Inherited Problems and a Proposed Solution

a lecture in the YNEZ Series

Advances in Music Notation

Department of Music
University of California
Santa Barbara, CA 93106 USA
Thursday, 28th February 2002 at 6pm

with additional footnotes: March 2002


This lecture expands upon the proposals I am making for a Graphic User Interface for developing music. The genesis of these ideas can be found in the previous papers to be found at this web site.
Part 1 of this lecture describes my view of the crucial problems in 20th century music notation and how these affected both composers and institutions over the past century. Part 2 is a description of how the problems can be tackled using software. I present a proposal for a GUI which incorporates a new paradigm for music notation, replacing the 19th century concepts currently embodied in standard music notation.

Part 1: Context

1.1 Personal background
My work and the software I use
1974-1993: Handwritten scores
1980: My first personal computer (Apple II) - and my first experience of programming
1993: Stockhausen starts using computers to publish his scores - Finale, FreeHand and Freehand Xtras...
2001: Freelance copyist - ... and Sibelius

1.2 The general context - inherited problems
1.2.1 The 19th Century
Contemporary common-sense was wrong
Space-Time equivalence
Ubiquity of tempo
Unlimited expressivity
High level structures not explicitly notated
The 19th century common-sense time paradigm had failed
In practice, even in music which has a tempo, local time is all important.
The whole point of performing music in real time, is to cultivate a tradition of performance practice...

1.2.2 ca.1910-ca.1950:
Invention of commercial recording
“Performance practice” is only vaguely understood
Sociological developments

1.2.3 ca.1950-1970 (The Avant-Garde)
Sociological developments (continued)
Common sense among the Avant Garde can be summarised as follows:
Standard notation is thought of as a sacrosanct cultural anchor.
“Absolute time” is still thought of as the “real” meaning of the duration symbols.
It is vaguely and wrongly thought that time is freely subdividable.
The most important alternative to standard notation is “Space-time” or “Pianola roll” notation.
There is an assumed equivalence of notation and performance

Earle Brown
The duration symbols are thought of as being strictly equivalent to (absolute, mechanical) metronomic time.
There is no attempt to deal with the typographical aspects of symbols - these are assumed to be irrelevant.
...description of the time continuum which exists from the smallest vibration to the longest duration.
Stockhausen continues to agree with Stravinsky's dictum. “Just do what I wrote.
A personal recollection (Helikopter-Striechquartett)

1.2.4 1970- present (2002) Collapse of the Avant-Garde The revival of Pre-Classical Music The changing role of institutions

1.3 A summary of the current technical problems

Part 2: A proposed solution

2.1 Social aspects of the proposals
2.1.1 The role of artists
2.1.2 Software development

2.2 A Graphic User Interface
2.2.1 The practical context
2.2.2 A proposed editor for developing music
2.2.3 Event analysis (“chunking”)
2.2.4 Other parameters
2.2.5 “Zeros” and Transformations
2.2.6 Legibility and other practical considerations

2.3 Further Notes

Part 1: Context

First I'd like to thank Curtis Roads very much for inviting me to speak here today. I have a very special background, and dont really fit into any of the usual bureaucratic categories - I'm neither an academic nor a practising composer, nor a technician in the traditional sense, nor do I have much experience of lecturing. So this talk is not without its risks. Thank you, Curtis, for asking me anyway.

Part of what I have to say today has to do with the way the meanings of symbols change according to their context. For example, you will not really be able to understand what I am about to say, unless you know something about who I am, and how I understand our shared cultural context.

So here's the general form this talk is going to take:

Part 1.1 deals with the special context in this room: I know, generally speaking, who you all are from the information presented at CREATE's web site and from what I've heard from Curtis Roads. But it is even more important that everyone here knows something about me, and I cant assume that you have all looked at my web site. So I'm going to read you a short description of my personal background.

Part 1.2 deals with the general context: This is the relevant part of the inherited culture of written music which we all share with the rest of the western world. Here again, I'm going to read this part of the talk. I'll be dealing with a very high level perspective on the history of written music over the last hundred years or so, and there would be a great danger of my losing my thread if I tried to improvise this. There are simply too many interesting side-tracks, and I really want to get on with Part 2 rather than getting bogged down in historical details. This section is not intended to be a definitive, potted history of 20th century music. It is supposed to give you an idea of the kinds of problems I'm trying to solve in the next section.

Part 2 will be longer and less rigid - this is where I'm trying to change the context I've just described. I'm going to enlarge on my previous proposals for the structure of a Graphic User Interface for editing music on computer terminals, and especially want to describe how this can work at the lowest level of percieved events. I want to talk about the the kinds of symbols which can be used at this level, how their meanings can change according to context, how a hierarchy of symbol-levels gets off the ground, and how all this can be expressed in real software.

