Divulgation Writings About Cognitive Parametric Music

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Divulgation writings about

Cognitive

Parametric

music

usevi



Divulgation writings about Cognitive Parametric

music



Published in 2017

Revision 6.0

Written between 2007 and 2016

This text has been translated to English by an automatic translator so it

may contain errors.

Busevín - Fernando Egido

Distributed under Creative Comons licenses 3.0 ‐ Derivate work not

allowed, with recognition of authority, and without commercial use. The

author possesses all the legal rights of the intellectual property of this

writing, as well as all the copy, exploitation and distribution rights.





5‐ Busevín ‐ Divulgation writings about Cognitive Parametric music

Index

Table of contents

Index ............................................................................................................... 5

1. Introduction to Cognitive‐Parametric Music ............................................. 7

2 The trilogy .................................................................................................. 20

Introduction to the studies .................................................................... 20

Introduction to cognitive‐cognitive parametric music .......................... 22

The context ............................................................................................ 24

3. Parametric neutralizations studies ........................................................... 26

4. Parametric modulations studies ............................................................... 27

Evolutionary lines of the studies ........................................................... 29

5. Parametric formalizations studies ............................................................ 32

6. Cognitive Dissonance .............................................................................. 46

References ............................................................................................. 61

7. Three Chants for Computer ...................................................................... 62

8. Homo homini lupus ................................................................................... 64

7. Characterization of cognitive‐parametric music ....................................... 69

8 Modelization of a cognitive parametric musical work ............................... 73

9. Glossary ..................................................................................................... 77







1. Introduction to

Cognitive‐ParametricMusicThere is nothing better to explain something than using a comparison with

another area. I will try to explain cognitive‐parametric music through a very

different sense of hearing, the sense of taste.

All of us have ever enjoyed a simple experiment that you can try whenever you want. If you drink a glass of sweetened milk, it tastes sweet. If the next

day, before drinking the same glass of milk, you eat a piece of toast with jam

and after that you drink the glass of milk, you will realize the glass of milk no

longer tastes sweet, it tastes different. We note that it tastes bitterer.

However, the milk is the same. This experiment applied to the sound, is what

we call cognitive‐parametric music. This phenomenon in parametric music

jargon is called parametric neutralization.

The fundamental idea of the cognitive‐parametric approach is that the

meaning of the materials which form artistic works is relative to the context

(as we'll see the parametric context) instead of being determined by its own

objective qualities as an entity.

Another example, this time taken from visual world, would be to see a graph

through a color filter. If we see a graphic through a blue filter, blue remains

undifferentiated (meaningless and neutralized in parametric jargon). I.e.,

blues will be equal to whites (they are not different from whites ones). Look

at the paradox that a color is undifferentiated when is observed with a filter

of the same color. This paradox, applied to the sound, is one of the

foundations of the cognitive‐parametric approach. We can derive from these

examples a basic cognitive rule. If we eat two foods we tend to ignore

(neutralize) what is the same in both, focusing our attention on what

differentiates both of them. This rule is the foundation of parametric

neutralizations and hence of parametric modulations. Intuitively, we can

understand that if we present a series of objects in the time (sounds or tastes)




its load of meaning is related to the difference and contrast with respect to

the previous one. We only perceive what differentiates them, staying

meaningless (neutralized) what they have in common.

We will see it more slowly; an object (a glass of milk) tastes different (means

something different, in the cognitive‐parametric music terminology)

according to the context.

Cognitive‐parametric music is based on the idea that the importance of the

musical events depends not on its physical objective properties but on how

they are perceived (perception that determines the construction of the

meaning). And, in turn, the significance is relative to the way in which the

interaction of some parameters on each other determines the meaning they

have for a particular Cognitive System.

“Notre perception est relative; elle compare sans cesse l´ objet qu´elle vient

d´appréhender à un autre perçu auparavant ou encore virtuel, localisé dans notre

mémoire. La différence ou l’absence de différence qualifie toute perception

(Grisey, Écrits, P. 29)

So far we have considered only a single parameter but what happens when

the interaction of several ones (properties) interfere.

We are going to see it more slowly. Milk is an object that has the property of

being more or less sweet (among others). "Sweetness", is a parameter

(property) that has food. We have seen that if two foods followed with

different sweetness, the second one seemingly is less sweet than what

actually it is (a form of parametric neutralization) but, what happens if we

define additional properties of foods and see how their interaction influences

the significance?

We will consider several properties of the food as parameters, for example,

bitterness, temperature, or spicy, and so on. If we make a very spicy food,

sweetness will be masked. If we try a very spicy food all we prove after it,

any other thing, will lose its flavor (it will lose the signification) will be

meaningless by the spicy context. Thus, the significance of certain properties

is conditioned to others. I.e., the significance of sweetness is conditioned to

the spicy. The significance of a property is relative to another, or what is the

same thing for the cognitive‐parametric approach, the significance of the




process that occurs in a parameter depends on the process that happens in

another one.

Each type of cuisine can be defined by a central parameter that determines

the other ones. For example, in Mexican cuisine spicy is prioritized over all.

So far, in fact, we have not made any progress regarding to the

nonparametric conception. However, having studied in such a way the

creative fact, it gives us an important question. Is it really necessary that a

central parameter determine the significance of the other ones during all the

time?

Cognitive‐parametric music is generating a parametric musical discourse in

which there is not any central parameter. We have seen that there are

different types of cuisines based each one on a central property, they can be

based on the spicy (Mexican), sweet (pastries) or bittersweet (Chinese).

What would differentiate a parametric cuisine from a nonparametric one is

that while in the parametric one all properties have the same importance, in

the nonparametric one there is a hierarchy of parameters wherein a

parameter is dominant.

Thus, a parametric music is characterized by the fact that there is no a central

or dominant parameter that determines the sound stream. For example, in

tonal music, the pitches are the central parameter. The structure of a tonal

work specifies how a departure from the original key to a more remote one

generates a tension which relaxes when it backs to the original key. In

nonparametric music, tension is associated to the characteristics of a

particular parameter. For example, in Xenakis´ stochastic music, the tension

and relaxation are produced by increasing and relaxing the densities of sound

masses. In general, the process of tensioning in a work is produced through

the concept of dissonance associated with a given parameter.

In tonal music, tension is produced by certain dissonant intervals as the

second, the tritone or the seventh. In Masses music, dissonance occurs by the superposition of events. The tension in the musical processes occurs in a

relative way to the parameter or property that dominates the others. There

is music, such as Cage´s random one, which does not consider tensioning

processes. Cognitive‐parametric music comes before the need to liberate

tensioning processes from the work's qualities associated with a particular

property or parameter of musical materials. For this purpose, it was

necessary avoiding the centrality of any parameter over the other ones. The




conclusion of the research process, to accomplish this, was the creation of a

series of parametric materials, such as the scale of parameters which, unlike

traditional musical materials, are not related to a particular parameter. Thus

a series of music materials were born based on the concept of parameter.

And the cognitive‐parametric music is born as the music that uses those

parametric materials.

By stripping traditional materials from their dependence on a property or

parameter of the sound, the tensioning process also may be unassociated

with a particular parameter. Therefore cognitive‐parametric music

tensioning is based on the idea of cognitive dissonance instead of a

dissonance associated with a type of material based on a parametric

centrality. Cognitive dissonance and cognitive tension are based on processes

of tension and relaxation which occur as a result of the recognition or not of

certain patterns or regularities, or by the listener´s ability to predict what is

going to happen. When the tension is associated with a property of material

is relatively objective, but when the tension is not related to an object

properties, as in cognitive‐parametric music, then the tensioning depends on

the cognitive processes produced in the listener brain, and therefore the

public can freely interpret the music.

This is the ultimate meaning of the cognitive‐parametric music, to release the

public from the composer´s intentions. Cognitive‐parametric music is a solution to the problem of how to ensure that the public can be an integral

part of the magic of the artistic fact. Cognitive‐parametric music achieves this

through a few materials, whose tension is not dependent on a parametric

centrality, but cognitive processes that occur in the listening. So the listener

can invent his own meaning of the work. Since listening is a cognitive process

that it is not associated with the intentions of the author. Other composers

have tried other strategies, like Cage through the total randomness.

It is very common in musical literature the description of certain works as visual or spatial, which tend to be works that in some way suggest and

facilitate their understanding through a graphical representation.

It is also common to hear about classifications of the listening experiences,

based on the way in which several listeners of the same work understand the

work by visual, emotional, or textual explanations. There are people who

understand music by an emotional experience, i.e. feeling emotions

(emotional understanding), while others may have a more intellectual




understanding of the same work, and represent the work as a figure (visual

or intellectual understanding), while there are others for which the music is

understood by finding an story (textual understanding). It is used as a vehicle

to try to explain in other way the cognitive‐parametric music.

Another way to understand the cognitive‐parametric music, in an intuitive

way, is based on the concept of synesthesia. Synesthesia is used by

neurophysiology for studying the phenomena of cross perception, and

explains the ability of some people to hear colors or to see flavors. The

neurological reasons for these phenomena are being studied today and they

are associated with certain temporary or permanent neuronal dysfunctions

due to any alteration of perceptual systems. Cognitive‐parametric music can

be, in some ways, explained from these phenomena, since it is based on the

idea that parameters can be inter‐defined. In the same way that a

synesthetic can taste colors, we can perceive the pitches through

rhythm. The interdefinitions, unlike the synesthetic, are not real but

semiotic. It is essential that there is no any central parameter for the

parametric interdefinitions to work.

Cognitive‐parametric music, seen from the perspective of synesthesia, tries

to get insights crossed through the parameters considered in the

work. Synesthesia crosses the perception of the senses. Cognitive‐

parametric music crosses the properties within the same sense

perception. Thus we can perceive the dynamics through the pitches or the

dynamics through the timbre.

You can see an example (https://youtu.be/2E89sda8JFs) of this parametric

interdefinition thought the concept of parametric morphing. In this example

we begin hearing a pulse (object which is perceived as temporal). By making

an upward glissando we get a voice like sound (object perceived as timbral).

So we have a sound object in such a way that is perceived as a temporal

object or as timbral object depending on its frequency. In this way we can

convert an object perceived as a temporal one gradually by morphing into

an object perceived as timbrical by slowly increasing the frequency.




Cognitive‐parametric music is technically defined by using series of formal

structures and materials based on the use of parametric materials as a sound

material.

The creation of parametric materials parts from the abstraction process of

traditional sound materials. It tries to interpret traditional materials in an

abstract way, from a parametric perspective. Schönberg taught us that it was

possible to take a sound material, like a melody, defined on a parameter (the

sound pitches) and reinterpret it in terms of another parameter, for example

the timbre, creating a melody of timbres. In the parametric jargon this is a parametric translation. Similarly, generalizing this procedure, we can create

materials such as scales of parameters, melodies of parameters, parametric

modulations, etc. Parametric materials derived from an abstraction of

traditional materials are dispossessed from its dependence on a certain

parameter.

Cognitive‐parametric music was born searching for music without any

parametric centrality. It was about questioning that there should be an

element that worked as organizing center for the existence of a sound

stream. The objective was creating sound flows that were not grounded from

nothing a‐priori.

My music seeks to be able to be interpreted by the listener in different ways.

It’s like a kind of multi‐channel broadcast in which each participant of the

public can choose one of the channels, interpreting the sound flow differently

from others depending on the chosen channel. The work is relative to the

person who listens. The magic of the sound fact takes place in the perceptual




system that listens to the work, I mean, what is heard is part of the artistic

event.

To dispossess the sound stream from its dependence from a process

associated with a central parameter we can create multiple concurrent

parallel processes, each one associated with a different parameter. The

listener will choose which one of these processes focus on, thereby

determining his personal experience of the work.

