the talk, and this fascination with the implications of curves also made its way into the initial prototype for the second notational model … but these curves were already abandoned by the time I actually started working with this ‘tempo staff’ concept in the brass trio from Wreck, the first of the extractable pieces from Wreck to use this notational approach. The irony here is that the opening section of the lecture takes a fairly critical stance towards the abundance of horizontal and vertical lines in my own earlier notation, as well as the notations of several friends, colleagues, and former students. And the curve was somehow meant to be the path out of the hegemony of these grids. And yet … in the end, what I’ve ended up with is horizontal and vertical lines. So, what ever happened to the curves, then?
There are two elements to the answer, one conceptual and one practical.
The conceptual problem is actually quite interesting. The curves of the prototype imply various shapes of accelerandi and rallentandi, but in truth these concepts only really work when set against the steady, ‘Euclidean’ grid of conventional Western rhythms.
The underlying problem is that the actual ‘surface rhythms’ within any given tempo-beat are notated proportionally in my notational model. It then becomes more or less impossible—or perhaps just excessively hypothetical—to notate these proportions against a shifting frame. A traditional accelerando/rallentando is a speeding up/slowing down of the pulse, against which all of its internal proportional subdivisions also speed up and slow down. In my model, the whole notion of the subdivision first requires some sort of conception of its frame … and if the frame is itself fluid, then the nature of these subdivisions becomes, for me, too vague. Or, to put it another way, what would the difference be—not just in practice but even conceptually—between a beat with a quick internal rallentando and a beat with the identical overall duration with evenly spaced beats with a decelerating curved tempo staff line? And how would I notate it?
An interconnected problem is revealed in the conducted ensemble pieces that use this notational model. I’ll talk about this in more detail below when discussing my experience of conducting these works over the last 5–6 years, but as a starting point, the fascinating challenge of conducting this material, in which any beat can potentially be any speed, and in which consecutive beats are more or less never the same, means that in effect every gesture requires the function of an upbeat. That is, every beat needs to show not only the starting point of the beat but also the (likely) location of the next beat. Each conducting gesture sets up the duration of its beat by simultaneously indicating where the next beat will fall, and as such this establishes the window of the duration of the beat against which the performers need to place their proportional subdivisions. So again the question is, how would one indicate a tempo that, in the midst of that gesture, also speeds up or slows down? It’s not impossible, but things start to become somewhat hypothetical, and any sort of rhythmic precision becomes quite unlikely. (Any good conductor will tell you how wildly problematic a decelerating beat is for ensemble alignment. Where, exactly … is it … going …. to .…. land?)
Which is all to say, for the time being, the notational system is limited to beats that are fluid in their speed from one beat to the next, but not with speeds that are fluid within a beat.
Strategies for Composing with Non-Geometrical Rhythm
In the earliest versions of this notation, my compositional approach was more or less similar to what I’d done through the improvisation transcription process outlined in the lecture. That is, I took sounds—in the case of both Wreck and A republic of spaces, imagined sounds—and loosely, intuitively assigned speeds/durations and metrical groupings for those sounds. Typically these were initially sketched through a loose space-time graphical notation and then slowly converted into more precise speeds and meters. In some cases—most notably in the Wreck solos for B-flat clarinet and alto saxophone—I sketched initially on graph paper and then imported scans of those sketches into the computer to make the transcription process a bit more rigorous. But in any case, the approach to the notation of rhythm and meter was fairly fluid, improvisatory, and reactive.
The bulk of the rest of this text will focus on various developments for how I’ve actually been working with these new rhythmic resources in the time since The wreck of former boundaries, and will give a brief introduction to some strategies I’ve been employing recently that approach material primarily as a collection of behaviors, rather than as a collection of things.