Part 3 I would be very happy, if this talk could end with an open discussion of the topics presented. Individuals, like myself, working outside “the system” need feedback. Culture is teamwork - by definition. I have brought some notes about topics I think of as “growth-points”.

1.1 Personal background1

I'm a freelance copyist and developer. I'm also a composer — I studied under Harrison Birtwistle at the Royal Academy of Music in London from 1968-1972.

I left college wanting to tackle the serious theoretical problems in music notation which had been left unsolved when the Avant-Garde collapsed in 1970.

The traditional institutional structures had proven incapable of solving these problems: Firstly, composers were expected to solve them, but composers have too many other problems to solve at the same time. They need to think about the poetic aspects of what they are doing, and their survival depends on their mastering short-term practicalities. Secondly, the other institutions (academic, government sponsoring, publishers etc.) only support rather short-term projects.

So I looked about for (and was lucky enough to find) a long-term strategy which would enable me to remain close to the things which interested me.

After working for Universal Edition in London for a couple of years, I became Karlheinz Stockhausen's principal copyist in 1974, and made an agreement with him which enabled me to get several months in each year free to devote to my own work.

Unfortunately, at the beginning of 2001, Stockhausen told me that he no longer wanted to continue with that agreement.

My work and the software I use
OK, so I'm a practical copyist with many years of experience creating complicated 20th century scores. Here are the relevant parts of my curriculum vitae in a little more detail.

1974-1993: Handwritten scores
For the 19 years before Stockhausen began to use computer technology to publish his scores, I copied them at a drawing board with pen and ink.

1980: My first personal computer (Apple II) - and my first experience of programming
I bought this computer because I wanted to reduce the amount of paperwork associated with an Abstract Data Type I was developing. I'm interested in algorithmic composition.

1993: Stockhausen starts using computers to publish his scores - Finale, FreeHand and Freehand Xtras...
In 1993, the then current version of Finale was hopelessly inadequate for the problems confronting us, and I had to find some answers pretty quickly in order to keep my job. I was already programming in C, and was thus able to write a special filter to improve Finale's postscript output enough for that to be edited economically in FreeHand.
FreeHand is a very powerful graphics editor, used routinely in the advertising industry. Its a great program, with lots of money behind it - but it doesnt know anything about music, so I began writing Xtras for it when that became possible in 1995.
I have never had to deny Stockhausen any of his most extreme demands as the result of inadequate software, and have brought a few example scores with me, if anyone wants to look at these later.

2001: Freelance copyist - ... and Sibelius
I'm currently looking about for new ways to finance my research & development projects. The commercial music publishing world is at present dominated by two major programs: Finale and Sibelius, and I have decided to learn the latter. I might just as easily have chosen the latest version of Finale. Probably I was irrationally influenced by the fact that Sibelius is a British program :-). Both these programs meet the minimum graphic requirements for publishing conventional music, and they can both be used to input such music in a commercially viable time - but, especially in non-conventional music, neither of them provide the precision, power and flexibility achieved by combining FreeHand with my Xtras.

1.2 The general context — inherited problems

As some of you may know from my web site, I think that written music has stopped developing and that something needs to be done about this. As far as I'm concerned, the lack of development results from the failure of the arts world to come to terms with the collapse of 19th century dualistic thinking, and I think we can get things moving again if we look these problems squarely in the eye. It has always been my dream to find a way to get music breathing again, and think that goal may not be too far away.

At the end of the 19th century, common sense (especially among artists), was that the physical (=mechanical) world had been essentially explained, but that a parallel, spiritual world existed, in which Art happened.

This underlying dualism affected developments in two important aspects of music: firstly, the theory of music notation, and secondly music's institutional structures. Interestingly, those institutions have also failed to solve the problems we are now facing.

In the theory of music notation the dualism becomes:

Real time = absolute time + expressivity

Socially, the dualism leads to a perception of artists as “heroes” who transcend the dead, material world. Over the years, this role-model for artists has led to the establishment of institutions for the promotion of such heroes. The reasons for doing this are becoming ever less clear. The institutions remain part of the problem we have to solve.

I'd like to include both of these problems - the technical and systemic - in what I'm going to say, because both of them are related to the main object of this talk - the software proposals I am currently making. Software not only embodies solutions to technical problems, but it also interacts with, and changes the sociological structures within which it is used.

1.2.1 The 19th Century

Remember, that this is not supposed to be a potted history of music's notation and institutions :-). This is just my version of the history of the crucial problems. Once you have understood this context, you will be better able to understand what I'm trying to get at with the solutions I'm proposing.