Cognitive‐parametric music was born, first, in a search for a meaningless of

the sound events. Removing the frame of reference from which a sound

event is understood was fundamental at first. Cognitive‐parametric music

began in a non‐alienated music search. I wanted to find a music in which the

meaning was open and occurs at the moment of listening and wasn’t given a

– priori by the composer. I soon realized that it was necessary a deep thought

about the sound objects significance. This led me to think about sound

semiotics. I developed strategies to break the usual meanings of sound

objects in my earlier works, such as End game. The concept of settling fact, which was based on cognitive models, allowed,

among other things, that the sound discourse were not defined by the stress

– relaxing process of certain material properties based on a parameter, i.e.

the dissonances or the removal and subsequent approach to a particular

starting point. The concept of settling fact associated to cognitive models allowed me, from the very beginning, that the process of tensioning of the

work depended upon the cognitive tension, not from the material tension.

The Emancipation of the tensioning processes, through replacing the

material dissonance by the cognitive dissonance, is what allows a material to

have multiple loads of multivalent meaning, and will allow its free decoding,

at last.

Reflection on the meaningless was based on the idea that any element can

lose its individual meaning by being stripped from its usual reference

framework. Some sound masses works (such as those from Scelsi and

Xenakis) have investigated with this. In these cases, a sound could lose its

significance losing its individuality by being integrated in a sound mass. But

in my case, I intend to find meaningless, not by a loss of significance arising

out of loss of individuality, but by means of unreferencing, without the

necessity of being integrated in a sound mass.




Thus, the concept of parametric neutralizations comes with which I get an

individual item to lose its meaning by the neutralization of its meaning.

Thus parametric neutralization was the first parametric material I worked

with. This material was closely related to the signification space. The

signification space is a logical function that maps significance to a particular

event in terms of another one. For example, we can conditioning the

significance of a parameter in terms of another parameter. This was

implemented and investigated in the works between End game and The

studies. Parametric neutralizations and parametric modulations were tested

in these works but, associated in each of them to a single parameter, never

to all of them at once.

In a natural way arose, as a result of this process, the need of making a work

based on the signification space in which parametric neutralizations were

made in all parameters at the same time, interrelating parameters with each

other rotationally through the signification space using a cognitive model. It

is then when there is already a consciously cognitive‐parametric music. And

it is put up in Parametric neutralizations studies. Parametric neutralizations studies arises before the need to generalize, in a

systematic manner, the procedures, used until then individually, to all

parameters at the same time. To do this I use a rotatory parametric

modulation structure in which in each fragment a single parameter determines to another third through the signification space, while the rest of

them remained neutralized. The goal was that the significance of a parameter

was conditioned to another, depending on a cognitive model. The

intelligibility of the process occurring in a parameter is associated to the

process that occurs in another one. So this was what it really signifies, and

not only a formal empty structure. I realized that it was necessary to base it

on some sort of cognitive strategy that helps listeners to recognize these

determination flows from one parameter over the other ones. It was then

when I realized that the settling fact should be based on some sort of

cognitive theory making possible the literal recognition of these structures.

Thus, now we can define, in a more precise way, a parametric work as series

of rotating parametric modulations in which in each fragment a parameter is

central which is neutralized in the following fragment, through a parametric

modulation based on a cognitive model.




So finally, I got a music in which there is not any center. However, the

attentive reader may have noticed that I have defined parametric music as

series of fragments in which any parameter was central.

But didn´t I said before that didn´t I want any central parameter?, effectively

the idea of this work is that the lack of a centrality follows, although in each

time a parameter is central, from the idea that if we see the work from a

distance as an entity any parameter has dominated the discourse. It is the

same like seeing a tree or the forest. 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 not any

parameter nor any parametric hierarchy nor any key parameter. The matter

is, of course more complex than what here can be explained, see the analysis

of this work for more detailed explanations. But, indeed, the objective of

being able to make a cognitive‐parametric music in which, from the

beginning to the end any parameter is central, became a goal that I would

later achieve.

The next step consisted in systematizing the concept of parametric

modulations studying it carefully. Parametric modulations used in Parametric neutralizations studies were very crude, at the end of the work I

thought making a deep reflection about multiple possible ways to perform

parametric modulations, which had barely been used in the first study. To do this, I create the parametric material easier to understand and the scale

of parameters. Parametric modulations studies are 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 defining the way in

which we produce parametric modulations 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, as a constant modulation

between parametric tonalities.

Let’s try to see it slowly but briefly. Parameterize a work consists of

enumerating the parameters to be taken into account in the work. As many

as you like, since this is what gives meaning, and therefore significance to

saying that the concept of parameter can be considered 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.

Xenakis in his book “Formalized music” proposes an enumeration of sound

properties of the sound events (timbre, duration, pitch and intensity) which

we can consider as the classical one. That is why I used it in my first two

studies.

For example, as in tonal music 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 parametric row (or series) depends on the parametric formal

concept of the work. For each parametric formal concept of a work of

cognitive‐parametric music there is a scale (or row) of parameters which, by

its properties, is the most interesting to accomplish its concept. This is what

ultimately defines how a parameter is a sound material for the parametric

form. Each work of cognitive‐parametric music is a problem for which a

parametric series is custom designed, and a particular parameterization of

the sound objects, and shall be used a cognitive model in the work that will

determine which parametric material is the most appropriate. Returning to

the parametric series we are speaking about, we can, on the basis of a parametric series, create scales of parameters such as subsets of the set of

all parameters considered in the work.

We can create several scales derived from this parametric series. For

example, if we consider all possible scales of 3 parameters, equivalent each

of them to a tonal parametric scale:

{timber, pitch, dynamics}, {timber, pitch, duration}, etc.

So, now we can define a parametric work in a more precise way as a music composed from the following items. A particular parameterization (which

entails a parametric series which 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 is that which gives meaning

to the conditioning of determination flows and establishes the load meanings

in the parametric formal context.




Somehow, with Parametric modulations studies I reached a first parametric

music paradigm. However, there were still several things to improve. We’ve

seen one. It was necessary avoiding that at each time a parameter was

central, and on the second hand, it was necessary to formalize more

accurately and formally the meaning of cognitive‐parametric music in order

to differentiate the parametric music from the standard one.

Moreover, I also should work with the concept of time and movement, issues

that were not explicitly present in the two earlier works, but implicitly.

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 it referred to the problem of movement in music.

So, I decided to integrate time and movement concepts. The integration, as

something unbreakable, of time and movement led me to reflect 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 window of the

psychological present. I found several perceptual theories about the

relationship between the psychological present and memory, which

corroborated my hypothesis (Dowland) and were used as cognitive models.

I therefore decided to formalize a theory of the relativity of time as sound

material derived from his intimate integration with the concept of the

movement of the material. I started doing a formalization of what could be a

relativistic system from that which not. But I needed something that would

allow me to avoid that the tempo would be 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 it is related to time. I generate a work with two

audio streams (two voices in the Boulez sense), each of them with a

characteristic pattern moving with respect to each other at a different speed

(movement problem) being the phase relative, each of them with respect to

the other, what is going to 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 formalizing algorithmically until the most unexpected detail of




the work. It would be the audio stream movement relative to another one

what would determine the psychological perception of tempo depending on

the ability of the memory to recognize patterns or not. If the memory

recognized patterns then there would be a perception of temporality that is

also associated with the window size of the psychological present. If there

would not be such recognition, then the perception of temporality is very

diluted and detached to the events of the movement of the material. The fact

that one or another thing happened is relative to different memory size of

the psychological present of each listener.

So, now we can define accurately a second cognitive‐parametric music

paradigm as a formal cognitive‐parametric system which formalizes the way

in which some parameters are determined by their position to other ones

with a particular pattern of movement. And a series of cognitive models that

define the way in which such determination will allow the relativity in the

listener. Cognitive dissonance will thus be relative to the listener, not to the

objective material qualities.

This is the last sense of the cognitive‐parametric music meaning, achieve that

the tension is not associated with the objective qualities of material defined

around a central parameter, allowing a cognitive tension that does not

depend on the material objective qualities but on cognitive processes that

takes place in the person who listens the work.

January 2013







2. The trilogy1

Introduction to the studies

The studies are three works born from the need to establish several

composing techniques in a better systematic and structural way. These new

composing techniques have been used and developed in previous works, but

it was necessary to explore their possibilities deeper in order to endow them

with

certain

formalism,

making

them

a

bit

more

rigorous.

The

studies

are

a

reflection of whether it is necessary that certain parameter dominates the

musical speech.

The starting point of the studies is in my previous works, in which I tried to

generate multiple simultaneous streams to enable multiple parallel listening

of the same work. Works like End game or Sounds stains are designed to

make their components highly ambiguous, allowing multiple readings. The

main objective is to get a relativism of listening in the public to create their own system of decoding the meaning of sound objects.

In these early works, I presented some unreferenced material from its normal

interpretation frame, forcing its reinterpretation. Following the Nono´ s idea

of “Infiniti Possibili”. I relied on the idea that an enough ambiguous material

can have multiple interpretations. This idea, that Nono could see as well in

the architectural spaces such as the crypt of the “Colonia Güell”, led him to

reconsider the relationship between physical space and sound profoundly.

This has been taken up in my work.

Gradually, from work to work, I became aware that in order to generate

multiple listening and unreferenced materials from their usual meaning, it

1 This was published fisrt time in January of 2012 as the chapter one of my

book

Towards

an

aesthetics

of

Cognitive

Parametric

music.




was necessary to seek meaningless of sound events or, even better, multiple

relative significance to its context. Rather than seeking the dissolution of the

perception of a parameter as an individual thing, integrating it into a cluster

as Scelsi or Ligeti, I preferred to neutralize the meaning of the sound

elements by the context. This led me to work in Sisyphus' regret or Sounds

for occupying

impossible

spaces.

The porpoise was to avoid the significance of sound objects. It was the

reflection on sound semiotics objects to get the meaningless of sound events

what took me to the concept of significance space. Like an extension of Nono´

s reflection, and its power to achieve multiple listening through the

neutralization of meaning. In works such as The return of the rebel man, Sound stains or Squashed fly on the tablecloth, all these ideas are already

performed and tested in my previous works as well as the parametric

neutralization.

The logical consequence of the development of all these works, was to carry

out a work in which the parametric neutralizations were made

simultaneously in all parameters and so was born Parametric neutralizations

studies. Then, I needed a model that would integrate these multiple

neutralizations and make them possible. It wasn’t enough to have

simultaneous neutralizations, it was also necessary to establish a global

structure which guaranteed that any parameter were central. This structure

couldn’t be based only on the dissolution of individual parametric elements,

but to seek the dissolution of its meaning. The integrated solution that

enables neutralizations, like the lack of meaning, was a gestural rotary

cognitive model that conditioned the determination flows of a parameter

over the others by turns, making sure that any parameter headed this

process. Parametric neutralizations

studies

was created to get a work

without any central parameter.

The reflection about the exhaustion of material dissonances –which had led

to the crisis of modern music‐ and the analytical thinking in dialectic

materialism ‐which was not able to explain the new social phenomena of

thought control‐ took me to contemplate certain relationship between both

of them. That’s how I found a shortcut through cognitive dissonance which




led me to redefine the limits of dialectical analysis technologies rather than

seeking for material dissonance2. In this sense, reading Sartre’s Critique of Dialectical Reason was an awesome source of inspiration because I found

possible a meta‐reflection on dialectic itself. See my texts “Intentionality of

methods”, “Rhizomatic systems against the dialectical ones”, “The myth of

confrontation and political ontology”.

Influenced by the reading of Adorno´s reflection on new music aging, I started

to think about a new music critical about dialectics but along with the

growing tendency of abstraction and the relationship between meaningless

and material changes. Besides, the tendency towards abstraction implies the

removal of any reference point that could be used as a privileged center. It is

important, therefore, to base the concept of the new, not so much on finding

a more dissonant material (in an dialectical sense) or an explicit content ‐both

totally disempowered and reabsorbed‐ but on the absence of centrality and

the unreferenced by meaningless and its logical consequence: the cognitive

dissonance.

Introduction to cognitive-cognitive parametricmusic

The cognitive‐cognitive parametric music is a possible solution to the

creation of music without a central parameter, which introduces new

compositional technologies based on new musical material that comes from

the concept of parameter.