As I’ve written about elsewhere, the process of writing The wreck of former boundaries started in almost every way with a blank slate. I intentionally put myself in unfamiliar places, I avoided any of the methods and mechanisms I’d used to make pieces in the past, and in particular I sidestepped all of the compositional methods I had traditionally used to start working on new pieces. Critically, this meant that the methods I had used to work with form, meter, tempo, and rhythm were thrown out the window.
It was a useful act. It opened up some new possibilities for me, and it forced me to rethink how and why I make decisions early in the compositional process. But it also revealed to me that I missed—indeed needed—the resistance, friction, and creative catalysts that those previous compositional procedures had enabled. The sketching and composing process in Wreck was somehow too loose, and the topographies of the piece were too uncertain and ill-defined to react to, to work against, to spark inventive solutions, particularly in response to formal and structural obstacles. So with the first of the two quartets from A way of making ghosts (2018–20), a pair of pieces based on the self-portraits of Gerhard Richter, I had the opportunity to carefully pick and choose which elements of my old compositional methods I could reincorporate into my working process.
The problem—and it’s a truly fascinating problem—is that if one has attempted to do away with temporal grids, whether that’s beats or bars or indeed even minutes & seconds, what, exactly, is the unit of measurement one would use in the formal sketching process? What are the ‘things’ against which one plans the durational events of a piece? In my previous, more ‘architecturally’ driven sketching process, these materials were beats, tempos, meters, sections, etc. (and, as a result, specific durations emerged from the interactions of those materials, even if durations weren’t the starting point), but here, in this new world I’d created for myself, I honestly had no idea what the temporal unit with which I might try to shape the formal design of a piece might be.
In the end, I started working with, simply, ‘units’. Extremely hazily defined, rough clumps. Blobs. A temporal chunk of … ‘thing’. If I had to pin it down: bigger than a second; smaller than five seconds; but in no way actually determined, and in no way mapped onto any other existing temporal measurement. Then slowly, through the process of working—with a method I’ll explain in detail momentarily—the actual temporal values would come more and more into focus, and actual durational details would grow steadily more well defined. This maintained some of the goal of the process I started in Wreck, sidestepping the top-down, the architectural, the skeletal, and keeping the more painterly, sculptural fluidity that I’d been seeking, but still gave me shapes and structural energies that I could work with and against as the composition emerged.
It is these shapes that are for me most important. My way of working with this kind of ‘sculptural’ construction process starts from a pivotal stance that the most important structural elements are not ‘containers’—otherwise neutral ‘horizontal’ demarcators of time, of proportion, of subdivision … in other words, boxes to hold stuff—but rather have energy, momentum, viscosity, and other behavioral characteristics. Their principal function is not in having duration, but rather in having or enabling movement. The earliest stages of the sketching process, then, are mostly about building this movement, defining its character and speed and behavioral traits. More often than not, these shapes are in flux. I try to build forms that are fluid, shapeshifting, and in various states of instability. And the boundaries of these shapes, too, are often dynamic spaces—they are porous or magnetized or crumbling or sudden.
To put it another way, the aim is to charge these spaces, which then give rise to materials—rhythmic and otherwise—that respond dynamically to those spaces. The rhythms that appear in my work since 2018 are all, at some level, the response to these charged, dynamic spaces. This returns in many ways to the analogies about curves from the lecture a decade ago. The curves of a river, for example, are a result of the relationship between the velocity of the water and the geological makeup (sand, granite, limestone, … ) of the land through which that water moves. What I am doing then in creating these blobs of ‘units’ in the early stages of the compositional process is creating the geological character of the space through which the material will move. And like the river analogy, these geological features are not static—they respond to the pressures and forces of the water: their boundaries move, they transform and evolve based on the intersection of their character and the character of the energy enacted on them. And that, I suppose, is really where that original first notational prototype model has gone in my work. Although the notational model hasn’t been useful for me since those first two Wreck solos in 2015, the principles behind that notation have made their way into the underlying compositional methods that guide how I work with these new, more fluid rhythms and rhythmic structures.
