On and Off the Grid in the Electronic Domain

The grid is a ubiquitous construction in the realm of digital music. Time is quantized by default in many production platforms and the grids that appear onscreen often represent the resolution of the quantization being applied. Sequencers, in particular, are usually designed to function according to a stepwise progression of time. Sequencers allow for the establishment of a sequence of control values to be sent to a device that produces, triggers, or transforms sound. I began to imagine how temporal transformations would unfold if the sequencer’s steps were not regular but rather, could themselves be composed of progressive rhythmic values. Thus, rather than rhythmic change coming from the subdivisions of sounds in relation to one another, it would be directed by its immediate context, in terms of an expansion or contraction of the space around the sound. These transformations can be imagined as grids that are skewed or distorted, or as superimpositions of multiple grid frameworks.

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Figure 21 (below): A sequence of transformations involving distortions and superimposition of grid structures in order to examine the combinatorial results in terms of their visual rhythm. A.

Orthogonal grid. B. Two orthogonal grids superimposed, the second superimposed 50% into the second square of the first. C. – E. Two superimposed grids, one orthogonal as in A, above, and the second linearly compressed by increasing amounts. F. Two superimposed grids, one orthogonal as in A, above, the second compressed logarithmically over the first. G. Two superimposed grids, one orthogonal as in A, above, the second rotated in relation to it. H. Three superimposed grids, one orthogonal as in A, above, the second compressed logarithmically over the first, and the third skewed. I. Free transformation of planes.

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The grid studies pictured previously are inspired by a compilation of grid structures called Grid Index (Nicolai, 2009), assembled by sound artist Carsten Nicolai. Nicolai, under his stage name Alva Noto, conceives musical time in terms of “grid-size rather than

tempo“(Darton-Moore, 2018). It is fascinating to imagine the complexity of the

superimposed grid frameworks in the images above mapped into the time domain of music.

I began to experiment with this possibility through the spatial interface of an electronic music sequencer.

Figure 22: The control interface for the sequencer that I designed and used in Unnatural Processes and Unnatural Habitats. Though the interface appears grid-like the functionality of flexibly altering step sizes and loop lengths was a design priority.

To experiment with this directly, I began designing digital sequencers in Pure Data (Pd) to control synthesizers. As in most sequencers, the device I developed allows for quantization of time steps and sound parameters. On the left side of fig.22 and moving

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downward, there are blocks of transformative processes that have to do with pitch and amplitude (pitch, volume, register, and accidentals), each of which can have its own period of repetition. These processes are sequential, superimposed on one another in manner of diagonal metamorphism. Time runs along the x-axis and precedes by discrete steps. Each step results in the output of a pair of midi numbers, one for pitch and the other for volume.

What is different about my sequencer is that not only can each of these cycles of parameters have their own periods, but the length of each subsequent time step may be changed. I can establish and modify changing rates of change, for experimental listening or in live

performance. Furthermore, any of these factors may be randomized. These sequencers make it possible to establish and transform temporal grids while listening to the results in the moment the change was made.

The first of my sequencer-based performance systems was developed in 2015, for a workshop in which composers Peter Ablinger and Winfried Ritsch brought Ritch's RHEA robot piano system to the University of Huddersfield. This project provided the first opportunity to use the sequencer I was developing outside of the studio, and also my first experience in controlling a live acoustic instrument with a computer. Originally, this tool produced only two numbers at a time, representing pitch and volume. However, the variable rates of change of each stage within the sequencer, controllable according to any logic whatsoever (to include chance) gave this tool a great deal of versatility. The elasticity offered by the system can be heard in the second movement of Unnatural Processes in which multiples of a single motive are transformed in real time by changing grid size (number of steps in a phrase) and time step size (pulse). I performed all three movements of Unnatural Processes live by interfacing my computer keyboard across a network to RHEA, who then played the piano keyboard with an array of servo motors stimulated by microcontrollers.

The performance follows a scored part and requires the performer to initiate, fine tune, and react to results of robotic processes set in motion.

Peter Ablinger’s interest in the nature and perception of musical time (2006, 2011), encouraged me in this project. His use of metrical and temporal plasticity in pieces such as Augmented Study for 7 violins, and 22 Kanons Fur Peter Lackner, both from 2012, exemplify his

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solutions to working with transformable temporal frameworks. The straightforward appearance of the notation, grid-like in aspect, belies underlying alterations in temporal reference points that result in abundant variety. Finding these works to result in similar experiences to those I had in mind when developing Unnatural Processes, I set about searching for other composers working with quantized temporal frameworks that yield smoothly curved experiences of time.

In pieces like Madrigale (1979), and Concerto (1975), Aldo Clementi reveals a very personal approach to designing with musical time. Gianluigi Mattietti points out that the Concerto not only slows, but that the texture simultaneously thickens as the piece progresses (2011). For the listener, both of these pieces thicken in terms of memory as iterations

accumulate. In combination with the slow deceleration in some of Clementi’s works, a progressive physicality is sensed as the pieces come into being over time.

Morton Feldman employed grids both as notational devices, and as compositional tools. However, the qualitative experience of listening to Feldman’s music, especially his later work discussed here, contrasts with the quantization implied by its grid-like notational image.⁸ Time in these works loses objectivity and becomes something felt by individual listeners, like a thick, humid quality in the air. A first glance at Crippled Symmetry (1983), for example, lends the impression that the notation is straightforward. However the regularly spaced appearance of the notes on the page belies a wealth of experiences for an active listener in response to this music. One such experience is the shimmer that seems to arise from the surface of the sound. The shimmer occurs when two or more timbre-pitch

aggregates, often two or more different instruments, elide. The shimmer is not located in the score, but rather in the coincidence of particular musical moments, when it is noticed and attended to by an individual listener.

8 In early works like the Intersections (1951-1953), Feldman used graph paper, however, I focus here instead on works that appear grid-like, while neither functioning or sounding grid-like. It is also the case that Vertical Thoughts 1-5 (1963) and Last Pieces (1959) employ notation that is anything but grid-like in appearance.

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Although this experience seems highly subjective, I encounter it most often in pieces like the aforementioned Crippled Symmetry in which Feldman establishes individual

temporal frameworks that exist simultaneously in the same piece. This suggests that a material basis for the shimmer resides within the uncertainty that accompanies these ambiguous time constructions. In other words, Feldman’s ambiguity creates the conditions by which a listener constitutes the shimmer. Musicologist Tom Hall (2007) proposes that the grid-like notation in Feldman’s later work has a meaning beyond its appearance, citing works like Triadic Memories (1981), and For Samuel Beckett (1987). In these works, the grid-like appearance of Feldman’s notation reinforces the presence of a time standard for individual performers, a temporal referential frame which a performer must adopt to play their part. However, composing a coincidence of independent grids offset from one another destabilizes a listener’s temporal frame of reference and perceptually liberates the whole from a metric standard. This is very close to the ideal I hold for my own recent works in which multiple temporal grids or simultaneous time frames are employed.