The History of Music can be understood as a process in which there has been

always a main control on an increasing number of parameters. Therefore,

from Baroque to our days the control over parameters such as the dynamics,

timbre, or the space has increased. The number of parameters that a

composer uses as material has indeed risen. This increase in the number of

2 In a conceptual level, the difference is quite clear, but inside the work itself it is not so clear

and the cognitive model that defines the cognitive dissonance is sometimes grounded on the

material

dissonance.




parameters has allowed new musical concepts. The melody of timbres and

certain concepts like the integral serialism or the spectral music would have

not been possible without the creation of various composing technologies.

These new ways of composing have favored the examination and control of

a larger number of parameters.

"The fact that then, as demonstrated palpably the Musical Offering and Art of

Fugue, instrumentation and instrumental timbres were not as defined as they are

today reveals a fundamental difference: the timbre did not operate as integral

composition ingredient in the sense that, since the nineteenth century, has led to

the melody of timbres and timbral organization scales in series " (Adorno,

dissonances, P. 141)

In these three works I have developed a group of formalisms, techniques and

concepts that allow us to use the parameter concept like musical material. In

Parametric neutralizations studies parametric melodies are used, that is to

say, sequences of sound objects in which only a parameter is central.

The concepts of scale of parameters and the modulation among scales of

parameters are improved in Parametric modulations studies where I

developed some parametric modulations techniques. The parametric

serialism is a new invention here, a new formula where a parameter row is

used as musical material.

Finally, in Parametric formalizations studies a formal method is created to

define, in a very precise way, what exactly is cognitive parametric music.

In a non‐cognitive parametric music the formal structure is defined by the

contrast in which certain parameters are related during the composition in

virtue of a central parameter. For example, in the tonal music the form is

defined by the contrasts of sequences, in such a way that in each of them a

certain group of pitches dominates being them the central parameter. These

parametric works have been created defining a sort of formal structure

established by the way in which the parameters are determined,

transforming the parameter itself into a music material.




The context

These pieces represent something very special for me. They are the result of

a long and extensive research over time. From each of them, the following

one

has

come

out

as

a

twist

of

screw

from

the

critics

of

the

previous

one.

Although I consider them as the best in my production, those ones that have

been premiered have not been excessively successful. In fact, they have

received bad reviews, no like other works of mine as Endgame or For Rachel Corrie, which have been more successful. There is in these works a strange

paradox, although they are the most original ones in my production, it seems

not so evident when they are listened. The three studies have been the most

difficult ones to compose because of their high structuring level, which made

very difficult to find new ideas that were also musically interesting. In spite

of all, I believe some of my most inspired moments are in these works. When

I finished each of them I feel the need of a new composition much freer and

less deterministic than the previous one; those innovations that I would put

in practice later again. They are an experimental process that has been

growing. I can say, by experience, that not always public and critic ‐and the

composer himself too‐ appreciate the works in the same way. In my case

there is a total divergence.

After Parametric neutralizations studies I did Isostasia which is a much freer

work, I also wrote For Rachel Corrie between Parametric modulations studies and Parametric formalizations studies , overlapped in time with Parametric modulations studies . In these intermediate works I expressed that

experimental need held back in the others.

It was about picking up a series of procedures used previously to define and

to establish them in a more precise and systematic form. That’s why the

name of the studies. The ultimate aim of them is to give rigour to these new

techniques as they are a clear embodiment of them.

These pieces are created as a political critic to the manipulation of knowledge

in our political situation, by thinking in terms of just one central parameter,

for example the budget or any particular class whose interest is put as

central. (See my articles on political parametric translations). That common

belief and lazy habit of seeing from one point of view our social reality wipe

out the rest of the social objects (see my political text “The myth of




confrontation and political ontology”) and generates tautological

processes that make these theories function as a self ‐fulfilling prophecy in

itself which carries with its own compliance. So, leads us to a desalination to

denounce that a certain idea is determined by a false centralization and put

it there for an interested power. In the same way, getting a musical speech

not based on the centrality of any parameter makes music become

desalinated too, allowing free decoding of the sound entities and their

relationship. There is no justification for putting a particular point of view or

a parameter as central. To denounce the falsehood of all kind of centralism,

(parametrical, racial, ethnical, social class, gender or any other nature) is the

base to build the possibility to see the reality in a more objective, open and

not manipulated way. Furthermore, these studies answer to a second

necessity,

to

be

integrated

in

the

paradigm

of

abstraction

and

meaningless

of materials. How? Well, by exploring the tension through cognitive

dissonances instead of the properties of materials.

These works attempt to answer questions of whether it is possible to

compose music not based on an absolute reference point, or a central

parameter. The conductive thread of these works is to put in question

whether it should exist a parameter working as central in the work, around

which the other ones are articulated.

These works are based on the goal of creating a kind of music that helps us

to deconstruct false centers settled in our lives. They are an attempt to give

us a different view of what is reality and how we live in it. In a world in which

all political systems seem to be based on a single centered thought,

disassembling centralities could point us to a different way of seeing reality,

and overcome our limits wondering about what we believe is possible.




3. Parametric

neutralizationsstudiesThe first work of the series is Parametric neutralizations studies and was born

in the classroom with De Delás where he proposed me to compose a work

for orchestra. The work was premiered at the XXIII Encontres in the Auditory

of the

Superior

Conservatory

of

The

Balearic

Islands, thanks to Matías Far, in

January 2003. The premiered was interpreted by the Palm of Mallorca

Orchestra directed by Daniel Tosi. It was composed between December 1999

and April 2001.

This work starts from the idea of signification space. The signification of a

parameter is determined by another one. In each fragment of the work a

certain parameter is the determinant, remaining the others neutralized, that

is to say, meaningless. The signification space is a logical function that allows

changing the meaning of a parameter in function of another one.

The signification space allows the Interdefinition between parameters and so

any parameter can be, in each moment of the work, the determinant of the

other ones. In this way it’s difficult to establish a central parameter. To

neutralize a parameter is to get that such parameter stop being perceived,

although it continues being there. Scelsi, Ligeti or Feldman are composers

that have experimented with the neutralization of certain parameters by

means of statism or either by means of an undifferentiated modification with

a random or non recognizable pattern for the cognitive human systems.




4. Parametric

modulations studiesThe second work is Parametric modulations studies, created for small

ensemble with percussion, clarinet and cello, and was premiered in October

28, 2009 at the IV Smash Festival in Salamanca by the Interpretation

Workshop of Contemporary Music of the Conservatory of Salamanca directed

by Javier Castro. The first version of the score was published in the journal

Quodlibet as a separata in the 30th edition of the magazine in 2004. It was

composed between November 2001 and January 2004. It was by 2011 when

I made a new revised version of the work.

With this second work I wanted to study and improve the concept of

parametric modulation, giving it a greater rigour expanding the number of

possible ways to perform parametric modulations. Its starting point is the

analysis of the concept of traditional modulation. Trying to define the

concept of modulation (in the exclusive field of music, not the concept of

modulation in telecommunications) applied to parameter scales instead of

pitch scales. In every modulation there are 4 elements: a parameter on which we

modulate, e.g. pitches; two hierarchies defined by that parameter, e.g. two

scales; and finally, a common element or transition strategy to move from

one another that may not exist, e.g. a common chord to both tonalities. The

concept of modulation has been applied not only to the pitches in music,

Stockhausen ‐referring to the work Telemusik‐ defines modulation as the

transition among passages with different characteristic. Starting from the

concept of parameter scales, in this study I’ve generated a process of

Perpetuum mobile of modulations among parameter scales. But also, this

work has directionality. The work begins establishing a clear relationship

between the determinations that little by little disappear. At the end, the

work culminates in a kind of parametric serialism in which any of the 4

parameters dominate the other ones.

A parametric modulation is the process in which certain parameter stop




being the determinant becoming neutralized, where its role is taken by

another one in the discourse. This work made me possible to abandon

gesture as a cognitive model to develop cognitive strategies for

determination flows. Substituting gesture with parametric Interdefinition,

through the correlation of significance space which sets the determination

flows.

The third work of the trilogy, Parametric formalizations studies started in

2007 and finished in October 2011. It is for a small chamber ensemble, string

quartet, piano, percussion and contrabass. This work represents an

advanced step of abstraction to the previous ones; it faces the problem of

the concept of the time in music.

It is very common to read in musical aesthetics literata that time is the “stuff”

of music and eventually all composers, sooner or later, have to deliberate

about time in their own work. It was something I had to consider somewhere

in the studies, and, in fact, it’s what I did in Parametric formalizations studies. I didn’t see the time as a single parameter but the possibilities regarding its

relationship with movement. For me, it makes no sense to consider the

problem of time in isolation, without taking into consideration how it coexists

with the movement and speed. Talking about time and motion as an

integrated entity, inevitably leads to relativity. Relativity is something that

has always been present in my music. Parametric formalizations studies creates an open perception of musical

temporality through the musical formalization of the concept of relativity;

not in the Einsteinian or physical sense of the term but in the most primitive

sense that this term has.

This involves integrating the concept of time and movement like spectralism

has integrated the concept of pitch and timbre. As pitch and timbre are two

phenomena that cannot be studied separately, in the same way time and

motion must be considered as whole phenomena. The point is the perception of movement is relative to the listener, so in order

to achieve this I create a formal system. In it the position of certain musical

material, respects others, determines the values of the parameters of other

musical objects. The perception of temporality derived from this concept of

musical object movement, which is so ambiguous that can be perceived

completely different depending on the listener. The formal structure of the




work is created to search different perceptions of the movement. (For a more

detailed explanation read my analysis of the work).

The second study compared to the first allowed me to avoid the gestural

character of the determination flow ‐which has never convinced me, really‐,

in the third I managed to eliminate the fact that each fragment had a central

parameter. In it all parameters are equally central in every moment and the

relative position to each other is finally which establishes the determination

flows. This is achieved due to an integrative cognitive model by means of

which it’s possible to substitute the rotational determination of some

parameters to others; formalism that defines the relativity through the

position of some parameters regarding others. “The settling fact” and the

rotational structures are substituted by a relativistic‐positional formalization

of some parameters with regard to the other ones.

Evolutionary lines of the studies

We can appreciate a line of evolution in these works: a process of abstraction.

Each new work gets more and more abstract than the previous. It's like if

every work represented a higher layer of abstraction. For example, this is how

we would see them ‐in an abstract, of course‐ if we compare them to the

world of transportation; Parametric modulations studies would represent

any way of ground transportation and Parametric neutralizations studies would be the train.

Musically speaking, we could say that just as integral serialism represents a

higher level of abstraction versus dodecaphonism ‐in the sense that only one

parameter is serialized‐ in the same way each of these new studies represent

a higher level of abstraction. As a consequence of it I ended up talking about

the “the settling fact”, which can be seen in End game and in my early works.

“the settling fact” has evolved through the process of abstraction and

formalization of the positional space concept, and it is no longer necessary in

Parametric formalizations studies.




In my first two studies it was necessary to generate a principle order, that is

to say, to establish the principle of a certain prediction of sound events. This

principle was called “the settling fact”. Since every principle of order is to put

something in an order criteria. And establishing implies relativity, i.e.

something that involves two elements; the order criteria and the elements

to be ordered. Thanks to the formalism developed in Parametric

formalizations studies I could create cognitive parametric music without “the

settling fact”, because the position of some elements over others is what

determines the value of other parameters.







5. Parametric

formalizationsstudies

.

The work represents the synthesis of four problems. On one hand, the

necessity to formalize and systematize in a more accurate way than in

my previous two studies my systems in the use of parameters as sound

material. On the other hand, touching the issue of time as sound

material, trying to deepen the problem of relativity in listening and,

finally, I also wanted to replace the concept of settling fact so that it

would not be necessary to establish some determination flows

through a central parameter, not even in a rotative form. The result of the synthesis of these four problems has been the

creation of an abstract formal system of relativity in which a theory of

the relativity of the musical tempo has been formalized. In this way I

have found something that was not initially on the problem, but which

become much important than the problem itself. It is memory. Since

from the relationship between memory and the movement comes the

relativity of

the

time

concept . Thus, this work tries to build, from

certain parametric relations, as basic architectural material of its

structure, a solution to a strictly musical material problem or ‐at least‐

“sound material”, if you do not grant me the benefit of calling what I

do “music”.

