Algorithms are structurally identifiable but can also be flexible. Not all algorithms are flexible, and it is of critical importance to recognize at which points and in which ways it is flexible. The relevance of this issue to musical performance is significant, because the choice being made regarding the sequential order affects the outcome. Understanding where choice and flexibility lies is to understand the algorithmic structure. An arithmetic operation may explain this question most clearly. We have an understanding that the order in which we perform different operations leads to different results. 


Additions and subtractions produce the same result regardless of the order:

A + B + C = C + B + A

But this is not the case when multiplication is involved:

A + B × C ≠ (A + B) × C

In this case the answers for the left and right halves differ because it depends on which of the two operations (addition and multiplication) is performed first. Multiplication is a dominant operator – doing multiplication first is a rule – so brackets are necessary to distinguish the latter expression from the former. 

Decisions about the sequence of actions can also be found in cooking recipes, such as in the well-known example of how to mix eggs, sugar, and butter in baking. Eggs and sugar are mixed first and melted butter added last in madeleine; sugar and butter first and then eggs in Victoria sponge; sugar and butter first, egg yoke next, and egg white last—after flour—for a Swiss roll dough. The resulting differences are significant enough that different dough types lead to different cakes. 


The above examples concern the question of ordering actions in a timeline. But the question also concerns the timing of the actions. Baking a cake is a case in point: it is not just about the order in which the ingredients are mixed. But it is also about the flow of the process. Let us call it an art of sequential processing. We look at some examples in music.


Let us look at a canon:

You can listen to it here (starting from 12'12'')

Canon is a type of composition where the same material (usually a melody) is played more than once starting at different times. It has one rule for performance: you follow and imitate the line/voice/person who proceeds you at an agreed time interval. This is what happens between the two duos in the Haydn example above: the upper two instruments lead the lower two who follow them. If you are in the group who follow the other, you don’t need to see the notation, you can simply imitate by ear what the first group play. In this way the information (the melody) is given on a moment-to-moment basis. Of course, you can have the notation and follow it, but ‘making musical sense’ of a canon isn’t just about playing the same material at a regular distance.


Making musical sense as a canon means bringing out the quality of imitation and the interplay involved in the chase. From the composition perspective, this implies that the material needs a degree of simplicity so that, when it is presented together with the imitating part, it can still be heard and followed. The material has a contour, gesture, or harmonic direction which makes the canonic juxtaposition interesting. In the Haydn example above, it strongly features melodic ups and downs; and the juxtaposition between the two groups produces a contrary melodic motion in opposite directions. Note that the time interval between the two groups is critical in the production of this motion. Imagine if the second group entered another measure later, so two measures apart, then the melodic motion wouldn’t be so successful, and it wouldn’t work harmonically either.


From the performance perspective, making musical sense implies an emphasis on the imitation and an appropriate choice of articulations for the canonic interplay. The sense of imitation comes not only from playing the same material but also from playing with the same character. While the two groups share the same character, they also need to play out the tension and contrast arising from the temporal distance (that the second group is one measure behind the first). 


There are many types of canon. When canons are understood as variations or varied imitations of a thematic material, the broader category includes transpositions, inversions, and retrogrades. (Fugue, as introduced in affordance, is one species of canon.) Bach’s Goldberg Variations is perhaps one of the most representative compositions in which many varieties of canon are featured throughout the piece.


Serialism can be understood to have taken the concept and technique of making canons further. It is a particular kind of algorithmic technique because musical material is generated according to set rules. Schoenberg initially considered it as a thematic invention, which later composers developed into an organizational principle.

You can listen to it here (starting from 43'52")

The left-hand side is the notation with the annotations identifying each pitch-class (numbers 0 to 11); the boxed labels such as P-0 (prime series at the root position) and RI-5 (retrograde inversion of the prime series at the fifth degree) denotes one type of variation made on the ‘prime series’ P-0. The right-hand side is a graphic representation of how these two series combine to constitute the musical form and fabric. Serialism conceives musical structure as a generative process: the technique is a means to both create and articulate a musical drama.


Karlheinz Essl, in his essay on algorithmic composition, positions serialism as an important contributor to algorithmic composition in the twentieth century. The influence of serialism is in fact not only in algorithmic composition but also in modern and contemporary music composition. Serialism’s procedural rigour for material generation has been made into an aesthetic criterion by many twentieth-century composers, contributing to today’s composition as a highly organized discipline in classical music.