Lets go back to the 19th century. Here’s the above dualism again:

real time = absolute time + expressivity
performed time = mechanical time + performance practice

Here's a list of reasons why I think problems arose. I'll go through these quickly and then give you a couple of real examples:

Contemporary common-sense was wrong: time philosophy and the resulting notation conventions had been stagnating since the 17th century.

Space-Time equivalence: Time was thought of as being equivalent to a dimension of space. The typographical (space) conventions (subdivision symbols, making bars add up etc.) are directly linked to the meanings of the symbols in time, and these meanings are linked to low level, absolute, mechanical time. Where this is not the case (e.g. in cadenzas) the typographical rules are not properly defined at all.

Ubiquity of tempo: Standard music notation assumed the existence of tempo, and real music became increasingly tempoless. Even now, at the beginning of the 21st century, there is still no theoretically sound symbolic notation for tempoless music.

Unlimited expressivity: There are no limits to what is meant by expressivity. Writers of music lose control, and performers end up doing more or less what they like.

High level structures not explicitly notated: The notation conventions lack a concept of “level of information”. The concepts “chunking” (subroutine) and “level of information” were developed in the late 20th century in connection with computer languages. However, 19th century notation does indeed use symbols having different levels of meaning: Trills and other ornament symbols replace groups of notes, Roman numerals stand for chord functions - but there are limits to the number of levels one can cram onto a single, two-dimensional sheet of paper. Notice that the interpretation of ornament symbols was a particularly thorny problem for researchers developing performance practices for ancient music during the mid 20th century.

Here are a couple of concrete examples to illustrate what I mean:

The first example is of typically flexible, slow moving, Romantic music: Notice that it breathes - something which got lost in the 20th century.

play example #1 from CD :
Bruckner 7th Symphony, slow movement, bars 1-9

The lengths of these notes are judged in relation to the lengths of other notes in the vicinity (the local context). The lengths of the notes are neither related to time segments produced by some mechanical measuring device, nor are they related to some persistent tempo. At these orders of magnitude, it is very difficult to remember any tempo at all. This music has nothing to do with relations to absolute time - its about building structural arches at very high levels, and those high levels are not directly notated in the score. One finds out where they are, and how to perform them, by learning a particular performance practice - i.e. becoming a member of a specific performing tradition.

The second example - also typical of late Romantic music - also contains faster music, - clouds of notes which smear the concept of simultaneity. There are, of course many examples of this kind of thing in other composers - for example Richard Strauss - but here is early Schoenberg. I'd like to play nearly four minutes of this example, to give you time to think.

play example #2 from CD
Schönberg's Pelleas & Melisande,
from rehearsal number 43 “Ein wenig bewegter”
to the fermata before rehearsal number 50.
In the Universal edition score, this is from page 75
to the middle of the lower system on page 91.

Clock time is irrelevant within such clouds, just as the sequence of characters in a word is irrelevant to the meaning of that word. Clock time is flat. Meaning depends on higher levels of information. Clock time no longer has anything to do with what the composer or performers mean.2

In both these examples it becomes difficult to see why one should stick to the conventions of standard music notation - for example making bars add up in absolute time. Symbols for “subdivisions” - so called “irrational” values - are also meaningless in tempoless music. I'll come back to this when I get to the 1950s.

So late 19th century notation conventions ceased to describe the things composers wanted to describe. They became unable to write what they meant.3

It had, of course, always been the case that notation represented an approximation, but the problem now became acute. Composers wanted to write higher levels of structure than the notation on the two dimensional page. Incidentally this leads to the notation of music becoming increasingly work-intensive - like writing computer programs without the use of subroutines. This is a very practical problem, which shouldnt be underestimated.

In this situation, concientious performers think of themselves as being in a tradition of unnotated “performance practice” (e.g. the school of pianists which begins with Chopin).

Before leaving the 19th century, I'd like to emphasise the following:

The 19th century common-sense time paradigm had failed.
There are interesting parallel developments in physics (Einstein) at the beginning of the 20th century. The lessons learned from that paradigm shift have not yet found their way into the theory of music notation. If anyone would like to go into that in more detail, we can do so later - but I must not get distracted here.

In practice, even in music which has a tempo, local time is all important.
The durations of notes are judged relative to the durations of other notes in the vicinity, not to some absolute, mechanical duration measured by a stopwatch or metronome. Absolute time is actually an unnecessary concept in music written with the standard symbols. If we want, non-dualistically to say that the symbols mean the corresponding performed notes, then we have to admit that the symbols dont have absolute meanings at all. The meanings change according to their local context.