“Form is a fluid. Material is a verb.”
I’ve been giving a lecture over the last few years in my various guest presentations that I’ve called, “Form is a fluid. Material is a verb.” The talk outlines some of the general principles above, and then goes into fairly minute detail to illustrate how I’ve actually been constructing these rhythmic materials on a technical level, including demonstrations of some of the Max patches that I’ve written and examples from some of the sketches from 27. Juni 2009 (2021) for E-flat clarinet and my recent Piano Concerto (2023). There isn’t space here to go into quite the same level of detail, but I’ll at least introduce some of the principles and techniques.
The critical starting point, as I mentioned briefly above, is that over the last several years I have shifted away from thinking about material as a ‘thing’ and instead towards thinking about material as a way of doing things. Traditionally we’ve conceptualized material in music as, simply, parameters. Pitch, rhythm, dynamics, articulation, register, timbre, and so on. There is a sort of objective reality to our conception of these attributes as … things. But the more I’ve thought about it, the more I think that’s wrong. Or at least it’s wrong for what I’d like my music to be. Those attributes are, for me, the results of things, and those things are, on the whole, actions, or at least states, behaviors, tendencies, etc. (Even when it’s not a ‘way of doing’, it’s at least a ‘way of being’.) And it’s not just that these are more ‘verb’ than ‘noun’. I’ve been working more and more with the idea of behaviors as my primary working method, which is to say, I am increasingly working with the way in which things act/interact.
So the spaces that I described above don’t get ‘filled’ with ‘things’. The spaces, which are themselves energized and have certain shapes and tendencies and dynamic attributes of their own, receive and interact with the energies or actions or forces that are put into contact with those spaces. The things we would traditionally think of as materials are the results or outcomes of that interaction. Their attributes (short/long, accelerating/decelerating, sharp/dull, separated/connected, whatever) are generally themselves not predefined; rather, their attributes are the result of an energy—or at least a conception of an energy—moving through a space.
I often talk to my students about this behavioral notion of material being very much like our own personal, human identities.
Who we are as people—our fundamental identity as individuals—isn’t defined through a list of attributes or traits. It’s not a list of objective actions (facial gestures, gait, vocal mannerisms), and it’s certainly not a list of surface-level physical descriptors (our height, our hair color, or even our posture). It’s instead the result of the interaction between a complex network of personal characteristics and tendencies (some innate, some learned; some fixed, some variable) and the environments and situations we find ourselves in, and of course the other people or entities also present in those environments and their behaviors and actions. Our identity is how we act, how we respond to a situation, how we interact with the world around us. A significant part of what I’ve tried to do in my recent sketching process—and this goes far beyond just rhythm and other temporal features—is to focus my thinking on why a particular event (texture, gesture, etc.) happens, rather than on what happens. I try to create underlying structures and scenarios that create their own rationale for how a layer of musical activity might behave, given that layer’s own tendencies, impetuses, energies, and trajectories. (This wonderful story-telling technique is another way of thinking about it, which I also often use in my teaching.)
In the two quartets from A way of making ghosts, this approach was still fairly loose, but I started thinking about material first as general roles or functions, then second as more specific local actions and behaviors, which then had to happen with a certain energy (roughly: dynamics, mapped independently as its own layer of activity) in a certain space (using many of the strategies I’d been working with to shape instrumental gesture in all of my tablature based works since 2008 or so—in fact this was the first compositional technique that I decided I needed to reinstate after the experience of writing The wreck of former boundaries).
In Self-Portrait, Three Times, Standing (15.3.1991–20.3.1991), the first of the two ‘Richter quartets’ to be completed (2019), there are two very simple overriding instrumental behaviors (drawing in many ways from the jazz traditions that are quite clearly central to the work’s identity), each with various sub-categories of behaviors:
solo (independent, outward, foregrounded; behavior is mostly around concepts of reworking, variation, flourishes, cascades, loops, runs; flamboyant, playful, wild; prioritize invention. // varying degrees of clarity vs. splintering, mostly through the degree of independence of various tablature layers: alignments vs independence (linked to density of covering, obfuscation, mutation, distortion, destabilization, etc.))