There is a wide-spread view that algorithms are mechanical. This goes against the grain of the Romatic idea of music being humanistic and anti-technical. Theodor Adorno’s suspicion on the processes of serialism, that the formal processes may be interpreted as intervening against the true expression of the musical material, may well to do with this view. However, I argue that there is nothing inherently mechanical about algorithmic processes. The structure of an algorithmic process may be formalized to the extent that it appears mechanical, but that is not the same as the process itself being mechanical


For example, making sense of the process as performance in the Schoenberg piece heavily relies on the articulation of the shapes as phrases with tonal characteristics on the piano. The same principle of characterization as observed in the performance of Haydn’s canon, applies: each ‘series’ has its own property and character. Out of thousands of possible series, which series are combined with which others, how their combinations are set in the temporal space, and how the mapping of the series constitutes the overall structure of the piece as a whole, are critical questions to the composition as well as to the performance.


I have discussed what musical performance can do to the sequential nature of select composed music. My next point is that musical performance can create a sequential process from compositions that have no algorithmic import in the compositional process. I have discussed the issue elsewhere, and it suffices to mention that, in such cases, algorithmic thinking offers a strategy for practicing as well as - more relevantly to this explosition - for the performer's listening in the act of performance. And the result is qualitatively distinct.

Now I want to ask a further question from the opposite direction: what does sequential, time-based nature of music-making (both performance and composition) do to musical performance as an event? 

Every musician has a design for performance. Musicians of classical music spend more time on the design (that is to say they ‘practice’), due to the presence of notation, the concept of musical work, and other factors. Institutionally speaking, we also invest a considerable amount of time into rehearsals to work on details of a design. 


But the communication of a musical design is a world of its own. The audience don’t necessarily know if what they hear is instantaneously created material, or instantaneously performed pre-existing material, unless they are familiar with the piece. For musicians working in contemporary music, this is a standard conundrum. We can also add to the list a pre-recorded playback of sound files, and real-time generation of material too.


The ‘liveness’ of musical performance as well as the ‘liveness’ of real-time algorithmic composition have attracted much discussion over the last three decades, particularly in electroacoustic music. Here the music can be composed in live. The liveness of a performance occasion that includes elements of real-time processing of musical material has posed interesting challenges. Attempts at creating perceptually meaningful instances of real-time processing as live events include Alvin Lucier’s I’m Sitting in a Room (1981), which is one of the older examples, where the live cumulative effect of the room acoustics of the performance venue features as the main musical content. More recent attempts are often in the form of sound installation, where the listener’s actions and movements determine the selection and developmental course of musical material.


Superseding and doing without the performer is one very viable approach to making sense of the ‘liveness’ in electronic music. Curiously, this can be seen as a way of bringing the listener into the position of the performer, at least to me, because the listener, in this new situation, experiences something very similar to what the musician experiences in performing music. It is the experience of enacting a design. For example, in Salomé Voegelin’s Listening to Noise and Silencewhere she discusses the listening experience of sound art, there is a striking resemblance to the performance experience.


In such a climate where the function of a live performer is becoming questioned, what characterizes the performer’s thought process during a performance? I think it is the sense of navigating through the present moment, grasping it within a real timeline, as if making a thread through it. This is a widely discussed point. Pierre Bourdieu (1977) positions speech above language to emphasize the power of practice as a reality in formulating thought; Bruce Ellis Benson (2003) argues that composing and performing are two facets of improvisation, which is not a self-contained world but a world of activity; Tim Ingold (2010) uses the image of weaving to illustrate this action-packed world. My point is that musical performance is a sequential process of making one decision after another in time. Mind you, I don’t imply that every decision is made on the spot. On the contrary, most musical decisions are made in advance. But enacting decisions is a real-time process. It gives the performance a quality that often divides good and less good performers.


Then it follows that the arresting power of musical performance can be understood as an evidence of efficient and elegant sequential processing taking place in the moment. My argument is that algorithmic thinking and musical performance have an affinity in that both are action-based processes. Adrian MacKenzie calls this common ground as ‘ontogenesis’, meaning that it is about how something comes to be, in contrast to ‘ontology’, which is about how something is. MacKenzie is citing Gilbert Simondon whose On the Mode of Existence of Technical Objects (1958) has had a profound influence on the philosophy of technologies in France and beyond. MacKenzie argues that ‘technicity’, which gives technical objects (in this case algorithms) a technical character, needs to be understood in its own constant re-structuring in changing context. He calls this re-structuring operation ‘transduction’. Transduction is a practical concept (coming from the word ‘transduce’, best known in the form of a ‘transducer’, a device that converts energy from one form to another), with capacities to develop and adapt, as well as to remember and anticipate, in a constantly new situation. 


We musicians are Protean, precisely because of the live information-processing expertise in the act of performing.  In everyday language, this expertise amounts to juggling as you go. (This is not entirely a positive factor, as this is also at the root of performance anxiety.) Juggling may not sound attractive in the parlance of Western classical music. But they shed light on something real and humane about every musician and every performing endeavour.