Relativity is, to me, a very important concept. Against the pretensions

of an absolute knowledge, I have always claimed that all knowledge is

relative to something. By relativity, I do not mean the Einstein's




relativity, but a concept of preeinstenian relativity applicable to almost

all fields of knowledge.

The concept of relativity has been always present in my music, with

the idea that the listening is independent from the intentions of the

composer and relative to the person who listens, and even different listening experiences of the same work for the same person at

different times. There is no a universal musical language and all

listening are relative. My music has always been based on the idea of

enabling relative and multiple listenings, providing great freedom in

the listener. With a type of new signs, which are unreferenciated from

their usual framework, it facilitates a new sound intelligibility with the

consequent

change

and

possible

brain

plasticity.

The

old

idea

of

a

new

music for a new world, works better if it is based on relativity.

Therefore, what I wanted to achieve in this work is an approach to the

problem of relativity in the most explicit way of all.

Relativity always refers to the position, and position to the distance

and the distance to the movement. That is why talking about relativity,

with respect to the musical fact, is to speak about movement. The work

is primarily a reflection on the concept of movement and the most

effective way to do so is through the formalization of ideas about what

movement is in music.

This work deals about movement, as we shall see, in its relationship,

not with meter or speed, but with the problem of variation. Here we

consider motion as the difference between two given times, by

measuring this difference by the evolution of the material. But for such

material on the time evolution were perceptible is necessary the

control of the way in which memory allows the recognition of patterns

allowing the cognition of the variation.

Thus, this work seeks to the relativity of perception of tempo musical

based on the different ways in which memory is related to the

recognition of patterns and therefore, with the concept of variation. A

person who has a good memory will perceive the work in a very

differently way than a person who has short memory, but even a




person with lots of memory may have different listenings according to

its fatigue that could diminish its memory.

Thus, this work is the result of a cognitive parametric model that

integrates the movement of material and memory so that against this background the temporality is perceived. It is not sought in this work

the recognition of rhythm, time or meter, but a deep sense of time. It

is not about to perceive a pulse, meter or speed, but the sense of

temporality that appears, under the background of the relationship

between memory and movement. It is about the psychological

experience of the tempo which, moreover, will be relative to each

person.

So,

when

speaking

of

time

I

do

not

talk

about

physical

time,

but to the psychological quality of time experience. That is, the time

significance, the significance space of time.

All we have experienced a moment that is eternal, perhaps a very

special kiss; perhaps a situation of extreme danger, at which time

freezes and seems to flow slowly. Our attention is so intense over time

that it seems not to flow. The time is quite significant and therefore

the significance is very high. A second means a lot. This is the

psychological significance of the time. However, in other moments the

time passes very quickly and we are not aware of it; for example,

watching a film or focusing our attention in a sport activity the

significance of time is minimum and its significance space little or null.

I'm certainly not the first composer who has been thinking about these

matters. As we shall see, Feldman and Grisey have developed

profound reflections on these aspects. Feldman is the great composer

of time and memory. I would say that he is the first composer who has

integrated the memory as sound material in its language. Grisey is the

greatest composer of movement and perception.

As we saw earlier, Grisey has established that the perception of time is

inversely proportional to the perception of the material. This law




specifies that if the time is not perceived, the perception of the

material is higher. In relation to this work model I say, paraphrasing

Grisey, when memory recognizes a slow variation of the material grows the significance of time and when the variation of material is

recognized the

significance

of

the

tempo

decreases. Thus, the work is

based on cognitive rules that establish that depending on how a given

memory enables a certain type of pattern recognition, and therefore a

certain type of variation, induces certain experience of psychological

tempo. But the reverse is also possible, certain experience of time

allows a perception on the variations of the material or not.

For Feldman, there is a great relationship between the form of the

work

and

its

scale,

this

reflection

does

not

exist

in

my

work

but,

in

the

same way that the difference between scale and form is determined

by the length of a work in Feldman (what for him is the justification of

long works), for me, the experience of the tempo is determined by the

relationship between variation of material and memory.

"Up to one hour you think about form, but after an hour and a half about its scale."

Form is easy, it is just the division of things into parts, whereas scale is another

matter, you have to have control of the piece; It requires a heightened kind of

concentration. Before, my pieces were like objects; now they're like evolving

things"(Feldman cited by Friedman in the introduction page XXVI.)3

For me, Feldman is the composer of the twenty century whose

reflections and conceptions about tempo and time are more

innovative and influential. And he is the first to relate the material

variation with time and the importance of memory in these processes.

"What is variation?" One thing stays the same, other things change. "And the slow

rate of change in terms of the useful materials is equivalent to the slow rate of

change to the metric structure" (Feldman, Feldman in Middelburg, P.222).

3 Feldman, M. , Give my regards to eight street ‐collected writings of Morton Feldman. Edited

by

Friedman,

Zimmermanm

and

Monk.

Exact

change.

Cambridge

2000.




"So the function of memory was very, very important, and also the function of

memory in relation to musical forms was very, very, important." …. I began to

rethink memory, and it´s very apropos the violin concerto. "Because I finished

reading the book 4 at that time, I was very impressed with the book, and it was

the beginning of my long pieces" (Feldman, Feldman in Middelburg, P.474)

The refinement of Feldman about models that relate other musical

aspects over time becomes really incredible.

"There is a direct relationship between the meter and the instruments that are

playing." "Each image seems to have its own meter and these images come back

again and again" (Feldman. Feldman in Middelburg, P.406).

Thus, the work is based on a model of perceptual system that

integrates the cognitive rules from Grisey and Feldman.

So, I began by trying a philosophical deconstruction of the concept of

relativity in the more abstract way, without being inserted in any field

of specific knowledge, and therefore, much less in physics or in

Einstein's relativity. From here, I developed a formal model for

modelling any relativistic theory (Chapter 3 of the book). This model

aims to establish the formal conditions which must comply with a

theory, formalized through this model, to be considered as relativist.

Subsequently, I define relativity applied to the movement in music and

after I see if it meets the formal requirements. One of the ways in

which this idea has resulted, it was when I was in search of a music that did not have any central parameter. Relativize something is achieved

by stopping that something being the center, which is what I have been

doing for long time.

I thought about how to formalize a musical discourse that did not have

any center. If a single event could set a privileged center, avoiding a

4 Book, which Feldman referred, is French A. Yates, The art of Memory , London 1966.




center might imply at least two events. Each of them could be the

center of the other. So, this was what suggested me the idea of having

two different but simultaneous patterns in such a way that the speech

could be understood from one or the other relatively. In addition, as

we have seen earlier, the problem of movement is another major problem in relativity, so I decided that these patterns would go at

different speeds and it would be this difference in speed what would

determine the value of the parameters of the sound events.

The idea of relativity is represented in my previous works because the

determination flows between parameters are not given a priori. The

position of the listener regarding the work is what has just established

the

determination

flows.

Here

the

relativity

refers,

on

the

one

hand,

to

a problem of the theory of knowledge. All knowledge is relative

because we cannot find an absolute truth (this is why my music is

focused on nothingness, since it is not based on anything other than

the vacuum of the impossibility of a strong foundation) and, on the

other hand, the problem of moral relativity, which states that there are

no absolute truths, but that is the position of an individual in its

environment which determines its ideas about the social reality and its

ethical concepts. And how social events ‐which are never fixed5‐ and

their cognoscibility may vary over time as the determination flows

changes.

In this work I have taken a step of a giant with respect to the other

previous studies, in the sense that I have replaced the concept of a

settling fact, like what puts certain element as center, by a formal

system that allows the position of some elements against others and

its different speed, to produce the lack of centrality. The concept of

position plays a critical role in my work since relativity is only possible

in relation to the position that elements have with each other. In my

5 See my articles, manifest by relativity and relativity ‐ parametric formalization




first studies the backbone was to establish, through certain structures,

how a given set of parameters were placed as central by turns. This has

now been replaced by a formal system that allows me that the position

of some elements against other is which determines its attributes

(values of the parameters that define it). This formal system allows that the concept of settling fact is no longer necessary, nor the

principle of an order that puts a centrality a‐priori to then change it.

This step is possible because there are two ways of doing that no

central parameter existed. Having in mind that from a distance no one

is more central than others (my first two studies), one way is by using

a

rotary

strategy

making

that

in

a

rotatory

way

each

parameter

be

central for a period of time. In the same way that in a group of people

can be established that each time one person rules by turns not just

one. And the second way, a bit more sophisticated, through a

formalism that allows us that the position of one sound event relative

to other determined its attributes. And this is what I have achieved in

this work. Therefore, there may not be a central parameter, but a

balance between all of them. This would be equivalent to a direct

democracy where there is not a leader and decisions are made directly.

To accomplish so, it is enough that each event is part of a different

reference axis parametrically formalized.

Finally, I have found, in the Doppler Effect, the basic idea that would

guide this work. Imagine two objects in motion. And imagine that every

one of them produces a certain sound. The pitch that each one

perceives from the other one, depends whether they approach or

depart and from the difference in their speeds. The Doppler Effect

exemplifies the best possible relationship between relativity and

movement in a physical way. Relativity again not in the Einstein sense,

but in the sense that something ‐the pitch‐ is relative to the position

and movement of two objects, which make sound, and that neither

can be considered as central with respect to the other. To achieve this,




I had the idea that the work was formalized in two distinct sound

masses whose pitches are determined by their speed and on its

position regarding the other. The work is, in a certain way, a

continuous perpetuum mobile which, although it is broken several

times, is as if the two objects give turns along a circle in opposite directions at different speeds, sometimes approaching and others

moving away to others. Speeds change as well, in the same way that a

constant modulation goes back in a circle and returns to the original

tonality, to the same point. The two sound masses represent two

perpetuum mobile interaction, while none of them is established as a

central axis with respect to the other one. Each one of the two sound

masses

represents

one

of

these

imaginary

parametric

axes.

The

Pitches of both sound masses are determined by the position of each

other. This determination changes throughout the work and defines

the formal structure of the work by changing the way the variation in

the position of a mass with respect to the other one, determines the

values of the parameters of the sound objects. Instead of the existence

of a form defined by the variation or the organization of several

elements with certain differences.

The formal structure is the organization to the way that it changes the

manner in which the position of a mass with respect to another

determines the characteristics of the sound objects, which is a

synchronous interdetermination. In the odd sections the position of

the cycle of a pattern with respect to the other cycle determines their

parameters. In the even sections, the way in which the position of an

item determines others depending on its iteration, occurs inside of

each pattern and it is not synchronous, Alternatively, in each section

of the work, in the odd ones, time is fundamental in the way that one

of the sound masses associated with an axis determines the other one

associated with the other axis, since the determination of one over the

other is synchronous (through the phase ‐as we shall see‐). Meanwhile

in the evens, the time does not intervene and the interdetermination




between the axes is asynchronous. This is one of the many ways in

which time is used as material in this work playing a structural role that

is the formal determinant. This is not a work in which there are

alternating slow and fast tempos, but there is an alternation of

sections in which the determination of positions is synchronous (odd) (over time) or asynchronous (even). In fact, to avoid possible

alternating tempos I keep the same metronomic indication for all the

work and therefore it is very important that the director works as a

mechanical metronome.

The fourth and central section is an exception to this rule, as we will

see

later.

The

odd

sections,

in

addition,

involve

in

each

of

theirs

appearances a growing complexity in the way in which the position of

an item against the other ones determines the rest of the parameters.

The function of this growing complexity is that varying slightly the way

in which the position of an axis determines the other one, occur major

changes in the speed of introduction of material, without being

actually real. The experience of time is not derived from metronomical

speed but in this ever‐changing speed of introduction of material.

