Musical performance is often considered as a finished product. In the performance of Western classical music with notation, the appearance of perfection often suggests excellence to the extent that, if it’s not finished or ready, it can be considered a 'failure' as musical performance. The standardisation of this concept is such that, even when the performance contains improvisation, the audience expect perfection as art. It is the quality of almost surreal completeness that we seem to expect from musical performance, and this is particularly pronounced in classical music.


But musical performance is also something that is made and put together by humans. It is an action. In this sense, it’s no different from building a house, cooking a meal, or learning a new language. I want to look at the process of music-making, but with reference to a particular type: algorithmic process. The background to this enquiry is that through my work as a performer of real-time algorithmic composition, I’m becoming aware that algorithmic thinking is everywhere around me, and particularly so in the field of musical performance.

While algorighmic thinking seems to underlie every human activity, the specific character of such thinking in musical performance is that it is fluid and non-visual. While it has many similarities to the algorithmic thinking in musical composition, the critical difference is in this character which also making its analysis as a theoretical construct challenging. Yet, the presence of efficient algorithmic thinking is detectable in two ways. First, in terms of the quality of outcome, that is to say the level of efficiency (even elegance) with which a performance achieves its aim with given resources; second, in terms of the quality of operation for musical performance as an activity, that is to say a methodology with which the musical profession is carried out.


An algorithm is a predetermined set of instructions for solving a problem or completing a task in a limited number of steps. We associate algorithms with mathematics and computers, but algorithm is an old concept describing a step-by-step sequence for solving problems. We can find examples everywhere, includingthe instructions for how to build a flat-packed bookcase.

Allow me to give some more simple examples. First is a description of a sequence of tasks that a child goes through in order to get ready for school:

The same sequence is expressed in an algorithmic construction:

Division by hand uses a step-by-step algorithmic process, working with two digits at a time:

Calculation tools such as an abacus use the same principle (of working with only one digit at a time):

Route finding tools give us two things: descriptions on how to get A to B on the left-hand pane, and a map with an overview on the right:

What is important in these examples is that we need to think of the process in terms of a series of actions. For example, the left-hand pane of a GPS program above gives you an instruction as a list of commands that are usually not inter-changeable. In all the cases above, we reach the desired outcome by following through step-by-step instructions at each local moment. The mind is focused on each task in front of you, rather than speculating what a given action may mean in the holistic view of the process.


Next we look at similar processes in music. The left-hand picture below is a tablature notation for the lute. In the right-hand picture, we have information about how to decode it. We see six horizontal lines (in both pictures) on which we have numbers (mostly 0 to 3 in the left picture). These horizontal lines denote strings to be plucked (in the ascending order where the lowest line means the lowest string and the top line the top string); the number ‘0’ is the open (un-fingered) string note, which has the longest length of the string for vibration; the numbers from 1 to 9 show ‘positions’ where fingers (those of the hand that holds the ‘neck’ of the lute) press the strings to shorten the length of the strings for vibration. Following the cues given in the right-hand picture, you can decipher the numbers into notes on the lute. Then you play these notes in the rhythms written on the top of the lines for each vertical set of numbers.  This notational system may appear to be an unnecessarily complicated approach to playing music to some readers. But the specificity of the instruction was of paramount significance in the age when no standardized notation was available. The specificity of the musical notes that are being communicated had to be derived from the specificity of a physical instrument as a concrete reference point. 

There are many notations that can be illustrated as systems that bear algorithmic principles, due primarily to the fact that much of the algorithmic thinking is embedded in musical composition. However, it is worth emphasizing that algorithmic thinking in composition triggers algorithmic thinking in performance. For example, notations bearing algorithmic principles (such as above) often leads the performer to an iterative process, where steps taken in the notation for identifying the sound are compared to the steps taken in performing it. The relation between performance preparation and performance excecution is close-knit. My hypothesis is that algorithmic thinking brings alternative modes to performative process, distinct from the modes that are practiced in the standard 'perfection' orientation. My aim is to explore examples of algorithmic thinking in music-making actions, in order to look closely at its significance in the time domain. Hence, it is hoped that this exposition has relevance to the broader area of the performing arts.


In this presentation I’m going to make three points:

  •  Affordances may be combined for the construction of a unique reality
  • Combinatoriality affects the quality of the outcome 
  • Making a musical performance is an art of sequential processing.


I’ll elaborate on each in separate sections titled affordancecombinatoriality, and sequence. They can be read in any order. There is no conclusion to this presentation, however. I present an argument from a different starting point in each section. They lead to the same conclusion: musical performance uses much algorithmic thinking in its process, and that it is of critical importance for contemporary musicians that they are, consciously or unconsciously, able to process necessary information and tasks algorithmically. But what I hope to highlight in between is that there are different musical reasons to use algorithmic thinking, though some of which are idiosyncratic. The structure of this presentation is designed to give the reader a three-dimensional overview of the proximity as well as complexity between the musical and mathematical processes. As in the argument presented, the order in which you read may alter the understanding you gain.

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