The whole point of performing music in real time, is to cultivate a tradition of performance practice by forming real events.
Symbols on paper have never told the whole truth about music. Attempts to deny the existence of performance practice, stored in human memory, quickly become uninteresting. Music is about performances in context. It is about memory not machines. Information, not matter. Software, not hardware.
A sociological aspect of this: The increased reliance on performance practice leads to an increased dependence on soloists and conductors. This is especially true in new pieces. It takes a great deal of rehearsal time to establish a new performance practice tradition. Because performers and conductors are the people who actually give concerts which generate revenue, they come to dominate the institutions.

1.2.2 ca. 1910-ca.1950

Written music continues with neo-classical time, the sun finally sets on late-Romantics (such as Richard Strauss). The beginnings of a recording industry. The rise of Jazz.

Invention of commercial recording
This has practically no effect on the written tradition, but is of crucial importance to the development and dissemination of Jazz and popular music. Recordings are canned performance practice. Jazz musicians work in small groups, and have a practical, undogmatic attitude to notation. Some inimitable performers become world famous: Think of Caruso, Bessie Smith, later Edith Piaf, Frank Sinatra. Recordings create globalised aural traditions, enabling music to develop by imitation, without reference to notation problems.

“Performance practice” is only vaguely understood
and is certainly not integrated into any notation theory. Composers (writers of music) try to pretend that performance practice doesnt exist (Remember Stravinsky's dictum “Just play what I've written - no more, no less.”). They are highly suspicious of “virtuosos”. For economical reasons (rehearsal time), they can only write music which has a Neo-Classic or Romantic performance practice. They repress the problem of time in favour of more immediately accessible topics (e.g. pitch). Composers have to write.

Sociological developments
(Remember that the Romantics believe that there is a sublime spiritual world, complementing the dead material world, and that this spiritual world is the only worthy environment for the human spirit.) In politics, the Romantic tradition loses two world wars. Kaiser Wilhelm and Hitler both ignored the material consequences of trying to realise their Romantic visions. (In the bunker under Berlin in 1945, Hitler actually said: “The German people are not worthy of my dream.”) Since that time, especially in Germany, modern liberal democracies regard charismatic politicians with great suspicion.

But composers, institutions and the general public continued to regard artists as heroes. This is particularly so in popular culture (this is the classic era for film stars...). Conservative, inherited attitudes persisted in institutions such as orchestras - while new music becomes increasingly problematic. Neo-Classicism is the only practicable alternative to continued Romanticism. In its denial of “expressivity” it is fundamentally at odds with the institutions which grew up to support heroes. Extreme Romantics finally lose control altogether. Most composers arrive at some kind of compromise.

1.2.3 ca. 1950-1970 (The Avant-Garde)

Sociological developments (continued)
In Germany and France, the situation is especially interesting: Stockhausen and Boulez, as young, hardworking, free-thinking composers become the focus of an attempt to transcend the past. The Zeitgeist is summed up in the term “Stunde Null” - Zero-Hour. Many continental Europeans are trying to forget the past. Young artists, who have no history, are needed to build a new culture.

So it is a whole new generation of composers who have to attempt a solution to the underlying problems of music notation. Interestingly, being unaware of the much larger picture, they even attempt to straddle the gulf which had opened up between the arts and sciences (The “Two Cultures” debate comes up again in a moment).

Common sense among the Avant Garde can be summarised as follows:

Standard notation is thought of as a sacrosanct cultural anchor.
This is really a mixture of technical and sociological problems. The attitude can be further paraphased as:
Lets keep the standard notation as it is (because it is sucessful, obviously very powerful, and everyone agrees about what it means). We can invent alternative notations for the musics it cannot describe.”
This attitude still persists today, because it is thought that introducing new ways of thinking about notation would be too difficult. I believe, however, that the existence of software now presents us with a solution to this problem.

“Absolute time” is still thought of as the “real” meaning of the duration symbols.
This assumption comes from the Romantics via the Neo-Classicists, and probably stems from Newton's time paradigm in the late 17th century.

It is vaguely and wrongly thought that time is freely subdividable.
In fact, Time is indivisible, all that can be done is compare tempi.4 It is non-sense to use subdivision symbols in music which avoids a perceivable tempo. But composers did this all the time - Tempo was itself undesirable, having been worked to death by the Neo-Classicists in the previous decades...

The most important alternative to standard notation is “Space-time” or “Pianola roll” notation.
This is a precise, low-level mechanical notation which cannot be performed correctly by human performers because it is illegible. Composers used it where they didnt want an “expressive”, non-mechanical result (standard notation being thought to describe mechanical time).