Memory will make possible a kind of recognition of regularities and will

determine whatever the listener focuses on, and thus, the

psychological experience of time. If patterns are recognized, it will be

significant, if not meaningless. The psychological experience of time is

in another different dimension from how the time is used as a material,

this is what temporal relativity achieves, which is not possible in works

in which the time experience and its structural use go hand in hand.

The work is a political critique of certain ways of understanding the

handling of knowledge in our political reality, mediated by the belief

that there is, or a central parameter (the economic, for example) or a

particular class whose interest is the central. (See my texts on political

parametric motion machinery) In fact, the base to support the belief

that a point of view about the political reality is the central one, allows




objectifying the rest of the entities (see my text The myth of confrontation and political ontology ) and generate tautological

processes that make theories that a certain element as central

function as a prophecy that fulfills itself, or that carries its own

compliance. The fact that a given element is settled as central is a form

of manipulation, and the deconstruction of what is the interest of a

class to put certain element as a central, always produces a release in

the form of unreification of the elements objectified by the centrality

and therefore a unalienation.

In summary we can consider the work as two‐voice polyphony, voices

in

the

sense

of

Boulez.

"A voice is considered as a constellation of events that are due to a number of

common criteria" (Boulez. Thinking the music today. P. 193).

Each one of these two voices moves at a different speed and is its

position regarding the other one what determines the values

parameters of the sound objects properties that are part of the voices.

Since any parameter determines to the other ones, there is no any

central parameter. Any parameter works as privileged center over

other ones. This scheme represents a definition of the relativity in

musical movement and it has been defined by a formal system (hence

the name of the work) that complies with the conditions settle in, the

predicative‐aggregative definition of relativistic formal systems (see

Chapter 3).

In this work the concept of parameter is used as musical material in

the same way that it is used in my other two earlier works. Parametric

scales, parametric modulations are present but in a more abstract way

since the formal structure of this work makes not necessary, as in the

other two works, the settling of the determination flows in a very

precise way. So, finally, unlike the other two works, the establishment




of determination flows is free to the listener from the first moment . The definition of the determination of the parameters around a parameter

that cannot be heard is what allows me this invention. And although

there are, as we shall see, techniques borrowed from previous works,

in this work the emphasis is in the cognitive pattern recognition

techniques to set parts in which (without a real objective change in the

sound material ) can be recognized patterns and others that do not,

being the listening relative for each person. The important thing in this

work is the cognitive tension developed between moments in which

patterns are recognized and therefore there is a comfort in listening

and moments where not. The cognitive tension is the searched in this

work.

Thus,

small

changes

in

the

material,

determined

by

the

way

in

which the two voices overlap produce real changes in the way they are

perceived. That is to say, and this is for me the fundamental, a constant

and linear change of the material produces exponential cognitive

changes in listening. There is a speed in the form in which the material

is developed, and a sense of the speed that causes changes in the

material.

It is very important for me the problem of the speed when introducing

a new musical material and the problem of the emergence of new

sound material and its relationship to memory. Feldman was a master

at this. The way in which got identical variations to produce sensations

of different speed of introduction of new material, and how changed

the speed of variations depending on the material. That makes

Feldman an exceptionally unique composer. In my opinion, that

multiple relations between material and time, experienced in a

different way in each of his works, made him one of the two most

essential composers from the second half of the 20th century. That is

why I investigate in this work the relationship between speed of

introduction of new material, musical movement and the perception

of tempo as three elements fused intimately. In the same way that

spectral music unifies the spectrum and pitch, an investigation about

the integration of these components (integrational models).




Thus, the work is, basically, a reflection on time as a basic sound

material not reducible to the rhythm, and its inseparable consideration

with the cognition of the movement. The relationship between

movement and memory is the core of this work. But not just any time but a time determined by the own sense that differentiates the

physical time from musical time. As we will see later, this work employs

cognitive recognition patterns techniques to create or break various

forms of time perception, the memory will be responsible for the

relationship between the recognition of patterns and the way in which

the music tempo is perceived.

All composers, sooner or later have to face the problem of time in

music, I would even say that one is not a composer until one does not

create his own idea about the sound time. In my case it could not be

otherwise, that it was associated with the problem of temporal

relativity. But it is necessary to have same experience prior to meeting

this challenge. This has cost me, nothing more or nothing less than five

years to do a work about these reflections. The process has not been

easy, whereby same ideas led me to others and with every idea new

problems arose that paralyzed me. I solved them as I could, and not

always in an adequate way which I would have liked more but, because

some solutions have left me uneasy, I already have a new way to try

another twist.

The cognitive dissonance is based on these phenomena. To the extent

that the sound stream is encoded through a number of regularities and

the necessary introduction of a certain variety within these regularities

and implies, in turn, a number of regularities in the introduction of the

variety. Cognitive dissonance occurs, among other possibilities, when

there are events that cannot be interpreted as produced by a variation

of the regularity or consistency. This is why in the music of Steve Reich

few cognitive dissonances occur, since the pattern of difference in

regularities is very stable. However, in Nono we have the opposite




case. The great variation in the speed of materials introduction gave

to his work an impressive cognitive density.

The work is dedicated to Lua because it was while doing it when she left. Many times, when she was already not there, I wondered why I

devoted so much time to this score, time that I regret not to have spent

with her. The paradoxes of destiny wanted that making a work about

time and memory, I ended up willing the time just only for her

memory.







6.

Cognitive Dissonance

The expansion of the musical material has been exhausted.

Adorno,

The aging of new music (1954)

Cognitive dissonance was composed from early 2012 to April 2013. It

is the first electronic work that can be considered fully parametric.

The work is dedicated to Gonzalo Alonso Hernández killed in Brazil

for his environment defense.

This work was premiered in December 2014 in THE II INTERNATIONAL

CONFERENCE SOUND AND AUDIOVISUAL SPACES: SENSORIAL

EXPERIMENTATION AND ACTIVE LISTENING. JIEM 2014 – 20th

COMPUTER AND ELECTRONIC MUSIC, as it was awarded in the open

call for its works.

Introduction

Cognitive dissonance is a term created by the cognitive psychologist

Leon Festinger in his work A theory of cognitive dissonance in 1957 [1].

Its main idea is that in a context of conflict, tensions are created which

relaxation requires some sort of cognitive effort involving certain type

of changes.




In cognitive parametric music, cognitive dissonance is interpreted in a

slightly different way. The idea is to replace the concept of dissonance

connected to a property of a musical material, which is defined on a

parameter (usually the pitches) that can be considered objective (there

is a well‐defined metric to measure it), by a dissonance not associated

with material properties, but the context in which those materials

acquire their meaning. Cognitive dissonance occurs when the listener

loses the intelligibility of the sound flow. This conflict generates a

tension that requires re‐thinking the logic of the work at every

moment, producing an additional cognitive effort in listening.

Cognitive dissonance depends on pattern recognition, being more

relative

than

the

dissonance

associated

to

materials

because

such

recognition is different for each person. The dissonance depending on

the material properties generates tension by the dissonances and its

resolution, the cognitive instead through moments in which the same

regularities are recognized but not in others. The resolution of a

cognitive dissonance occurs when there is a new intelligibility or sense

about what is happening.

This work is investigating about how cognitive dissonance research

began in the trilogy of the studies. The idea of the work is based on the

superposition of several patterns that move at different speeds,

resulting that it is possible to recognize certain regularities at moments

but no always. The recognition of these regularities will depend on the

relationship between short‐term memory and long‐term one. The

alternation between moments where the information provided by the

memory allows patterns recognition at times generates cognitive

tension. Cognitive dissonance is the tension that occurs, in the listener

of the work, when the expectations about the speech sound are not

accomplished. Cognitive dissonance moves into an ambiguous ground

between order and disorder, since there is no cognitive dissonance in

a total disorder.




If we compare both with the clip play. The dissonance of the material

consists of throwing the ball as far as possible, while the cognitive

dissonance consists of kicking the ball right on the line, nor further

away nor closer. One uses the force, the other precision.

Cognitive dissonance parts from the idea that dissonance is relative

and it depends on the context. The dissonance associated with a given

parameter is the way in which it has traditionally generated the

concept of musical tension. In tonal music dissonance derived from the

rudeness of (horizontal or vertical) overlap in certain intervals (the

explanation of Helmholtz [2] is still the most common used, while

recent

researches

improve

it,

at

least

in

a

relative

form,

in

several

respects [8]).

Helmholtz model sets that the dissonance between a pair of complex

tones is produced by the interference between its sinusoidal

components. Such interference creates a few beats that produce a

certain roughness. Helmholtz associated this roughness with

dissonance. Today the concept of dissonance is better explained by the

critical band (to see it in a more detail, I recommend: Plomp, Levelt

[8]), (for a good explanation of the phenomenon of the critical band

read [9]), which although it differs from Helmholtz model, it can be

considered as an improvement. Parametric music is always and

exclusively based on the critical band model.

Adorno showed us about Berg´s work, (for example the violin

concerto) that dissonance is somehow relative and in a non‐tonal

environment a series of tonal chords may constitute a dissonance.

Adorno formulated a concept of dissonance that does not depend on

the material, but on the context. Integral serialism and dodecaphony

expanded the concept of dissonance associated with material, with

tensions associated with other parameters (such as noise associated

with the timber or extreme dynamics associated with the intensity). It




also happens in a simple way, generating the concept of cognitive

dissonance, although it was not explicitly defined (as quoted from Berg

[3]). Enlargement of the dissonance associated with materials led to its

end, generating a debate on the topic of what was called the depletion

of the dialectic of material (see Adorno the aging

of

new

music

[4] and

Metzger response [5] the aging of the aging of new music). Serialism

extended the concept of tension to other parameters, not only to the

pitches, certain dynamic, timbral and rhythmic structures generated a

tension derived from the properties of the material, but not directly

linked to pitches. Here, the introduction of the noise as generator

element of tension. Thus, in certain serial works the result of the

tension

of

the

work

derives

from

the

superposition

of

several

types

of

tensioning associated with different material properties. There is a

tensioning of the pitches, another rhythmic, etc. Serialism has

expanded the type of tension. Little by little, it changed from a

tensioning process depending only on a property of materials, to

tension process dependent on several different materials, contextual

relative factors, and processes based on several material properties.

For me, one of the precursor composers of cognitive dissonance is Luigi

Nono. Especially in his fragmente String Quartet which generates

an incredible tension, that cannot be explained by the dissonance of

the material used. I.e. The objective quality of material dissonance is

lower than the real tension. However, we can perform the opposite

operation and check that other works that use very high doses of

objectively qualified dissonant materials do not generate even

remotely similar tension levels. Here, the problem of the exhaustion of

the dialectic of the material. A new objectively more dissonant

material does not warrant a higher tension. There are two metrics for

cognitive tension, one already has been seen, the correlation (or lack

of correlation) between tension and material objective qualities.

Modern neuroscience, gives the other one since cognitive dissonance

causes the intensive use of the neural circuits that manage errors. (See




reference The cognitive neuroscience of music Perezt, Zatorre [6]). While the traditional tension shoots another type of neuronal circuitry.

But, in any case, the sense of global tension is always a mixture of both,

consciousness cannot differentiate the tensioning. For example, if you

have a headache for two reasons at the same time, you will only feel a headache, perhaps more intense, but you will hardly know what pain

intensity is caused by what, not even whether it hurts for two different

reasons.

Parametric music picks up this second concept of dissonance and

releases the dissonance with respect to its dependence on the material

properties.

In my works I have used the cognitive dissonance concept in three

different ways.

At End game I got several overlapping simultaneously processes of

different forms of dissonancing a material according to its parametric

properties, each one in a different way generating a type of cognitive

context which created a focus on one of these processes. I got the

resolutions fall in moments of greater dissonance from the material

through the use of cognitive models. This would be the embryo of the

cognitive parametric music (see [10]).

