Introduction to Cognitive-Parametric Music

For an easier text to understand you can read this divulgation one

What is Cognitive-Parametric Music?

Cognitive-parametric music is thus technically defined as the use of a series of formal structures and materials that are based on the concept of the parameter as sound material.

The consideration of the concept of parameter as sound material parts from the abstraction process of traditional sound materials by interpreting traditional materials abstractly from a parametric perspective. Schoenberg taught us that it was possible to take a sound material like melody, define it within a parameter (the sound pitches), and reinterpret it in terms of another parameter such as timbre, which creates a melody of timbres. In parametric jargon, this is referred to as a parametric translation. By generalizing this procedure, we can also create materials such as scales of parameters, melodies of parameters, parametric modulations, etc. Parametric materials derived from an abstraction of traditional materials become disassociated from their dependence on a certain parameter.

Cognitive-parametric music arose from a search for music without any parametric centrality. It questions the need for an element that acts as an organizing center for a sound stream to exist. The objective is to create sound flows that are grounded from nothing a priori.

The listener is intended to interpret my music in different ways. My works are like a kind of multi-channel broadcast in which each participant can choose one of the channels, interpreting the sound flow differently from others depending on the chosen channel. The music is relative to the person who listens. The magic of the sound fact takes place in the perceptual system of the listener; what is heard is part of the artistic event.

Disassociating the sound stream from its dependence on a process with a central parameter can create multiple concurrent parallel processes, each one associated with a different parameter. The listener will choose which one of these processes to focus on, thereby determining his personal experience of the work.

Cognitive-parametric music was first born out of a search for a meaningless of the sound events. Removing the frame of reference from which a sound event is understood was a fundamental first step. Cognitive-parametric music began by searching for non-alienated music; I wanted to find music in which the meaning was open and revealed at the moment of listening, and wasn’t given a priori by the composer. I soon realized that a thorough reflection on the significance of sound objects was necessary, which led me to the field of sound semiotics. I then developed strategies to break the usual meanings of sound objects, which can be heard in my earlier works like End Game.

The concept of settling fact, which was based on cognitive models, allowed, among other things, the sound discourse to not be defined by the stress, as in the relaxing process of certain material properties based on a parameter (e.g., the dissonances or the removal and subsequent approach to a particular starting point). This concept associated with cognitive models allowed me to understand, from the very beginning, that the process of tensioning depended upon the cognitive tension, not from the material tension. This emancipation of the tensioning processes, by replacing the material dissonance with the cognitive dissonance, is what allows a material to have multiple loads of multivalent meaning and will at last allow for its free decoding.

The reflection on the meaningless aspects of sound was based on the idea that any element can lose its individual meaning by being stripped from its usual reference framework. Some sound mass compositions, such as those from Scelsi and Xenakis, have been investigated with this in mind. In these cases, a sound could lose its significance and individuality by being integrated into a sound mass. In my compositions, however, I intend to discover the lack of meaning not by a loss of significance arising out of the loss of individuality, but through means of un-referencing, which does not require a sound’s integratation into a sound mass.

Thus, the concept of parametric neutralizations occurs when an individual item loses its meaning through the neutralization of its meaning.

Parametric neutralization, a material closely related to the signification space, was the first one I worked with. The signification space is a logical function that maps the significance of a particular event in terms of another. For example, we can condition the significance of a parameter in terms of another parameter, a process that I implemented and investigated in the works between End Game and The Studies. I tested parametric neutralizations and parametric modulations in these works but only associated each of them to a single parameter, and never to all of them at once.

What naturally arose as a result of this process was the need to create a work based on a signification space in which parametric neutralizations were made in all parameters at the same time by interrelating parameters with each other rotationally using a cognitive model. This produced an already consciously cognitive-parametric music, which is clearly represented in Parametric Neutralizations Studies.

Parametric Neutralizations Studies arose before my need to generalize the procedures for applying parametric neutralizations to all parameters at the same time in a systematic manner. To do this, I used a rotatory parametric modulation structure in which a single parameter in each fragment  determines  another third through the signification space, while the rest of them remained neutralized. The goal was that the significance of a parameter was to be conditioned by another, depending on the cognitive model. The intelligibility of the process occurring in one parameter is associated to the process that occurs in another.I soon realized that it was necessary to base the process on some sort of cognitive strategy that helps listeners to recognize these determination flows from one parameter over the others. I then determined that the settling fact should be based on some sort of cognitive theory that would make the literal recognition of these structures possible. Thus, we can define, in a more precise way, a cognitive-parametric work as a series of rotating parametric modulations in which a parameter in each fragment is central and then neutralized in the following fragment, occurring through a parametric modulation based on a cognitive model.

Finally, I was able to produce music in which there was no center. However, the attentive reader may have noticed that I have defined parametric music as a series of fragments in which any parameter is central. But didn´t I say before that I didn’t want any central parameter? Effectively, the idea of this work is that there is a lack of centrality at the macro level, although in each time a parameter is central; in other words, if we see the work from a distance as an entity, any parameter can be seen to dominate the discourse. It is the same as seeing a tree or the forest, where if we see a tree, we don’t see the forest. If we focus on a particular fragment, a concrete parameter will be the determinant, but if we look at the overall structure, there is no key parameter nor any parametric hierarchy. Of course, the matter is somewhat more complex than what can be explained here (see the analysis of this work for more detailed explanations), but, indeed, making a cognitive-parametric work where any parameter is central from beginning to end became a goal that I would later achieve.

