Thinking Music Parametrically

1.   Towards the Concept of Parameter

In the last decades, thinking parametrically is a new trend and many different fields of knowledge are incorporating this new way of thinking. The main reason is the immersion in a digital world in which the computation has obtained great importance. The languages used in computer science to modelize and formalize the world have proved to be very useful and a source of inspiration to other areas of knowledge. One example of it, it is the appearance of a growing movement in design called Parametric Design or Parametric Architecture.

We can find several definitions of Parametric design in these references:

Parametric design is a process based on algorithmic thinking that enables the expression of parameters and rules that, together, define, encode and clarify the relationship between design intent and design response[1]1[2]2.

Parametric design is a paradigm in design where the relationship, between elements, is used to manipulate and inform the design of complex geometries and structures. The term ‘Parametric’ originates from mathematics (Parametric equation) and refers to the use of certain parameters or variables that can be edited to manipulate or alter the end result of an equation or system. Parametric design is not a new concept and has always formed a part of architecture design[3]3.

For example, Nigel Morgan acknowledges the Parametric Design as a source of inspiration for his Parametric Composition book4.

The decision of exploring computer-assisted composition (CAC) under the banner of parametric Design was inspired by a recent movement in digital creativity: Parametric Design5.

James Tenney was the first composer that explained parametric thinking in music in his book Meta-Hodos6. In this book, he created a certain parametric concept as analytical tools to understand contemporary music. In his explanation about contemporary music explains, how in a natural form, the history of music tends to parametric thinking. Anyway, his dissertation is only analytical. For him, everything was parametric. Parametric concepts were aesthetically neuter. The most important parametric analytical tool concept was the concept of parametric focus, parametric texture, and parametric articulation. He explains how in the measure that in the twentieth-century music the pitch is no longer, the only parameter new analytical tools and concept are necessary to explain a non-pitch centered music. He shows how the materials of new music are changing and, in order to fully comprehend them, a new approach with different concepts is needed. His main idea is that the new increased complexity in materials needs a phenomenological explanation based on its sound characteristics and in how they are perceived.

An attempt is made to demonstrate the great importance that has been given in 20th-century music to all parameters of musical sound; that whereas in early music the responsibility for the articulation of musical ideas was given to the pitch-parameter. The other parameters have begun to carry more and more of this responsibility, sometimes even to the extent of replacing the function of pitch altogether ([5] P.18)

He used in an implicit way the concept Parametric Centrality through the concept of

formative parameter regarding Varese´s piece Density 21,5.

We have so far dealt with an example in which the determination of the formal profile shifts from one parameter to another within the same clang In many clangs this form-determining function is given to one parameter only, and it is possible to speak them of a primary formal determinant- or formative parameter- for the clang as a whole([5] P.61-62).

He made what we can consider the canonic definition of the parameter in music.

Any attribute in of sound by which we are able … to distinguish one sound or sound-configuration from another. ([5] P.59)

His approach to parametric thinking is, as we will see, in the Cognitive-Predicative paradigm. In this book, he also made a new approach to the perception of form-theory applying principles of Gestalt psychology.

The parametric approach has also an epistemological reason for appearing, caused by the fact that if we see reality (social one) by a point of view defined parametrically what we perceive is parametrically biased, so in order to get objectivity, we must see the reality in a parametric neuter way. If we do not avoid parametric centralities we will get parametric bias. For example, Fernando Egido in his texts [6]7 [7]8 [8]9 showed how certain social phenomena could be better explained without parametric centralities. So, according to this if we do not analyze a problem with the correct parametrization we will not be objective. In a similar way Ruy Sardinha states in the text “Parametrization as Mediation”[10]that:

“The entry into what some have been calling the “age of parametrization” demands great analytical effort in order to grasp its various biases. As a background, we have the idea that a reality, a society or complex – or multiparametric – natures could no longer be grasped by traditional analytical methods – analysis understood herein as the division of this complexity into simpler units. Instead, they would require more appropriate methods and instruments, from the so-called complex thought to the multiparametric design or technology. The search for greater control over the production processes and the effort to not let yourself succumb to the hazards and contingencies of life underlie this background. Old issues accompanying Western reflection on man’s relationship with nature and with the artifacts created by him since the dawn of the great ancient civilizations are reissued. It is worth remembering that in ancient Greece, techne, which was creating the necessary knowledge of what did not exist in nature, dependent on human will and action, will also chair the operative actions

– such as agriculture and medicine – able to conduct nature to distinct ways. Such operationally aimed at, among other things, freeing man from random domain and contingencies. This need of operational acquaintance about nature posed to man the need to deal with hazards, with contingencies. That is why another meaning of techne opposes technique to techne, which is chance, contingency, suggesting that technical knowledge prevents man from the contingencies of chance. We can thus observe that, from its beginnings, there is a tension between freedom and determination in the development of a knowledge that tries to deal with contingencies, with chance, with what man does not control, what escapes its control, involving the need to prevent against these hazards. Well, we are dealing still today with this tension between chance and determination, with the need to control that which escapes us. Thinking therefore in technologies or methodologies that can encompass the various parameters that make up the reality poses or renews the issue of control when dealing with contingencies [9].