In the first two studies I used cognitive dissonances to structure formal

sections using parametric materials, dissonances are integrated in the

concept of parametric cadences, which are nothing more than

strategies to provide, to the works based on parametric materials, the

possibilities to resolve using cadential structures not depending on the

material (see [11]).

In Cognitive dissonance and Parametric formalization studies, cognitive dissonances are no longer so aimed to create cadential




resolution of structural tensions moments, but, through integrational

cognitive models I aim the association of dissonance sensation with

sound pattern recognition tasks, concerning the relationship

between long and short‐term memories. (See [11]).

The difference between a cognitive dissonance and the traditional one

is very thin, in fact, it can be said that the dissonance associated to

material with the pitches (defined by Helmholtz as classical dissonance

[2]) is a very simple example of cognitive dissonance that uses the

cognitive model of Helmholtz [2].

Even more, from traditional classification, dissonant intervals weight

has a certain relative character. A tritone will be consonant in a music

in which there are only seventh, second and tritones, but dissonant in

a context of thirds and fifths.

By contrast, we can better understand the concept through the

comparison of these two videos. On a same synthesis engine, shown

in the min 3:30 (very similar to the one shown below), the synthesis

engine of cognitive dissonance is based on the same as this patch.

However, works around the concept of objective dissonance

associated with material (2:17 min) could show a moment of strong

dissonant tension generated by a controlled distortion. Feedback

with biquad filters inside the object p live that manages the entire live

electronics. The Gaussian, which can be seen throughout the video ‐

min 4:22 ‐, is a stochastic engine, based on

Gaussian distribution curves, something widely used in contemporary

music, whose pioneer is Xenakis [7]. This video shows the concept of

objective dissonance of the material.




Explanation of the work

This work tries to inquire about the replacement of the concept of

dissonance associated to material with the concept of dissonance

associated

to

the

cognitive

tasks

derived

from

the

listening.

The

advantage of the cognitive dissonance is that the tension of the work

is not based on the material objective properties, but in the manner in

which the material is processed. Thus, we find a way of saving the

possible depletion of the dialectic of materials. But in order to the

tension not be dependent on material properties associated with a

parameter, it is necessary that any sound parameter be central in the

sonorous discourse. To avoid this centrality the composer has

developed a number of compositional techniques that make possible

that any parameter works as central. For this purpose he has created

a series of algorithms in which the sound objects are treated as datum

axes. The work uses multiple simultaneous datum axes, none of them

determining to others, nor working as central. For more details consult

the composer´s book “Toward an aesthetic of Cognitive Parametric music” in which he speaks about the cognitive parametric music as the

set of compositional techniques that allows a music without a

parametric center, using the very concept of parameter as sound

material.

The first works that explore the cognitive dissonance are The studies in

which the dissonance associated to material properties, and therefore

to a particular parameter, is no longer possible.

The work is a superposition of several reference axes in which the

parameters of the sound objects are determined by their

relative position to the other ones ; in such a way that any datum axis

cannot be considered as central. Each reference axis works as a pattern

repeated at a different speed. The position of each pattern with

respect to each other is measured by the phase. We have a very




deterministic system, with cross determinations, for example, the

timbre of a datum axis is determined by the pitch of another axis and

the pitches of the events of this axe are determined by their position

with respect to a third axis.

In each part of the work, there is a different number of reference axes,

as well as different crossed interdeterminations. These techniques

have been used for the first time in Parametric formalization studies, although I have only used two axes in this work, up to ten axes in

Cognitive dissonance have been used in multilayered juxtapositions

and crossing instead. In addition, certain characteristic parameters of

electronics,

such

as

the

cut‐

off

frequency

of

the

filters

or

the

envelopes

shape, have been applied. The complexity of such formalization has

been only possible thanks to its implementing on “Max / Msp”.

However, because the synthesis engine based on phase vocoding,

which has been designed entirely by the composer himself, is so heavy

that it could only handle an axis at the same time, the generation of

the work was divided into two distinct phases. The generation of a

series of patches of Max with different axes and different crossed

indeterminations produced midi files (a form of saving events of

Datum axes). Events were converted into audio (interpretation of the

score, seen from an ancient perspective) in another patch with the

engine of synthesis, which reproduced only one axis at a time. Finally,

I had to do an enormous job of post‐production work with Pro Tools to

mix all the individual sound files.

The algorithms used to generate the midi files (the writing of the score

in a usual creation) are very deterministic. They rarely use random

variables. The work is intended to operate as a live electronics but the

high computing requirement avoids its interpretation in real‐time.




As a result, not only the generation of the score but also its

interpretation has been made with” Max / Msp “. Only the post‐

production has been carried out with Pro Tools.

For example, here we see a note generation patch that represents a layer containing 10 simultaneous axes of reference.

Score of the work

Each one of the ten sliders allows settling the speed of

pattern repetition (they can be modified at runtime execution of the

patch). These sliders feed the objects generafase (these objects have

been programmed by the composer himself, they are not available in

max) that generates a phase between two different speeds. This phase

is passed to the object devuelvexnotas that generates a series of midi




events associated to a midi channel. This object is the only one that

includes random variables for the voices conduction, from a given base

note. Finally, these midi events are recorded as midi data, in the

standard max object rec, and dumped to standard midi files which,

subsequently, will be converted into audio using the synthesis engine designed in Msp for this work.

Each fragment of the work uses a different patch, similar to this one

but changing the reference axes that interact to generate the phase,

their number and the way the phase is converted to midi events.

Here we have another more complex patch, with a greater level of

encapsulation where the wires that join the damidi18t objects

between them, represent the cross parametric interdeterminations

between the reference axes. The crossed interdetermination between

the axes is no longer matched by groups of 2 in this patch but by groups




of 4 in a much more complex way. That is only possible with a higher

level of abstraction in the encapsulation of objects. As I have

progressed in the work the patches became more and more complex.

This, for example, is used in the final part of the work. There are

approximately 20 patches like this, each one of them with their own

idiosyncrasies.

Finally, midi files are reproduced in this patch where they were

converted into audio files through several objects representing the

synthesis engine and introduced alternatively. Each reference axe

from the same stratum ‐or layer‐was usually reproduced with a slightly

different

synthesis

engine.

Each

axis

is

represented

by

a

midi

channel.




The object phasevocodersamplerstereol~ is used in this case, but it

changes for each midi channel. In all the work there are only 5 different

types. Each one of them is equivalent to the concept of traditional

instrument. If you get the feeling that there are more than five timbres

it is only because parametric music induces you to believe so. This

patch allowed me to shoot notes events during the development of

the synthesis engine, hence the aspect it has. Those who have worked

with Max will understand me. It may not be very elegant but it is not a

patch designed to be shared. This patch allowed me to change the

tuning with just one click.




In this example, we can see the skeleton of the synthesis engine, which

can be clearly seen as a classic 8‐voice synthesizer. The magic of each

of the voices resides in the fftvoicebus2estereo~ objects. In the picture

above, on the right, in the buffer, you can see how an audio file is

loaded to be analyzed by fft real‐time in stereo, and so the cost of high

computational. This means that if there were four active voices, the

file would be scanned 8 times simultaneously, meanwhile the pointer

to read the files is in a slight different position for each one, the reason

why computing weight was very high whereas timbre nuances earned

exponentially. Hence there are those immediate timbral changes

within the same event and the stereo image.




And here is the final mix screen of Pro Tools.




Each object represents the mixdown of the mix of all the axes of

reference of a layer and, at times, multiple layers together in premixes.

Therefore, it is not possible to make analytical conclusions based on

this graph. For example, the second file of the 9‐10 tracks is a mixdown

of 8 layers, each one containing between 5 and 12 reference axes.




References

[1] Festinger. Theory of Cognitive Dissonance (1957).

[2] Helmholtz,

H.L.F.. On the

Sensations

of

Tone

as

a Psychological

basis

for

the Theory of Music. New York: Dover. (1877)

[3] Adorno, Alban Berg. The master of the tiny transition.

[4] Adorno, The aging of new music. (1954).

[5] Metzger. The aging of the aging of new music.

[6] Peretz, Zatorre R. J.. The Cognitive Neuroscience of Music, Oxford, (2003).

[7] Xenakis, Iannis, Formalized Music. Pendragon Press. New York. (1992).

[8] Plomp, r., & Levelt, w. j. M. Tonal consonance and critical bandwitdh. Journal of the Acoustical Society of America, 1965, 38, 548‐560.

[9] Dowling and Harwood, Music cognition. Academic Press. Orlando Florida.

ISBN 0‐12‐221430‐7. (1986)

[10] Busevin, End of game analysis (2000). Unpublished.

[11] Busevin, Towards an aesthetic of parametric music. ISBN‐10 84‐615‐

9191‐7. (2011)

Other

references

Tenney, J. A History of ‘Consonance and Dissonance‘. New York: Excelsior

Music Publishing. (1988)

Schönberg, Arnold, Theory of harmony. University of California Press.

Berkeley Los Angeles. Translated by Roy E. Carter. (translated from 1922

third edition).




7. Three Chants

for Computer Three Chants for Computer was selected and premiered in the Call for

Works of the SID 2015 Conference (Sound, Images and Data) that took

place at New York University Steinhardt in July 2015.ço

This work experiments with one of the most advanced materials I have

created under the concept of Cognitive‐Parametric music. Parametric

morphing, based on the parametric interdefinitions. This work was

finished in March 2014.

The parametric interdefinitions are based on the idea that a parameter

can be interdefined by another. An example from everyday life is the

interdefinition of the distances and the time it takes us to travel them.

This idea is collected in the parametric music in a special way through

multiple materials that depend on the parametric interdefinitions.

The most important parametric material derived from the parametric

interdefinition is parametric morphing (second chant 3:20) in which

time is interdefined into timber using a certain threshold of perception

for parametric interdefinitions. The way in which parameters are

perceived depends on others. So for example, a pulse sequence that increases its frequency begins to be perceived as a timbre from a

certain speed threshold.

An example of this is the second chant (3:20), based on a model of

granular synthesis with 5 FoF (implemented in Csound (Function d´

Onde Formantique)). We start from a very small grain, representing a




pulse that is repeated at a very low‐frequency (0.5 Hz) which is

gradually accelerated. It seems that time is accelerated until it

becomes even faster. From 16 ‐20 Hertz (depending on each person)

starts crossing the threshold from which it is perceived as a note and

thereafter, rather than perceiving it as a pulse that accelerates, it is perceived as a gliding with a definite timbre. The object passes from

being recognized as a temporary object to be perceived as a timbral

object by altering the frequency only. I.e. the time is interdefined with

the timbre through the frequency. The effect of passing from an object

perceived from a parameter to an object being perceived as defined

by another parameter, by a system controlled, by a third parameter ‐

which

is

the

only

one

that

changes‐

is

called

parametric

morphing.

This

is the first work in the history of music in which this technique is

performed.

We can see here above an example. It is the beginning of the second

chant 3:20. It starts with a bass note that you will hear as a pulse. When

performing an upward glissando we get a moment of transition

morphing in which little by little pulse (time) becomes voice (timbre).

When, later on, performing the inverse glissando downward we will

get back to the original pulse.




8. Homo homini lupus The main issue of this work is a sounding reflection about how human

beings build its own concept as specie and how this determines our

limits.

One of the main topics about how humankind thinks itself is human

nature. This topic is as old as humanity invented language and we can

trace it back to Plauto who two thousand years ago, in his work

Asinaria, stated that “ Homo Homini lupus “, which is used as the title

of the work. Later on Hobbes popularized this assertion as a definition

of the selfishness of human nature.

The main idea of the work is the use of the limits of voice recognition

as a reflection of the limits of humankind thinking. What makes

possible to recognize us as humans?. Which one is the limit that makes

possible to recognize the voice as a timbre?.

This metaphor is made sound trough three different strategies. One,

by experimenting with the limits of the voice recognition as a

metaphor of how our thinking as specie determines our limits.. Two,

by experimenting between the individuality of the sound and its

integration into the sound fluxes as a metaphor of the polarity

between individuality and collectivity as one of the main topic of

human nature. And three, by experimenting about the velocity of

change in the parameters affects the voice recognition.

