divulgation writings about cognitive parametric music
TRANSCRIPT
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Divulgation writings about
Cognitive
Parametric
music
usevi
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Divulgation writings about Cognitive Parametric
music
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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.
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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
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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)
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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
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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
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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
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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.
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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
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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.
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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.
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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
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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.
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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
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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
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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.
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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
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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.
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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.
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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
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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.
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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.
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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
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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
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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.
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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.
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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
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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
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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
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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.
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"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.
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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
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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,
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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
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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
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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
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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).
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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
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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.
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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.
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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.
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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
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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
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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
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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.
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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
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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.
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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
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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
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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.
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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.
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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.
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And here is the final mix screen of Pro Tools.
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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.
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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).
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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
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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.
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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
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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.
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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
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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.
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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.
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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.
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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.
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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.
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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}
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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
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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
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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
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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.
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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
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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).
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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
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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
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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.