There are basically two different forms of using the concept of parameter into music. The first one (algorithm paradigm) that thinks the musical composition as an algorithm controlled by certain input parameters, and the (Cognitive-Predicative paradigm) that thinks the parameters as musical materials of the work itself. These two different approaches are not opposed neither incompatible and, as we shall see, they share common topics. Each of these approaches is rooted in a different concept of parameter11; algorithm-paradigm is rooted in the use of the term in Mathematics, and the predicative-cognitive approach is rooted in the use of the term in Logic.

It usually happens that there are multiple uses for a word. The use of the term “parameters” is not an exception. The term “parameter” has been used in many different ways in a different context, and the meaning of the word tends to vary over time for historical reasons.

Mosterin and Torreti [12] define the use of the term “parameter” in Logic as

In the formal language of a theory of first-order, there are Logical constant parameters and variables. The Parameters are the names or individual constants, function signs and the predicates or relational signs. Although logical constants and variables are common to all first-order theories, parameters are different and characteristics of each particular theory. In fact, the parameters of a theory determine the existence of its language (the set of formulae that can be built with those parameters) and its type of similarity or signature, that is the same that the type of similarity of the systems upon the theory can be interpreted. Logical constants meant always the same, with independence from the system upon which we interpret the theory. The parameters and the bound variables have the same fixed meaning in all the interpretations upon the same system, but change their meaning when changing the system. Free variables change their signification upon each interpretation [13].

For example, Busevin uses the definition of “Parameter” as a predicate to define in an explicit form of how he uses the parameter concept in his Cognitive-Predicative music.

In general, when I say “parameter” I refer to its logical meaning. In logic, to say something from something is to assign it a predicate (a parameter). So, to be able to describe an object, means assigning it some predicates, we can say for example:

The table is red

In logic, such enunciate is named as “atomic enunciate” and is formalized as Pa, where “a” means the object and “P” the property. Therefore, “red” is a predicate that is assigned to the object “table” and therefore, it is a parameter.

Therefore, an entity is defined for all the things that can be predicated about it. But it is not possible to apply some predicates to certain objects. This way, we cannot say that:

The G sound of the fourth violin string is red. Simply, sounds do not have an attribute of color.

Therefore, objects are described and parameterized by their properties. Intuitively, we can say that an object is defined by those properties that can be said about it, that can be predicated on it. Intuitively, we can see that parameterize an object is to enumerate the set of properties that do characterize it[14].

the complete article can be downloaded from academia at:

1 [1] Woodbury, Robert (2010). Elements of Parametric Design.

2 [2] Jabi, Wassim (2013). Parametric Design for Architecture.

3 [3] Parametric Design: a Brief History”. AIACC.( )Retrieved 5 April 2014.

4 [4] Morgan, Nigel Legard, Phil and Cook, John. (2015). Parametric composition Computer-Assisted Strategies for Human Performance. Tonality Systems Press.

5 [4] Morgan, Nigel Legard, Phil and Cook, John. (2015). Parametric composition Computer-Assisted Strategies for Human Performance. Tonality Systems Press.

6  [5] Tenney, James. (1961) Meta-Hodos. A phenomenology of 20th – Century musical materials and an Approach to the study of form.

7 [6] Egido, Fernando. (2000). Las posibilidades epistémicas de los sistemas rizomáticos frente a los basados en flujos de determinación sobre una centralidad.

8 [7] Egido, Fernando. (1996). Escritos Mutantes la intencionalidad de los métodos.

9 [8] Egido, Fernando. (2011) Towards and Aesthetics of Cognitive-Parametric Music. Auto edition.

10 [9] Sardihna, Ruy Tramontano, Marcello.  Parametrization as mediation. v!rus online journal. issn 2175-974x. N. 11  ( (consulted October 2015).

11 This is not the complete truth, same algorithmic composers have used the concept of the parameter as a property or sonic events, as the input of their algorithms.

12 [10] Mosterín, Jesús Torreti, Roberto, (2002) Diccionario de lógica y filosofía de la ciencia, Alianza Editorial Madrid.

13 [10] Mosterín, Jesús Torreti, Roberto, (2002) Diccionario de lógica y filosofía de la ciencia,(P. 439-440)

14 [8] Egido, Fernando (2011) Towards an Aesthetics of Cognitive-parametric Music, P. 71