- each phrase assigns discrete roles, behavioral styles, and soloistic attitudes
- four ‘degrees’ of internal instrumental polyphony/physical gestural independence, including the function/clarity of pitch materials
- various degrees of distortion and/or muting (including destabilizing instrumental mechanisms)
- pairings of multiple soloistic instruments when new phrases begin simultaneously in those instruments
accompaniment (supportive, secondary, dependent, conditional; ensemble-oriented; fixed, steady, stable; central, inward; responsive)
- vamp (chordal, repeating, looping, supporting)
- ‘pad’ (shimmering, flickering, elongating, resonating)
- ‘hype-man’ (call & response, affirming, echoing)
In more recent works—in particular in 27. Juni 2009 (2021) for E-flat clarinet and 25. April ‘05 (in progress) for solo bassoon, which are companion pieces based on overpainted photographs from Gerhard Richter, very much in the same model as the ‘mirror image’ pair of quartets of A way of making ghosts—this approach has become significantly more systematized. Like A way of making ghosts, and indeed like all of my work since 2000, the driving organizational force is phrases. And again here the initial phrase structures use the rough, undefined ‘units’ (loose blobs of unspecified time) as their initial sculptural starting point. Here, though, the phrase structures are independent for a wide collection of various behavioral tendencies (I meticulously avoid referring to these as ‘layers’ … but so far I don’t have a better alternative term!), the intertwining of which creates formal structures that twist and morph and leak and surge in tangled four-dimensional shapes, constantly in flux, and endlessly the result of these underlying forces and flows. For now I’ll just focus on what’s happening in the temporal domain, and then I’ll briefly introduce a bit of what happens elsewhere in this sculpting model.
The temporal structures start with rough ‘blob’ phrases that demarcate tempo/meter behavioral units. At each node—each starting point of a new phrase—a probability model of the relative likelihood of beats with a particular range of speeds is assigned, using a very simple random number generator. (There are five speed ranges, from slow to fast (30–46, 47–62, 63–78, 79–94, 95–110 BPM, spanning the full range of tempo options on the tempo staff), and seven degrees of probability (from 0 (no possibility that a value from this range will appear) to 6 (high certainty that a value from this range will appear).) These probabilities are always transitional across a phrase, moving from one set of probabilities at the beginning of the phrase to another at the end. The values at the end are then either simply the values that begin the following phrase—in which case everything is just continuously transitional—or, in circumstances in which two or more other rough ‘blob’ phrases in one of the other ‘layers’ also start at this point in rough-blob-time, there is a sharp break and a juxtaposed new collection of probabilities. This same general organizational principle runs throughout the planning structures at this stage of the composition process, and determines whether materials/behaviors/structures are transitional from phrase to phrase or if there are sudden/abrupt changes at the end of one phrase and the beginning of another.
For each tempo/meter behavioral unit phrase, a behavior description emerges. (Like the probability windows, these are either transitional (light lines in the example above) or sharp juxtapositions (thick lines, above).) These behaviors are constructed intuitively, principally in response to the randomly generated probability figures, plus superimposing some larger structural tendencies (principally responding to the randomly generated probability figures that appear further down the road, in essence giving shape to middle-ground tendencies and trajectories). To give a quick sampling of the kinds of tempo/meter behaviors that appear in these pieces:
hiccup; revving (ooom-pah); sluggish, with little ciphers/glitches; gimp waltz; decelerating, unspooling; unstable/jerky, constantly changing gear; waves; lilting; liquid, languid; off-kilter, bouncing, briefly stuck/frozen; etc.
