Fabrics of Music
Abstract
Music is, arguably, the most abstract of art forms. Because of this, there has
been some argument concerning its 'meaning', or at least, its relationship to
other subjects. Throughout the history of music and still today, most forms
of music include examples of pieces which associate themselves with other
subjects. Most obviously, in the west, these would include Beethoven's Pastoral
Symphony, Couperin's xxx, ..........examples of direct association with or
imitation of extra-musical things...
At a more complex level, there are many examples of music - admittedly usually
at a less obvious level - which uses particular methods of usually long-term
structuring. One of the principal ideas here is that of number. These might
include...
In addition, many analysts and commentators have commented on or made reference
to music's more or less abstract association with other subjects - for instance,
Bach is often described as 'architectural', and some modern music as
'mathematical'. The latter description, at least, is usually quite wrong
as most pieces which can be seen as having an association with 'numbers',
for instance those using the twelve-tone system, do not utilise any
particularly 'mathematical' processes, and even if they did, it is not clear
how this would necessarily influence the 'sound' of the music to make them
appear 'mathematical'.
Of course, most people use the term 'mathematical' in association with music
in a strictly pejorative sense and usually mean that they do not like the
music, (we will deal with why later), and they do not like mathematics,
both or which are seen as 'cold' and 'inhuman'.
However, and especially recently, with the increasing use of computer
technology in musical creativity, there are increasingly ways of using
mathematical, geometrical and statistical processes into sound, either
through MIDI, (Musical Instrument Digital Interface) or the generation
of audio files and signals. Essentially, the interesting area here is
the success of such 'mapping' in musical terms and perhaps more importantly,
what the ability to undertake such mapping says about the way in which
we understand and perceive musical expression.
If you like, if the use of the 'mapping' of mathematical, geometrical,
statistical and algorithmic processes into music provides at least the
basis for some form of musical communication, does this say anything
interesting about both the status of the mathematics and the music, does
it help to confirm the Platonic idea that there is something 'real' about
mathematics that finds a reflection in music, or is it simply a reflection
of logical patterns that we perceive anyway?
If this problem - does there exist a 'preset' link between mathematics,
nature and human perception, or is mathematics as problematic in terms of
its reality and certainty as any scientific or other philosophical speculation?
- lies inevitably at the heart of these speculations, then many other issues
occur before this point. They include the following:
1 Performing
* The nature of performance itself, influenced by the fact that music that
exists principally on tape is by its nature unchangeable, except by
re-composition, while a 'score' remains apart from its many possible
'live' manifestations.
* 'Case studies' of performers and performance, for instance Glenn Gould,
(also relevant to technology.
* The link with technology and composition resides in the status of different
sorts of 'scores' - a traditional paper score, an abstract 'aural/oral
tradition' 'score', a 'traditional' electro-acoustic tape piece, an
editable MIDI 'score', a computer programme generating, manipulating
or contributing to performance.
2 Communication
Introduction
* The nature of music and its various manifestations - the idea that it can
perform with equal success many roles and functions and mean many things to
different people and peoples.
* The nature of our perception of events and specifically sonic events and
the concept of 'information'.
* Scientific and Philosophical views of reality and certainty and their
relationship to aesthetics:
* Music and Philosophy
* Music and Language
* Chomsky
* Music and Mathematics:
* Number Theory
* Complexity
* Chaos
* Game Theory
* Combinatorialism (20*19*18*17*16...) and language cf Steven Pinker
* Kant/Wittgenstein
* Knowledge and Progress
* Music and Psychology
* Psychological and pyschoacoustic effects of sound.
* Behaviourism
* Cognition
*
Also:
Artificial Intelligence: if you invented a computer programme that composed
'convincing' music, what would this suggest, that is Turing, etc...
* The views of non-musicians, and especially scientists, concerning music;
references to music in scientific and philosophical literature.
* Views concerning mapping and equivalence between different media, including,
for instance, an equivalence between Bach harmonisation of chorales and
Mathematical derivation. In the latter cases, you need to know where you're
going in order to do it properly.
* Left and Right-handedness!?
* The idea of mapping - for instance tension/release & the bit in Hofstadter...
* Aesthetics versus Certainty - Popper.
Technology
* The use of technology in music and its effects on the medium:
* The recording of music: Digital Distribution, MIDI, Audio Editing
* The aesthetics of computing and computation in relation to creativity within
music.
* The interface
* The aesthetics of the interface and ways of thinking
Listening as a form of Virtual Reality, (also reading and cyberspace).