This work experiments with the relations between the sound

movement and the voice recognition. A literal imitation of the voice it

is not intended but an ambiguous one. There is an ambiguous

continuity between the voice timbre and timbres quite related to voice

changing by morphing. To provide this I have used a voice synthesis

system based in format synthesis (FOF algorithm). There is only one

Csound patch which is controlled by 30 parameters that change slow




or fast, or become fixed. Everything is controlled by several algorithms

which input is the difference. I never use a parameter combination

quite near to human voice, always there is a parameter which is

different from which should be from the human voice recognition

providing overtones and distortions over the voice timbre. It is not pretended to give a closed vision of human nature but to provide a

sound flow that facilitates to each listener its own human nature

concept.

Same times the voice is clearly reckonable sometimes not, and this is

different for each person but the patch is always the same..

Sometimes the voices work together in such a way that they are heard

just

as

a

single

voice

from

which

several

times

individual

voices

can

arouse. The tension between individuals and the collective is one of

the mayor reflections about humanity. Very intensive use of

microintervals are used using the critical band phenomena to generate

the relation between individual voices and its integrations as one. The

use of the movement as a main factor to recognize the voice is

intended as an reflection about how the history determines the form

in which we see ourselves as the mirror of the others.

The work has been produced using a parametric algorithm (

completely designed and programed by the composer) That is a

superposition of several reference axes in which the parameters of

the sound objects are determined by their relative position to other

ones (in such a way that any datum axis can`t be considered as central).

Each reference axis works as a pattern repeated at a different speed.

The position of each pattern with respect to each other is measured by

the phase. We have a very deterministic system, with cross

determinations, for example, the timbre of a datum axis is determined

by the pitch of another axis and the pitches of the events of this axe

are determined by their position with respect to a third axis. The only

parameter controlled by the composer is the duration time of the

pattern.




In this screen you can see the control panel of one of the patches. In

red you can see the patterns duration and the midi channel, in green

the object that represents the patterns and that are treated as datum

axes and re blue circles represents he phase matrix in which you can

se the relative position of each patter regarding the last one that begun

its cycle.

Technical Explanation




The work has been made in several phases. The first one consisted in

programing the Csound and Max / Msp patches. The Max patches

generate the midi files that will be used to feed Csound. The patches

used in this work are based in a parametric algorithm that avoids any

centrality In such a way that any properties of the sound is more

important than any other one. The used algorithm uses as its input the

different velocities of the patterns used to generate the midi

messages. This algorithm have been published in the paper Cognitive

models and relativity formalizations in parametric music and its

algorithm treatment in Max / Msp. In the second phase the midi files

are converted into sound by Csound using a patch that uses the FOF

algorithm:

The core of the Csound patch is: ai1 fof kfamp1, kfund+kincremento, kform1+kincremento2, koct1, kband1, gkris, gkdur,

gkdec, iolaps, ifna, ifnb, itotdur ;

The patch uses for each individual voice more than 30 different

parameters, each one controlled by control change midi messages.

Initially it was programed to run in real time inside Max but my

computer could not run more than 32 FOF object at the same time so

I decided to make it in non real time as in the old times. In each fragment I used a different Max patch with slightly differences

in the form in which the parameters were handled.

Finally, all the fragments were mixed in Pro Tools 10.







9. Characterization of

cognitive‐parametricmusic

Characterize does not mean to define. As I have already mentioned at the

beginning, I do not pretend to normalize but to explain, seeking

understanding, against the establishment of standards or rules. Now, I'm

going to expose the features that characterize cognitive‐cognitive parametric

music, avoiding a standard definition. With all of this I just pretend to open

the field up to the future creations, collecting what they empirically are.

The fundamental characteristics of Cognitive‐cognitive parametric music are:

1. Using the parameter concept as sound material.

2. Avoid the establishment of any element as central in the work.

3. Release of listening through the ambiguity, and the multiple meaning of

materials through strategies that allow the relativity of listening.

4. Replacement of the concept of dissonance associated with material

properties by the dissonance associated with cognitive processes (cognitive

dissonance). And the replacement of the sound flow stress, based on stress‐

relax processes associated to a parameter ‐either the density or the pitches‐

by a cognitive process derived from cognitive tensions caused by the

abstraction of materials. Abstraction obtained from the absence of a

parametric center.

5. Establishment of multivalent principle of sound flow order through settling

fact, using cognitive models.

6. Formal thought derived from a mobile system of interrelation and

interdefinition between the considered parameters.




7. Establishment of forms of interdefinition of parameters either through

integrational cognitive models, gestural models, psychoacoustic models, or

correlation of signification spaces strategies.

8. Definition of the form as a structure that defines a relationship of the

parameters in continuous evolution. The way in which the parameters

interact must be mobile throughout the work.

9. The concept of traditional material is reduced to a minimum. In its place

the parameters, as sound material, understood as a model that takes the

center stage and integrates all the parameters through a formally structured

changing relationship (first studies) or formalized structurally (third study).

10. Each parametric composition is defined or characterized by a significance

space, which assigns to each difference of a sound property, a changing

meaning throughout the work according to the formal scheme or time.

The fundamental techniques of Cognitive‐cognitive parametric music are:

1. ‐Parametric neutralization.

2. ‐Parametric modulation.

3. ‐ Parametric formalization involving a parametric interdefinition (not all

formalization are worth).

4. ‐ Parametric interdefinition through the correlation of the signification

space.

5. ‐ Parametric interdefinition through cognitive‐perceptive or

electroacustical models.

6. ‐Establishment of settling facts through pattern recognition strategies and

artificial intelligence.

7. ‐Establishment of settling facts through cognitive perceptual, gestural or

psychoacoustic strategies.

8. ‐ Integrational cognitive models that modelize the way in which the

perception of a few parameters influences the perception of others.

9. ‐ Establishments of Rotary determination flows through gestural

strategies, and/or cognitive models, and/or electro‐acoustic and/or

psychoacoustic models.

10. ‐ Meaningless of objects through the functional multivaluing of the

multiple ways in which a sound object can be significant.

11. ‐Establishment of determination flows through the cognitive models.




Parametric

neutralizations

studies

Parametric

modulations

studies

Parametric

formalizations

studies

Formal definition of

parametric

neutralization.

Parametric neutralization

applied simultaneously to

all parameters.

Improved and extensive

use of parametric

modulations.

Use of a formalization of

the concept of the

relativity of temporality

perception.

Gestural strategies to

establish cognition of

determination flows.

Use of the parametric

interdefinition through

the significance space,

by induction.

Interdefinition of the

time through an

integrational cognitive

model between

movement and memory.

(Integration of Grisey

and Feldman´s cognitive

rules)

Use

of

basic

parametric

modulations (entropic). Meaningless

of

objects

as multivaluing. Modelling

of

the

idea

of

the Doppler effect.

Use of gestural cognitive

models. Use of gestural

settling facts.

Settling facts defined on

pattern recognition‐

based cognitive models.

Use of cognitive models

that relate the current

memory window with

the perception of

temporality.

Parametric

neutralizations.

Entropic parametric

modulation.

Parametric themes.

Parametric scales.

Parametric delays.

Parametric melodies

Parametric inversions.

All of the previous one

plus

Parametric modulation

by parametric

interdefinition.

Parametric scales.

Parametric tonalities.

Parametric serialism.

Parametric

transpositions.

All used in two previous

studies.







10. Modelization of a

cognitive parametricmusical work

A cognitive parametric musical work consists of four main components, each

one is defined as a set.

Parametric structure is that which defines the strategy by which any

parameter is central.

A set of cognitive models is that which defines the form by which the

listening cognitive system will perceive the work and how cognitive tensions

are produced.

Furthermore, the integrational ones specify the form by which one

parameter influences the perception of another one.

A set of parametric materials is that which defines the parametric materials

that will be used.

A set of parameters is that which defines the kind of parameters that will be

used or modelized in the work. Each parametric work has its own musical

concept that requires an optimal parameterization of the musical objects,

that is, the best suites for the work concept.




Work Cognitive

dissonance

Parametric

formalizations

studies

Parametric

modulations

studies

Parametric

structure

Formalization of the

relativity and

temporality of

perception.

Formalization of the

relativity and

temporality of

perception.

Rotative system of

parametric

modulations.

Cognitive

models

Several models to

generate cognitive

dissonance based on

integrational models.

Perceived pace

model of James.

Integrational model

of movement and

memory. Perceived

pace model of

James.

Modelization of the

Doppler Effect.

Differential

asymmetries in the

distribution curves of

probabilities in the set

of considered

parameters.

Use of parametric

interdefinition

through the spatial

signification by

induction.

Parametric

materials

Parametric

formalization

Parametric

formalization

Parametric

modulations

Parametric tonality

Parametric serialism

Parametric scales

Parametric cadences

Parameters

set

{Pitch, beginning of

the note, end of the

note, timbre,

dynamic, envelope,

cut‐filter stereo

position}

{Pitch, beginning of

the note, end of the

note, timbre,

dynamic}

{Pitch, duration,

timbre, dynamic}










11. Glossary

Settling fact. At an abstract level, a settling fact is an event that puts himself

or any other thing else as central. A settling fact is what puts a principle of

order on a number of elements. The settling fact can be either formal or

informal. Formal is when the order principle is explicit and normative. For

example, establishing the alphabetical order of all the words in a dictionary

is a formal settling fact. It is informally, obviously, when some objects are

sorted by not specified criteria.

In music, a settling fact is a kind of material ordered in an implied manner

which induces that, from this material, listening orders the rest of the sound

objects in the same way.

In music it can be made not consciously following the most obvious cognitive

rules (those that give rise to the most primitive music). I.e. using an implicit

order of elements, which are best suited to cognitive strategies of pattern

recognition that occurs in a “natural” way. It takes place in a natural way

because, by default, the human being prefers what it is better recognized,

even if they do not know why it is so. In a context of "naturalness" it does not

make sense to talk about settling fact, since it is taken for granted. The

meaning of this term and its usefulness comes when we want to establish

principles of order opposed to what best fits to pattern recognition or that

"naturalness". For example, if the musical moments of rest fall in strong

dissonances. To get this several inconsistencies between different fields of

pattern recognition are created, as in End game. In this way, it does make

sense

to

talk

about

settling

facts,

to

define

a

more

ambiguous

or

difficult

order to process.

I am not the inventor of the settling fact, Schönberg already knew it, for

example, he sat in his harmony the following cognitive rule (speaking about

the tonal chords link)

"(…) thus, repetition will generally be avoided, except our aim which is to give to any chord

an extraordinary significance. At present we can have this aim with one chord only, with the




Iast degree, the one that gives the key. By repetition we will lend this chord prominence in

our little phrases and thereby express the key, event fat present not very convincingly. The

most practical arrangement for this repetition is simply to put this chord first and last;

because the first and last impressions leave the deepest imprint .” (Schönberg, Theory of harmony, Page 42)

Here we see (italics are mine to emphasize the cognitive law), how the master

of masters establishes a musical rule based on a cognitive model.

You can object that it relies on an intuitive knowledge that when Schönberg

wrote it, it did not exist, which is that, as we know today, the basis of a

neuronal founded cognitive science. But, if something has confirmed

cognitive science it is that almost all the artists’ intuitions were based on

cognitive laws. As for example all the principles of visual recognition today

accepted

and

anticipated

by

impressionism

and

Van

Gogh

about

how

the

brain can reconstruct information from an apparently imperfect

representation (pointillism). Only when they have been well established, we

can use same rules in a different way as they were created, and there is

where comes the concept of settling fact, in the sense of relying on the

foundations of cognitive science, to generate structures deliberately

incompressible, to generate ambiguous inductions, getting cognitive

dissonances.