From here, I use a fairly simple Max patch that I designed that spits out 1) a number of beats in a bar, generated through a simple randomizer ranging from 2–7; and 2) the speeds of those beats, in BPM, which are drawn from the relative probability for each of the five tempo span ranges at that moment in the phrase structure. (In the example shown below, the probabilities for the five tempo ranges are 1, 0, 1, 6, and 3; the randomly generated meter is 5 (see lower left of the image); the randomly generated beat durations in BPM are 64, 90, 109, 103, and 84.)
Critically, these speeds/durations are unordered lists. I then decide on the actual ordering—the shape of the beats of each bar—following the tempo behavior description. An example from 27. Juni 2009 is shown below, which demonstrates this process. I’ve been given from Max the number of beats per bar and the speeds of those beats. Each individual beat-tempo is then (re-)ordered following the tempo/meter behavior descriptor for its phrase (oompah // stretched >> winding down), which gives a clear ‘character’ to the speed/beat structure of each bar, and each phrase. To return to the water analogy above, this is the first stage of establishing the geographical conditions of the space through which the material will flow.
In addition to illustrating the organizational strategies of each beat, the example also shows a bit of the next phase of rhythmic organization: each beat can also then be subdivided. The maximum number of subdivisions within any given beat (which ranges from none, which is to say a single attack in the beat, to five) is its own ‘phrase’ structure, similarly transitional/juxtapositional. And likewise, these subdivisions are again unordered within a bar (in the example below, 3211 / 313 / 1111 / 12 / 112 / 22112). They’re assigned to individual beats following ‘surface rhythm behavior’ characteristic descriptors, which again are assigned per phrase, and again follow the same principles of transition as the tempo/meter behaviors described above. In the example below, the descriptor from the previous page (not shown) was “looping, swelling / accumulating, encrusting (building up little loops), increasingly ‘spinning’,” which then has a sudden juxtaposition midway through the example page to “drawn, stretched, pulled / little interruptions, hiccups, wobbles.” (Note that although these ‘blob-phrases’ exist prior to the construction of the actual metrical structure, once that structure is established, the ‘blob-phrases’ then snap into alignment, magnet-like, to the new downbeats once they’re created.)
The example above also shows a few—though not all—of the other behavioral phrase trajectories (‘layers’) that are part of the organizational structure, including dynamics (which again guide both the available range of dynamics and shapes/behaviors of those dynamics across a given phrase), the level of distortion or modification (timbral transformations, behavior of performance techniques and gestures for mouth/embouchure/breath materials), the rate of change of pitch-related activities (in effect, ‘harmonic rhythm’), the behavior of fingerings (levels of independence of rhythms in the pitch/fingering materials and degrees of independence between the two hands), and gestural behaviors and shapes in the pitch/fingering materials. The mechanisms for each of these are roughly similar to the Max-generated structures outlined above that generate the surface rhythms for the ‘mouth/articulation’ materials.
Again as mentioned above, in these two recent solo works these intertwined phrase structures are all in various degrees of independence from one another. The goal here was to push the ideas of fluidity, of curves, of endlessly transitional and transformational states—which were originally really only geared towards my thinking about rhythm—deeper into the organizational structure of my work, further sidestepping the more ‘container-like’, architectural phrase structures of in my pieces from roughly 2001–18 and enabling a highly dynamic and kinetic approach to form.
Experiences & insights from conducting, and some possible future developments
The wreck of former boundaries is unconducted, even in its full 35-minute ensemble formation. There is a network of types of cues between players that help to organize the piece, and players are typically grouped into small chamber music formations that share tempo/meter structures, with one of the players designated as a leader. This is supported further by an on-stage computer monitor that assists the interaction with the electronics materials that are scattered throughout the work. The two works that comprise A way of making ghosts were originally designed to also be unconducted, using the same kinds of cueing schemes found in Wreck. In practice though, neither of the two quartets have ever been performed without a conductor. Carl Rosman conducted the first two performances of Self-Portrait, Three Times, Standing (15.3.1991–20.3.1991) in Buffalo and Taipei. I’ve conducted the remaining performances and the studio recording, and also conducted the premiere and recording of Self-portrait, 1996 (2020) with Ensemble Musikfabrik, as well as the premiere of the Piano Concerto (2023) that uses the same rhythmic notation. I’d like to focus briefly on my experience of conducting these works, introducing some of what I’ve learned about this rhythmic model in the process as well as a bit of where I think this approach to rhythm might go in the future, some of which stems directly from these conducting experiences.