The next step consisted of systematizing the concept of parametric modulations and studying it carefully. The parametric modulations used in Parametric Neutralizations Studies were very crude, and at the end of the work I considered thoroughly demonstrating the multiple possible ways to perform parametric modulations that had barely been used in the first study.

To do this, I made the parametric material and the scale of parameters easier to understand. This led to Parametric Modulations Studies, which is a constant modulation between scales of parameters. Just like a tonal work whose structure can be defined, among other manners, by the way in which modulations between tonalities are made, we can define a parametric structure by the way parametric modulations are produced between different scales of parameters.

The scale of parameters is the parametric material par excellence, allowing us to define what a parametric work is structurally and acting as a constant modulation between parametric tonalities.

I will try to explain it slowly but briefly. In this context, parameterizing a work consists of enumerating the parameters that are to be considered in the work, which can be as many as you like since this is what gives meaning, and therefore significance, to understanding the concept of parameter as compositional material. In the same way, we can choose one melody or another based on its suitability to a given musical structure. We can choose a type of parameterization or another based on the parametric idea of the work. In his book Formalized Music, Xenakis proposes an enumeration of sound properties of the sound events (timbre, duration, pitch, and dynamics, which he calls variables rather than parameters), which we can consider as the classical interpretation. That is why I used it in my first two studies.

In tonal music, for example, a melody is chosen for its possibilities of integration as material in the form. And in serial or twelve-tone music, series are chosen by the adequacy of its properties to the serial concept of the work. In cognitive-parametric music, the choice of the number of parameters taken into account as a parametric row (or series) depends on the parametric formal concept of the work. For each parametric formal concept of a work, there is a scale (or row) of parameters which, through its properties, is the most interesting for accomplishing its concept. This is what ultimately defines how a parameter becomes a sound material for the parametric form. Each work of cognitive-parametric music has a parametric series that is custom designed with a particular parameterization of the sound objects, used alongside a cognitive model that will determine which parametric material is the most appropriate. Returning to the specific parametric series we are speaking about, we can, on the basis of a parametric series, create scales of parameters that are subsets of all parameters considered in the work.

We can create several scales that are derived from this parametric series. For example, if we consider all possible scales of 3 parameters, the equivalent to each of them is a tonal parametric scale: timbre, pitch, and dynamics, timbre, pitch, and duration, etc.

So, we can now define a cognitive-parametric work more precisely as a piece of music composed of the following items: a particular parameterization (which entails a parametric series that can be decomposed into several scales of parameters) as a structure that defines the way in which parametric modulation is performed. And a cognitive model which gives meaning to the conditioning of determination flows and establishes the load meanings in the parametric formal context.

Somehow, I reached the first parametric music paradigm in Parametric Modulations Studies, but there were still several things to improve, one of which we’ve seen. On the one hand, it was necessary to avoid that at each time a parameter was central, but on the other hand, it was necessary to formalize the meaning of cognitive-parametric music more accurately and formally to differentiate the parametric music from the standard kind. Moreover, I also should examine the concept of time and movement more closely, issues that were implicitly but not explicitly present in the two earlier works.

I soon realized that the relationship between the size of the present window memory and the size of the sound objects determined the experience of psychological tempo and indicated the problem of movement in music, so I decided to integrate time and movement concepts within my music. The integration of the two, as something unbreakable, led me to reflect upon the relativity of time in music in a natural way, since the relativity of perception of psychological tempo was related to the way in which memory was capable of retaining certain materials, depending on the size of the psychological window present. I found several perceptual theories about the relationship between the psychological present and memory (e.g., Dowland), which corroborated my hypothesis and were used as cognitive models.

I, therefore, decided to formalize a theory of the relativity of time as sound material, derived from its intimate integration of the concept with the movement of the material. I began by formalizing what could be a relativistic system and what could not, but I knew that I needed something that would allow me to avoid making tempo the central parameter in the work.

Finally, I found the key in the phase concept. The phase is something that is not directly perceptible, but is related to time. I generated a work with two audio streams (or two voices in the Boulez sense), each with a characteristic pattern moving with respect to each other at a different speed (movement problem). The relative phase will  determine the rest of the sound parameters considered in the work.

I had found the solution. First of all, I had a very rigorous formal system that allowed me to algorithmically formalize all the  details of the work. The relative movement of one audio stream to another would determine the psychological perception of tempo, depending on the ability of one’s memory to recognize patterns. If the memory recognized patterns, then there would be a perception of temporality that is also associated with the size of the psychological window present. If such recognition did not occur, then the perception of temporality would be very diluted and detached from the events of the movement of the material. The fact that one or another thing happened is relative to the different memory capacities of each listener.

We can now define accurately a second parametric music paradigm as a  cognitive-parametric system that formalizes how some parameters are determined by their position to others with a particular pattern of movement, as well as a series of cognitive models that define how such determination will allow the relative listening. Cognitive dissonance will thus be relative to the listener rather than the objective material qualities.

In summary, cognitive-parametric music seeks to disassociate tension from the objective qualities of the material defined around a central parameter, allowing a cognitive tension that does not depend on the material objective qualities but instead on cognitive processes that take place in the person who listens to the work.

Busevin, Endgame analysis. Without publishing.

Busevín, Towards an Aesthetics of Cognitive-Parametric Music, 2011, ISBN-978-84-608-3022-1.

Peretz I,  Zatorre R. J. The Cognitive Neuroscience of Music, Oxford, (2003).

Xenakis, Iannis, Formalized Music. Pendragon Press.1992, New York

Dowling and Harwood, Music Cognition. Academic Press.1986, Orlando Florida. ISBN 0-12-221430-7