So, a settling fact, in music, can be based on the intuitions present in

traditional music or on the cognitive science that allows us to decode the

order of musical objects and relations between its parameters in completely

different ways. At the same time, going against cognitive laws, we can create

cognitive dissonances replacing the usual schemes of stress relaxation by

systems based on moments in which all sound objects are recognizable and

moments in which cognitive dissonances occur. I think that the master of the

cognitive dissonance is Luigi Nono, who is, in some ways, the creator of

Cognitive‐cognitive parametric music since the incredible tension that produce his works is based on cognitive dissonance (at least, this is my

interpretation). He definitely was going ahead, even, of his own knowledge.

But, for me, what demonstrates the mastery of Nono is that his intuition (I

call it intelligence and know‐how. We, the composers working after Nono,

have to settle our creative lack with knowledge, concepts, and strategies

that, even being quite refined, are going behind him. I was trying to unravel

the secrets of the fragment e when I found several fragments that gave me




the key to the cognitive‐cognitive parametric music. One of them was to see

how his music clearly works around the concept of cognitive dissonance,

although ‐of course‐ he never thought about it in these terms.

Settling not only means “placing”, it also means above all “position”, since

all knowledge is relative to the position that one has with respect to what is

known (see Sartre, being

and

nothingness, all knowledge is tetic and

positional). Settling fact is to put a position in stricto sensu. After setting the

position, a principle of order is determined. So, my music parts from no‐

where to the extent that, nothing is anything a priori, being the positions

what generates the loads of sense. As, according to Sartre, ontological loads

derive from an absence and lack of being, therefore, in my music cognitive

intelligibility (loads of sense in the musical context) derive from the listening

position front what is heard setting through the settling fact.

The Settling fact is based on the idea that listening is intentional and

positional, and that both its intention as its position can be conditioned

musically.

Listening Conditioning. We say that a listener is conditioned when he expects

a particular object on the basis of which has just appeared. In tonal music, for

example, the listener is conditioned to expect after a great dissonance a

resolution or to interpret a series of structures of succession of chords as cadences. Behind each listening conditioning there is a cognitive rule. But

precisely, this foundation allows us to make an abstraction of this procedure

and apply it in a more abstract and systematic manner to other parameters.

Stravinsky was able to do this brilliantly generating a sound flow where the

rhythmic had more importance in the sound discourse than pitches. Thus,

through frozen and de‐linked from its function and significance tonal

harmonic structures (once neutralized) were able to create a conditioning of

the rhythmic‐based listening (here if it is merely rhythmic and not in the

perception of time). Stravinsky managed to displace the pitches by the

rhythmic as the settling parameter of the tensions and resolutions of the

music stream. This process of abstraction based on the idea that a work is a

going and coming of tensions but where you can change the parameter that

defines the tensions, opened the doors to the tune of timbres of Schönberg

where tension is produced by the timbral change and later to the music of

sound densities; like Xenakis himself, where the global density of events




produces stress or strain. These parametric translations were the foundation

of cognitive dissonance.

To abstract the concept of dissonance and use it without a tonal context, to

be applied to any type of material, even to the psychological stress caused by

the variation of the speed of the material, there are two types of listening

conditioning, the historical and learned ones which are shared by a

generation, even sometimes several, and others that occurs only inside the

work itself.

I can't resist the temptation to quote to Schönberg to talk about the historical

ones.

6(regarding to parallel octaves and fifths) octaves and fifths were not bad in

themselves bad, but on the contrary, were in themselves good; that they had

merely come to be considered outmoded, primitive, relatively artless; that there

was no physical nor aesthetic reason, however, why they should not on occasion

still be used.. And if one considers that these rules, in the form 'Thou shalt not . . .'

were spread abroad over centuries, then it becomes clear that the ear forgot the

sound once found to be euphonious, and its use aroused antagonism because of

the oddness the new always has about it. I am saying that, since progression in

parallel octaves and fifths was not practiced for centuries, the ear was disposed to

regard the occasional appearance of such connections as new, as odd, whereas the opposite is always actually the case: they were old, only forgotten. (Schönberg7,

Treaty of harmony .) P. 68)

6 Indeed, there is a way of interpreting from parametric music the reason for the prohibition

of the fifth and octave parallels, and it is the loss of significance that has a material when it is

repeated insistently. As we have seen several times, this leads to their neutralization. In the

context of a tonal music, the neutralization of the fifth or octave can have enormous negative

consequences.

7 I am going to pay here a homage to Schönberg, not only for being the creator of serialism,

but because he introduced many elements of modernity ‐quite often forgotten‐ that make me

to claim he was the first composer, as far as I know, that justified a rule through a cognitive

rule in his theoretical writings. He was also the first composer that consciously neutralized

parameters to highlight others in the invention of the melody of timbres. He was the first

composer who used the parametric neutralization and besides, he was an innovator in the use

of

vocal

and

instrumental

techniques.




Thus, listening conditioning, which makes to interpret certain sound objects

as correct or not and to place them before or after another, form part of the

establishment of a type of music as the normative for a time. In addition, it

lays there one of the reasons about the trends in the evolution of the material

referred by Adorno: creating new relations among materials, the historical

conditioning of these materials gets lost and with it the tremendous nuances

associated with them.

And yet, a listening conditioning may have validity only in the work where it

is inserted as it is used in cognitive‐cognitive parametric music; see the End game analysis to see this in more detail in its application in a real context.

Cognitive dissonance. A cognitive dissonance occurs when the brain has

established a specific criteria of elements ordering and an element appears

unexpectedly, it was not the expected one according to the cognitive

principle deduced by the cognitive systems. Cognitive dissonances replace

traditional dissonances in my music, and the flow of tension relaxation occurs

by the greater or less quantity of objects that are cognitive dissonances. See

the text for more information (pages 53, 178).

Significance space. It is a semiotical function which assigns to a certain value

or difference a significance in a parameter conditioned to another

parameter. For example, with regard to the colors associated with a physical

spectrum. Each language associates a word with a range of visual spectrum

to define them. So, if the continuous change of wavelength produces colors,

at what time can we say that a brief increase is already a different color? This

is what defines the significance space, being subjective in contrast to the

physical one. The relativity of significance space is being demonstrated in the

language. It is curious that different systems have been created to describe

the colors in different civilizations. If colors have great significance for

survival, many different words are created to define colors, whereas there

are few words when colors are not relevant. Thus, the space of significance

is a new space created as a consequence of an objective difference (the

difference between two wavelengths), that assigns a relative and subjective

meaning to this objective difference that can also vary over time, and be a




function over time, i.e. a certain difference may not be important at a given

time (being neutralized) or be so. This is a very important issue for the

cognitive‐cognitive parametric music, that a particular variation of a physical

and objective parameter (the difference between two pitches) suddenly has

a certain importance in function of time (the temporal development of the

work) or another parameter, i.e. that the significance of a parameter is

conditioned by another one. Thus, Parametric neutralizations studies is based on that, in same moments same parameters are neutralized and

differences physical objective does not mean anything, when at times these

differences mean much. This creates a great job of encoding and decoding

leading to cognitive dissonances and the tension of the work in the brain. In

Parametric modulations studies a common significance space of various

parameters around another common element is created to make

modulations between various fragments.

Determination flows. A determination flow is when something determines

another thing in a certain direction. For example, classical Marxism

establishes that infrastructures determine superstructure and, therefore,

establishes a determination flow between infrastructure and superstructure.

There are certain fields of knowledge where determination flows are fixed

and others where determination flows are mobile and can be inversed. For example, within some sociological theories, in certain historical moments

may be certain determination flows inversed by historical causes.

Determination flows are associated with the problems of implication and

causality. There are fixed determination flows that occur when something is

cause of an effect, then the cause ever determines this effect, or mobile,

when two elements are related in an open manner and any of them can be

determined by the other one or by a third determinant.

A reversal in a determining flow occurs when certain element is no longer determined by the other one becoming the determinant, which can cause

cognitive dissonance.

Cognitive strategies can be used to establish the determination flows, i.e.

models of cognitive theories to set determination flows, or psychoacoustic

models that take advantage of the way in which a parameter determines the

threshold of perception of another (this has been especially exploited in my

works of electronics reason by which I have hardly spoken in this text).




Tautological time. A tautology is something that is absolutely true, but it does

not bring any new information. There is no truer statement saying that A is

A. But there is also no assertion more little useful and meaningless. The

tautologies are meaningless; they do not say anything about reality. By that,

I mean as tautological time certain moments in my music that have so many

simultaneous reads that end up being meaningless. It is what I want to get:

the listening relativity encouraging everyone to use different strategies to

decode and give meaning to these meaningless and subjective structures.

Cognitive model. A model is a simplified representation of a studied

phenomenon. More precisely, we can say that a model τ is an interpretation

of a theory T, if and only if, all the statements of T are real in τ. If we have a

theory about a certain cognitive phenomena, a model is, therefore, an

interpretation of that theory. A cognitive model is a model of a cognitive

theory. Thus, we can, starting from a cognitive theory, create a model such

as interpretation of this theory that satisfies for some reason our creative

concerns. But it can also be used less precisely, as a scheme, which describes

the interaction of a number of items within a system. In this way, opposite

the theory which establishes the interaction of these items in such a system,

we can take a model based on the rules of this theory, so that everything the

model says is compatible with the theory. For instance, we can take a series

of cognitive rules drawn from cognitive science and establish a valid model

for application in our work.

But we can also, take a model and change it and apply it changed. Here I use

the word model in all these ways, depending on the context. Modeling is to

create a structure based on a theory whose result is a model.

For example, we can model in many different ways a musical work from

different theories. We can also take the conglomerate formed by the listener,

its cognitive system, and the parameterization of the work, and modelize it,

creating a model based on a theory that explains how it works the magic of

the moment in which listening occurs.

Another example, we may, regarding a tonal music theory, model a work of

art taking into account only the significant parameters to this theory. And we




can create a cognitive model that explains how we perceive the work, taking

into account only these two parameters. For that reason, this cognitive

model would be a model of the tonal theory but not of the integral serialism.

Integrational

cognitive

model. It is a cognitive model in which, in reference

to a previous model, several items from the model are integrated for having

an interdependent relationship. For example, we may have a cognitive theory

that stipulates that the perception of each one of the parameters is

independent from the other ones and create a consistent model with the

theory that models the significant parameters of the theory.

But, we can also establish an interdependent relationship about how each

one of the perceptions of a parameter determines the perception of the

others, if so; we will say that it is an integrational cognitive model. You can

criticize me and say that this term is not necessary because a model can

express infinite interdependencies between parameters. Indeed it does, the

sense of using this adjective is to underline the difference between models

that have account in an explicit way and others that do not. This difference

does not exist in the field of science. This difference expresses the difference,

non‐existent in science, between the formal modeling (which it does not

consider the relationship between parameters and considered them isolated, serialism) and the naturalistic modeling (which models taking into account

the way in which these parameters interact, the spectralism).

Parameter, see page 94

Listening positionality , is the listening property of focusing on a particular

type of element based on the obtaining of the award to recognize certain

patterns. When we say that listening is positional, and, therefore, relative, we mean that the listener has a directional component determined freely,

normally around a series of cognitive rules. Listening positionality determines

the intentionality through which the information loads of the sound materials

are interpreted, and which focuses on processes. It is what allows us, for

example, in a telephonic conversation with lots of noise differentiate

between conversation and noise, to the point of ignoring what does not add

information. It is the basis of the possibility of the signification space applied



to music. The significance loads derived from the focus of listening in a

certain process but not in another one.

Infinite series , series defined by the 12 notes by joint degrees. It has certain

properties such as to be symmetrically from several points of view, or being

very neutral and meaningless. So it used very often in my music, since End

game. You can find it on other composers, as for example, in Ligeti ´s concert

for cello.

Parametric translation. It is the process by which changes the decisive

parameter in the interior of a system. Applied to the history of music we can

say that, with Stravinsky, when the tonal paradigm changes to the rhythmic

one a parametric translation occurs, by which, the rhythmic removes the

prominence of pitches. A parametric work is characterized by establishing a

sound discourse based on constant parametric translations, in the end none

of the parameters has been a dominating center throughout the work.

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Divulgation Writings About Cognitive Parametric Music