I only learned I’d be conducting Self-portrait, 1996 two days before getting on the plane to head to the rehearsals for the premiere. The story is a good one. The ensemble called and said that they thought it would be useful to have me conduct initially in the first few rehearsals, since there were enough challenges in each instrumental part without also having to worry about responsibilities for the unusual beat structures plus all the cueing and interactions between players. I agreed that I could help do that, and spent a bit of time the next day doing some quick preparations and conductor-oriented score study. While I was packing, I called Carl back, and said: “Should I maybe pack a suit … just in case?” He replied, “I think you’d better.” Which is not only how I stumbled into the wonderful experience of getting to conduct with Musikfabrik in March 2020, but also—and this is a much longer story for another day—how I found myself with a pandemic-length amount of time at home to think through ways of making conducting and performing a much more central part of my musical life. (Geklappt.)
But when the actual rehearsals started, everything suddenly clicked. First of all, it was the most fun I’d had in a decade. It was, frankly, a blast. But more than that, the physical, almost dancelike movements that these meters and rhythms required were exactly what I’d been trying to make for years. Those who know me know that I’m often conducting to myself (just a little thing I do to occupy my brain … when I’m walking, sometimes when I’m out running, when I’m on the train, etc.)—and when that music isn’t someone else’s, when it’s just something I’m imagining or inventing or sort of casually improvising in my head, the sweeping, uneven, unsteady, kinetic, rebounding, swooping, popping gestures that I usually use are exactly the kinds of things I instinctively found myself doing on the podium in those first rehearsals. These rhythms—these things that, even in the fairly open, honest, even sort of vulnerable language of the professorial lecture were still presented as a kind of intellectual problem to solve—were the physical musical experiences I’d been searching for for years.
Anyhow, as I say, it was a joyful experience, and I’m not exaggerating when I say that it was a life-changing one.
As I’ve had many more experiences to conduct these works in the five years since, one of the things that’s really struck me is that there really are no models for this kind of conducting. It doesn’t really fit any of the things one typically learns when studying conducting, except insofar as the basic beat patterns still match what one would do with normal meters. Most critically, there are no places where one can simply give an upbeat, set the tempo with the right amount of precision for the impulse on the downbeat, and then more or less just beat time in a nice, small, clear but unobtrusive way. Instead, the little bits of problem-solving that a conductor needs to do for a tempo change in a more conventional setting—thinking about how to prepare that new tempo, how to approach that new downbeat so that it has all the correct energy and clarity to get whatever happens in that next beat to do what it needs to do, or how to get the ensemble to align in that new moment—happen on every beat in these pieces. I’ve found that I need to think of each conducting gesture—that is, each beat—as an upbeat. Each gesture needs to not only give the impulse of where the beat starts, but also has to immediately show an arc that will establish where the next beat will be. The players’ ability to place their proportional subdivisions, particularly when there are aligned attacks or events, requires a sense of how long the beat is going to be. In the end this means that the gestural language that I’ve used to conduct these works is a bit different from what I’d do in other circumstances, and is certainly bigger, loopier, more curved, more exaggerated, and frankly probably more physical. I’ve had to invent a technique on the fly that attempts to make all this tempo fluidity and instability feel and look inevitable rather than unpredictable and uncertain. (Which, again, has been loads of fun.)