There is an assumed equivalence of notation and performance.
It is assumed not only that a performance can be inferred from a notation, but also that the reverse is the case: that the notation can be inferred from the performance. This idea derives not only from the false assumption that time is equivalent to a dimension of space, but also from the false assumption that performance practice can be completely ignored. If notation and performance were completely equivalent, composers would have total control over performances. The power of graphics was thus grossly overestimated. This situation led not only to the writing of some very beautiful looking scores :-), but even more importantly to the idea of creating music directly in space on recording media.
Recording devices were machines for converting space into time. I think it is no accident that electronic music begins to be developed in this post-neo-classic period. Electronic music, created directly by splicing tapes together, does indeed remove the dimension of performance practice from the act of composition.

One of the implications of the proposals I'm making is that it should be possible to build recording devices which read and interpret symbols. Current digital technology is a step in this direction.

Here are a few examples of how some of the leading composers of the time fit into the picture im painting of the period (in no particular order):

Cage: When he uses standard notation, he has the inherited Neo-Classical attitude to it. Use of other notations leads to uncontrollability and Chance as ideology: He makes the best of a world out of control. Eventually his graphics no longer try to notate time at all.

Earle Brown: I include him here, because I remember an interesting encounter with him while I was preparing a score of his for Universal Edition around 1972. He was adamant that having square noteheads would influence the performers to play the beginnings and endings of notes more cleanly, more mechanically. This is a good example of what I mean when I say composers thought of notation and performance being equivalent.

Boulez: A good description of the notation-performance equivalence can be found in “Boulez on Music Today” (1963)5. He describes the achievement of “Striated” and “smooth” time by using notations specialised for one or the other.6

Stockhausen: For obvious reasons, I'll say a little more here - but remember I'm not a musicologist, I'm talking from personal experience of working with the man for 27 years. The definitive text on Stockhausen's attitude to time (and hence notation) is “ time passes...” (1956/57)7. In that essay:

The duration symbols are thought of as being strictly equivalent to (absolute, mechanical) metronomic time.

There is no attempt to deal with the typographical aspects of symbols - these are assumed to be irrelevant.

There is a fascinating description of the time continuum which exists from the smallest vibration to the longest duration.
He distinguishes three main areas: Pitch (shorter than ca. 1/16 sec.), the durations used in rhythm and metre (ca. 1/16 sec. - ca. 6 sec.), and longer durations. In my view, music written with the standard symbols is organised around the concept of an event. (An event is the equivalent in time of an object in space.) In my terminology, Stockhausen is saying that the smallest events which have a pitch are ca. 1/16 sec. long. I see this as an example of the way our perception chunks information when this becomes too much to handle. All our perceptions seem to be layered in this way. At the machine level, the durations of events and the durations of high frequency vibrations both occur on the same time axis, but at the symbolic level (the perceived level) they are experienced and notated in different dimensions. In two-dimensional symbolic notation, events lie at the crossroads between the vertical and the horizontal.

In the 1950s, there was no mature concept of chunking. The subroutine had been invented (or discovered) in the late 40s or early 50s, but as far as composers were concerned, computers and their languages were still in the realm of science fiction. So Stockhausen saw (and sees) no essential difference between mechanical and perceivable time, regarding mechanical time as being fundamentally percievable.

Consequently: a) he saw no reason why he shouldnt use additional, “accurate” symbols for describing absolute time (e.g. metronome marks such as 72.5). There is much wishful thinking of the form: “Musicians and audiences will learn to hear these values in future, even if the present generation cant.

And b) he ignored the part played by tempo in the concept of “subdivision of time”. Indeed, he saw (sees) no obstacle to the use of unlimited degrees of subdivision, and introduced a concept of “Fields of imprecision” to describe what happens when increasingly complex standard notation is used. (This also relates to Cage, Boulez and the concept of chance.)8

Stockhausen continues to agree with Stravinsky's dictum. “Just do what I wrote.”

A personal recollection:
(this comes from a much later period, but it fits in here, because Stockhausen's basic attitude has not chaged): The score of his Helikopter-String-Quartet has two parts: The first part is his original score written in standard notation (the colours just make the relative heights of the glissandi easier to see); the second part consists of screen shots of what he saw while using Protools for the mix-down for the CD. (I edited the screen shots, and we made a few helpful additions while preparing the score for publication.) I well remember him saying that the second part of the score is the real score. I think he wishes players could read such notation.

1.2.4 1970- present (2002) Collapse of the Avant-Garde

The leading members of the Avant-Garde give up attempting reforms of the notation and revert to using the standard notation in some form or other. This currently means writing various kinds of Minimalist, Neo-Classicic and Neo-Romantic music. Only notatable music can be written! Standard music notation stops developing.

This was an emergency solution. How else could composers keep writing, and at the same time work within practicable rehearsal times?