Composing
Aesthetics versus Certainty
Inevitably, one of the key areas here is the effect of technology on what we do
in music. This is a wider issue than simply the use of recording, MIDI & Audio
file editing, synthesis, computing, software availability and development, etc.,
but also involves the effects of this technology on the aesthetics of composing,
performing and listening to music.
This in turn would appear to be rather similar to the way in which the
developments in computing, information theory, artificial intelligence, etc.,
are having such a profound effect on other, especially scientific interests -
especially mathematics and modern physics. In these fields, developments in
technology have cast light, or more usually doubt, on some of the most basic
ideas of reality, thought and communication. Can they do the same for music?
Also, just as most discussions of modern physics need to relate 'classical'
physics with post-relativity physics, so we need to investigate 'classical'
music with 'contemporary' music - is this valid???
Look at potential relationships between the 'change' around the beginning of
the century - in art (figuration/abstraction), in music (tonality/atonality
(yuk!), and physics (classical, modern)...
Any others???
Introduction
The title of this thesis is taken from David Deutsch's book The Fabric of
Reality. It is one of a number of essential texts for any one who wishes to
have an informed understanding of current ideas in science and philosophy. It
is certainly ambitious - self-consciously so - in seeking to draw together four
'strands' of current scientific and philosophical thought into a single, once
again, current, view of the world. At the same time, it is written with a
commendable modesty - some of the ideas may be wrong, (although having thought
them through he does not think they are currently wrong), and certainly, all of
them will become wrong, or rather all of them will be superceded at some point
in the future. Indeed, his certainty concerning this latter point forms one of
the central tenets of the book. Having spent some time and effort over the
years arguing, discussing, agreeing, disagreeing, about many different ideas
this is indeed an interesting and productive approach.
So what has this to do with music? Why should a musician, in particular want to
read a book such as the above and more especially, what would they get out of it?
At most, music can metaphorically contemplate certain ideas in an abstract way,
but a way that is ultimately governed by such unscientific rules such as those
of aesthetics and taste. Indeed, these are presumably by definition not rules,
but conventions which cannot be described as true or false, on or off. Is not
the search for beauty one of personality combined with abstract form, and this,
surely cannot be converted into a calculation, a formula, a computer programme
or a set of axioms and rules?
This is the tone of many 'normal' responses given when people discuss music -
that most abstract of arts. Many contemporary pieces are criticised because
they are 'mathematical' - not because they are mathematical, but because
subjectively, to these listeners, their sound is summed up in the word
'mathematical' and the word 'mathematical' is summed up by - dry, unemotional,
dissonant, anti-intuitive, atonal, expressionless, ugly... the list goes on,
revealing more about these people's view of mathematics than it does about the
music. in question, (although it does reveal some interesting points about the
relationship of the music in question to 'people' in general).
Move to the other perspective and you see a different view: mathematicians and
'scientists' often have an extremely high opinion of music and musicians,
although one can often see trends here, too - Bach is often cited, and the word
'architectural' is often cited near that of Bach. The classical composers -
Haydn, Mozart, Beethoven, are usually not far behind. In most cases there is a
glaring shortage of contemporary composers. Some writers in this area have been
at pains to try to include music with their theories - the most obvious example
being Hofstadter's Godel, Escher, Bach, where the great musical architect is
placed alongside a mathematician and a graphic artist in a full-blown attempt
to understand the nature of communication. (In my, and in many other people's
opinion, the book is wonderful, but the references to Bach do not work as well
as the references to Escher, which in turn don't work as well as the references
to language...).
So the horrible truth must be accepted - most people's view of music is of Bach,
the classics, the popular romantics or some form or other of 'Popular' music.
Ultimately, some of the key questions concerning art and music also concern
mathematics. I have neither the knowledge nor the time to go over all of these
questions in the detail that they really require, but I would re-direct anyone
who is interested to the relevant books mentioned in the text and the
bibliography. The most substantial would appear to be one concerning truth and
the status of mathematics. Music is not about truth as such, at least not in
the way that mathematics is, and yet it has been pointed out (Penrose), that
certain works of art, including some of the more distinguished works of music
can appear to be of such quality that they appear to be from 'something other'
than 'just' the human brain. This is highly contentious language, but, perhaps
strangely from the point of view of a musician, it is in exactly these terms
that some mathematicians write concerning their own 'art'. Indeed, for some of
them, it is exactly this 'beauty' that seems to point the way to what they would
claim to be the proof of mathematics' truth.