The other significant thing that I’ve learned through the process is, I think, much more interesting. This is something I’ve talked about publicly in various contexts over the last few years (for example here) but haven’t yet had the chance to put it in writing. Often the physical experience of conducting new music is strangely disappointing, especially for those of us drawn to conducting because of its physically expressive connection to music-making, a way of kind of embodying sound through sculpted movements, shapes, and somatic energies. Often the beat structures in certain strands of the new music repertoire are disconnected from the physical, musical activities of the players, so the conductor’s role becomes less directly expressive, less directly musical, at least when it comes to the physical gestural language. To be clear, I still enjoy that work, but it’s nowhere near as rewarding as situations in which my physical gestures and the physical gestures of the performers—that is, the gestures of the music—are intertwined.
What I’ve found in conducting these recent works of mine is that the process of sculpting a beat, of deciding exactly how long that beat is going to be, of figuring out how that beat is subdivided with all of its gestural intricacies, is an extremely collaborative experience. I, as the conductor—indeed as the composer—don’t really ‘set’ the tempo here. It’s a thing we as players set together. I’m listening to the activities of the performers, usually driven by one or more primary voices in the texture, and I’m both guiding and responding to the musical realities of the moment. There’s a push and pull, that, frankly, feels to me very similar to what I feel in, say, conducting rubato in 18th or 19th century music. I find the dynamic nature of this approach to rhythm—to the fundamental aspects of speed and duration outlined in the lecture a decade ago—to be incredibly rewarding. The physical and the sonic are not only connected, they’re entirely dependent on one another.
The process of conducting these works has also revealed some of the shortcomings of the notational system in its current state. For starters, I’ve come to think that my current approach of allowing 81 discrete tempo/speed options is probably unhelpful. As it is, these days I usually overrule what the Max patch spits out if there are two or more beats with nearly identical speeds. I tend to allow the speeds to sort of ‘snap’ into an agreed shared speed instead. (If the patch spits out a bar with two beats of 79 and 80, I’d generally just make them both 80; if it was 69 and 71, I’d just make them both 70; and so on.) With my students I’m usually fairly strict about making them clearly justify any tempo indication that isn’t one of the standard historical Maelzel metronome markings, and that’s simply because a) the deviations from one click to the next are actually still really quite small gradations, perceptually, and b) those historical tempo indications have all sorts of repertoire links, gestural identities, and characters that are pretty easy to quickly replicate. (Like most conductors, I have my own list of tempo mnemonics that I use to quickly remember tempos without a metronome.) One is tapping into a history or lineage of tempo, not just setting a number. So my sense is that, given all the fluidity and unpredictability of the beats, and particularly in connection with the collaborative flexibility I described above, I could probably significantly reduce the number of gradations of possible tempos that I give myself to work with. Maybe not exactly to the historical metronome mark options, but … at least pointing in that direction.
I am also finding that, in the ensemble works in particular, the proportional subdivisions of individual beats would really benefit from sometimes reintegrating some traditional ‘normal’ subdivisions (of 2s, 3s, 5s, whatever), particularly if it allows me to have clearly aligned syncopations off the beat, which, at the moment, my more graphically notated system makes quite difficult. I suspect that in future ensemble works with this rhythmic notational approach I’ll find ways to reintegrate clear subdivided grids of pulses, when that’s musically appropriate. In any case the development of these new notational models was to give myself the compositional tools that I needed in order to work with and represent a set of rhythmic options that traditional Western musical notations couldn’t accurately depict, not to then also permanently eliminate the opportunity to work with those traditional rhythms in the process.
Beyond that, I am still interested in seeing what might be possible with this otherwise abandoned conception of ‘curved’ tempo staff activities. It’s an interesting practical and conceptual problem, but not an insurmountable one.
In any case, it’s been a fascinating 10-year project, and one that’s had quite a significant impact on my work. I ended that lecture a decade ago by saying, “In any case, I’ll keep working,” and that seems as good a place as any to end here as well.