Stockhausen again: Following the experience of trying to work with non-notated pieces in the late 60s, and at world exhibition in Japan 1970, he now recognises the extreme importance of developing and preserving a tradition of performance practice. Especially in his late work, performance practice is now crucially preserved in the recordings he has sanctioned. He goes to great lengths to train specialist performers how to perform his pieces. These performers are intended to be the seed for a new tradition. Apart from the use of recordings, there is no current alternative to using the methods practiced by the followers of Chopin.

For practical, systemic, institutional reasons, many composers have tried to revive the Romantic vision of the Artist-as-Hero - and in doing so to play down the music world's failure to solve its underlying technical problems. The image of the composer as poet whistling in the woods while the notes land on the paper as if by magic, is a tried and tested way to survive commercially. But as I've already pointed out, the Romantic dream has become discredited, and the position is by no means comfortable. The revival of Pre-Classical Music

The world has used this breathing space in the development of standard notation to revive performance practices for ancient music. As in the case of jazz, this would have been much more difficult without the existence of recordings.

Apropos recordings: As I've said, recording devices are sophisticated machines for converting space into time and vice versa. They can exactly reproduce a performance of a series of irregular durations. Notice that metronomes can also be thought of in this way: as primitive recording devices. In a culture without recording devices, metronomes provide the only universal alternative to personal tuition when one is trying to give meaning to (or retrieve meaning from) a notation. Its not surprising that metronomes became increasingly important to the 19th century time paradigm, even though in practice musicians were becoming more and more flexible... The changing role of institutions

I'd like to end this historical survey by telling you a story about how the internet is changing the way institutions work. I think its very important to try to keep one eye on the overall picture.

The story is about my web site and, in particular, about my essay “The Notation of Time” (1985).

For me, “The Notation of Time” marked a personal breakthrough. I had decided that solving the fundamental problems in music notation was more important to me than becoming a composer. While continuing to keep my nose to the drawing board as a practical copyist, I had been able to stand back from the problems of day-to-day composition, and look more dispassionately at the problem of music notation. The essay became a frontal attack on the standard notation and the reactionaries who thought they could take advantage of the Avant-Garde's collapse. Apart from containing an early version of the above historical survey, the essay places great emphasis on maintaining a strict distinction between the typographical rules governing symbols (in space) and the meanings of those symbols (in time). It clearly benefits from my having spent years pushing ink about on paper without having to think too much about the symbols' meanings.9 It could only have been written by a copyist.

On a sociological level, the essay was published in “Contact” magazine in 1985. Contact was a journal of contemporary music, and a means of communication between young composers - it was an idealistic enterprise, subsidised the Arts Council of Great Britain. My essay had, of course been rejected by more scholarly journals because I'm not an academic, and it didnt follow the usual rules. Contact magazine ceased to exist in 1986 or 1987, and the essay was soon forgotten, except by myself and a few close friends. Since that time, I've been pushing these ideas at people in the academic world whenever possible - but the academic world had its own rules, and nobody took these things really seriously until I was able to publish them on the internet in 1999. Even institutions cant afford to ignore accessible ideas that may contain a seed of truth. This is a good example of how the internet has begun to revolutionise the framework for research and institutions.

1.3 A summary of the current technical problems

The proposals described in Part 2 of this talk will address the following problems:

Part 2: A proposed solution

2.1 Social aspects of the proposals

Before I go on to talk in detail about the technical aspects of the solution I'm proposing, I'd first like to say a few words about its social aspects.

2.1.1 The role of artists

It seems to me that the role of artists needs to be rethought. My own view, is that we no longer need heroes because it is no longer thought that the (material) world is ultimately explainable. We no longer need a dualistic opposition between material and spiritual worlds.
Artists can no longer pretend to be above nature, but we do still need a few iconoclasts working outside particular human systems - reminding us that those systems are intrinsically incomplete (remember Gödel). This also has a lot to do with the question of interdisciplinarity.

The difficulty for this kind of artist is that he/she cant expect any help from the institutions. On the surface, this probably sounds as if I'm an anarchist - but thats not quite true! The answer lies in further precision, and thinking in terms of levels. I have always thought that individual freedom of thought has to be financed with moneys earned with other services to the community.

In short, I think artists have to become independent of those decadent institutions which still expect composers to solve their own technical problems while continuing to be “heroes”.

2.1.2 Software development

The problem of music notation cant be separated from its social aspects - its about communication, and is an intrinsically social phenomenon. So we need to think carefully about how the current, systemic problems can be overcome.
The sociological aspects of software development are only just beginning to be understood. Most current software has been developed for commercial reasons, and is the result of user demand. Such software tends to support existing, perceived needs within the existing socio-economic structures, and so to support those structures.