Alternatively, there are others who completely disagree.
Over the last century a new form of music has arisen as a direct consequence of
the advances in technology we have all experienced...
As is further described in Chapter 2?, a large proportion of these speculations
was initialised by my own investigations into certain processes, implemented in
software, involved in the generation of sound events through a form of
algorithmic stochasticism. What began as a modest write-up of two modest pieces
of software has expanded beyond all my intentions. The possible ramifications
are themselves potentially substantial, although for one not usually accustomed
to expressing himself in these terms it feels uncomfortable to express this,
but in the process of trying to understand and explain them to my own
satisfaction over time more and more areas of music and sound perception have
become necessary. In addition, however, my own activities in 'non-electronic'
composition and a fundamental failure on my part to accept or understand some
of the deep 'divisions' within musical expression throughout the world have
also played a strong part. As an example - in attempting to understand the
nature of predictability in music, both in terms of the composer and the
performer, (if such a distinction is made), one is forced to investigate the
nature of the western 'score', and also the nature of the interpreter's
relationship to it. This is clearly something to do with the level of
unpredictability in any performance. However, following that, is the method by
which we are able to judge the interpreter's performance, or even the quality
of the score itself. For many of us involved in creating and/or teaching these
ideas, we make these judgements on a regular basis and may think of them in
rather obvious and mundane terms. Ultimately, though, by what mechanisms do we
come to our conclusions and have they any basis in 'reality' or 'fact' beyond
our own, and possibly our peers, opinion? How often do we make such judgements
on 'instinct' or through 'intuition', or complain that it is impossible to
really explain such intuitions because of the complexity of inter-relationships
lying behind our judgement and experience. On a day to day level we may,
through necessity, be quite happy with such bland and bald statements, but on
reflection, how justified are we in making them? To put it another way, can
anyone seriously believe that someone with no experience or even understanding
of a particular tradition can make superior judgements to those with such
experience and understanding? And yet we know that art is at least to a large
extent a matter of aesthetics, not truth.
Music is a peculiar subject of study, not least because of its potential range
of interest. We may find it hard to believe that some of the Ancient Greeks
considered it one of the four most important subjects to understand - even
more surprising, maybe, when we consider that the other three were Astronomy,
Arithmetic and Geometry. Perhaps this surprise is the result of the role and
function of music over the last few hundred years. Music is now seen principally
as an entertainment or a commercial tool. For many in the west, its inherent
abstractions are either non-existent or irrelevant, and the principal form
utilising these abstractions is apparently debarred from them for reasons
which are more to do with perceptions of society than ability.
However, all is not gloom. In those areas of philosophy in which discussion of
a subject and a subject interconnections are allowed, (as opposed to endlessly
discussing the nature of discussion), music has been used to illustrate certain
aspects of human perception. Of course, in the humanities, music is seen as a
somewhat 'different' and even 'lofty' subject when compared to the dirty
practicalities of Literature, Language, Sociology, Politics and even Philosophy.
In most academic establishments, Music as a subject is seen as, while firmly
within the humanities, a 'semi-detached' subject, whose staff and students are
similarly semi-detached. At the same time, while most Music Departments
principally consist of a majority of students whose main interest is in
performance, and where the principal staff interests tend to revolve around
one or other area of Musicology, there will often be found, again, in a
semi-detached position, a more or less thriving sub-department involved in
particular areas of what is now called 'music technology'.
The peculiarities of studying music in our society are compounded in a number
of other ways:
The Study of Music in Western Society
The Role of Music in Western Society
The Perception of Music by the Sciences
The Range of Music
When all these factors are taken into account, it can be seen that, in fact,
Music is a highly varied and multi-facetted subject. From the vast commercial
area of popular musics, through the gentler, more fragile and informative Folk
and World Musics, through the more abstract and prestigious Classical musics
throughout the world; from popular music technology through Audio technology
and the huge markets for Audio equipment of all standards, through more esoteric
uses of these technologies, through the development of computer applications to
manipulate information for all these areas; from the architectural and
mechanical areas of acoustics to the psychological and physiological areas of
psychoacoustics; not to forget music therapies and other areas on the boundaries
- the uses of sound to understand areas of the natural sciences - bioacoustics,
oceanography, radar; through all these areas it can be easily seen that music
is a part of a continuum stretching from the most abstract of artistic theories
to the most basic of human expressions to the most esoteric of scientific
methods. In fact, I feel that the latter is not entirely true and for
particular reasons that will be investigated later.