We are however here trying to transcend the systemic problems of decadent institutions, so we cant expect much support from that direction.

Recently, the world has seen how software developed in a non-commercial context can cause great sociological change. Browsers and the internet arose out of a need discovered within scientific research establishments. They were not the result of public demand, and were not developed from existing, commercial software. The revolution they caused, happened when the commercial world and the general public discovered that they made life more profitable and/or interesting.

So I think that the proposals I'm making could be developed, like browsers, in a non-commercial context, before they are let loose on an unsuspecting public.10

2.2 A Graphic User Interface 11

This presentation develops ideas which have been evolving in my previous papers. These papers can be found at my web site.

2.2.1 The practical context 12

My proposal is for a Graphic User Interface with which music can be edited and developed. The software and its context have four interacting regions:

Notice that the User is part of a double feedback loop. The score can be edited (object creation, writing) - whereby default values are taken from the libraries - and performed so that the events can be heard (listening, event perception). Going the other way round the diagram, something can be performed (event creation), resulting in visible relationships in the score (object perception). This double feedback loop was I think responsible for the development of written, western music. The current breakdown of this double feedback loop is, I think, responsible for the current lack of development in written music.

2.2.2 A proposed editor for developing music 13

Traditionally of course, scores have been written on two-dimensional paper, and “performance practice” has been developed and stored in the minds of composers and performers.

We are dealing here with music represented on computer screens. The proposed GUI consists of nested editable windows.14 The libraries which contain the generalised spatial and temporal definitions of the symbols and analog controls are stored in corresponding, interdependent libraries.

2.2.3 Event analysis (“chunking”)

This is the process whereby each event in a series of events (represented in a space-time diagram) is given a separate symbol (or name), and the event's name is connected to the space-time info at a lower level. Consider the following space-time diagram:

As far as a machine is concerned, this is a single, undifferentiated curve. People however instinctively break such curves into manageable chunks. Such chunks can be labeled just by putting a dot on each peak (the dot might be oval, like a notehead). Alternatively, the labels could be numbers or letters or duration symbols etc. giving more precise information about the event.

The lengths of the “events” can be classified, irrespective of the existence of a tempo, using a logarithmically constructed trammel. Using the classic duration symbols means that legibility can be improved later (horizontal spatial compression, use of beams), and it becomes easy to develop closely related higher level notations.

It would be useful, if standard notation of tempoed music could be a special case here. Standard notation has evolved to be very legible, so it would be a pity to throw away that advantage. A histogram can always be constructed from the lengths of the events (for example by first sorting the lengths into ascending order), so if the diagram contained lengths having proportions 2:1 (as in classical music without triplets), then it would be very easy to construct a trammel to produce a transcription similar to classical notation. If there are no such proportions in the original diagram, the user might relate the trammel to the shortest length, or try to ensure maximum differentiation in the resulting transcription. In any case, the user should have control over the trammel and the transcription.

I'm using space to demonstrate the algorithm here, but non-dimensional numbers (or bits in a MIDI stream) would also work. Note that beaming (which has been used freely here) improves legibility, and has no other function as far as this transcription is concerned.

2.2.4 Other parameters

The use of trammels is generalisable for other parameters. Consider the following:

In addition to using the durations trammel (as previously), this transcription has been made with a trammel for “dynamics” (the height of each event, see above left) and a trammel for “pitches” (the colour of the event, see below).

(Any steps you can see in this scale from black to white result from limitations in the GIF standard.
The scale is conceptually continuous.)

Interestingly, the perception of equal steps in both pitch and dynamic is related to logarithmic steps at the machine level (both the vertical scale and the gray scale in the above diagrams should be considered logarithmic).

The “pitch” symbols are purely arbitrary here (e.g. I could have used alphanumeric symbols, and/or the grayscale might have denoted some other parameter - e.g. synthesizer patch). I've done this to make it clear that there is but a short step from here to something like standard notation - and I'm trying to rescue as much legibility as possible...

Once the actual values have been chunked and given a label (symbol), the windows S1 and A1 can be completed in the score (GUI). The A1 windows contain the actual, precise values taken from the machine level of the original events. No information is lost.

It is quite conceivable, that more complicated symbols could be similarly defined at this stage - for example staccato dots and accents, classifying particular envelope forms.

All these trammels (or their numeric equivalents) connect symbols with their generalised meaning, and are stored in the library S1 together with the definitions for how each symbol moves about in space. (The library is, of course, a software module which can be selected and changed by users.) Library S1 might also contain a precise default value for each symbol, for use when inserting a new event in window S1, but the default value could also be a function of the local context at which such an event is inserted (e.g. the pitch of leading notes is sharper than other notes...). There may be feedback between the S1 window and its symbol library (see Music Notation and Agents as Performers). The default value is not necessarily just the mean value of the possible range, though this might be a good place to start before getting more complicated.

2.2.5 “Zeros” and Transformations

The character set for event lengths (flags etc.) needs to be complemented by a set of symbols for vacant spaces between events. The traditional symbols for rests would seem to be the logical choice (legibility preservation).

Many parameters may have symbols for transformation. But this is not true of durations. Durations already have a time component, so they cant transform - there is no such thing as an event whose length changes (!)... Transformation symbols for other parameters may include

2.2.6 Legibility and other practical considerations

Here is the transcription from §2.2.4 again:

Legibility can be improved, and a higher density of information achieved, by:

Group symbols such as beams and omitted dynamics might be defined for the second level symbolic window (S2).

The “pitch” characters are not necessarily related to pitch - they can also be used for other parameters. This would reduce the number of symbols whose spatial behaviour has to be defined. Such symbols have abstract uses - they could, for example be used as general-purpose slider knobs. Possibly alternative representations for each parameter should be available (e.g. dynamics with the traditional symbols or as noteheads)


2.3 Further Notes

These notes were the same as the notes I made in Developing Music with Software Tools 2.2.

Footnotes March 2002

I gave the lecture on 28th February 2002. These footnotes were added in March 2002, after I had returned to Europe.

Footnote 1

Except for the removal of references to publisher's problems, this section (1.1) duplicates material first presented in my presentation “Developing Music with Software Tools”, delivered at the Centro tempo Reale in November 2001. return

Footnote 2

I recommend listening to the whole piece while following the full score. How should one notate what the performers actually did?? return

Footnote 3

They become involved with conflicting concepts. It becomes difficult for them to know what to think or what they mean. . . return

Footnote 4

At this point I demonstrated in real time why the subdivision of a single segment of time is impossible. See also the argumentation in “The Notation of Time”. return

Footnote 5

Pierre Boulez: Penser La musique aujourd'hui (Paris, 1963); English translation by Susan Bradshaw and Richard Rodney Bennet, as Boulez on Music Today (London: Faber and F aber 1971, especially pp. 91-94. return

Footnote 6

As far as I'm concerned, there is only one kind of time. The different forms of this time should be notatable within the same notation paradigm. I think Boulez gets involved with ambiguities (bottom of p. 93) for two basic reasons: 1) as a post-neo-classicist, he assumes the notation-performance equivalence (ignoring performance practice) and 2) because both “striated” time (where there is a perceivable tempo) and smooth time (no tempo) can be notated using both 1950s standard notation and pianola roll notation. And there is no clear dividing line between striated time and smooth time. When does a tempo cease to be perceivable? return

Footnote 7

Karlheinz Stockhausen: ...wie die Zeit vergeht... in German in Texte zur Musik Band 1 (DuMont, Cologne 1963 - now available from the Stockhausen-Verlag); Also in Die Reihe #3 - English translation as “ time passes...” by Cornelius Cardew, 1959. return

Footnote 8

a)The footnote to Stockhausens Klavierstück I says that the complex time proportions (notated with subdivision symbols) should be worked out and played as tempo changes, but this does not get us very far because the tempi still have to have mechanical orders of precision.
b) Notice also that the mechanical level corresponds to “hardware”, and the perceived, symbolic level to “software”. See the chunking procedure in Part II.
c) Notice that there are neither objects (in space) or events (in time) at the purely mechanical level (the level Stockhausen is dealing with). I think that objects (space) and events (time) are created by our perception as a strategy for reducing the amount of information it has to handle. Before chunking occurs, what we perceive is purely amorphous. See also e.g. Goodman: Languages of Art - Hackett Publishing Company Limited, 1976- : “Experiment has shown that the eye cannot see normally without moving relative to what it sees; apparently, scanning is necessary for normal vision ”. So time is necessary for normal vision. Something similar can be said of ears: holding them stationary drastically impairs their ability to perceive three-dimensional space. If there are no events or moving objects, time and space cease to exist... return

Footnote 9

The Notation of Time also benefitted from my having begun to program computers (1980), and from my having read (among other things) Douglas Hofstadter's “Goedel, Escher, Bach: An Eternal Golden Braid ” (Basic Books, 1979). return

Footnote 10

As I pointed out in “Developing Music with Software Tools ” , I think that the development of music can be led by software, not only because it reduces our dependence on institutions but also because software can be understood and used by people who understand neither how it was written nor the design decisions which have been taken. It is not necessary for users to be experts on the design of user interfaces. The whole point of those design descisions is to make the software transparent, so that users can get on with what they want to do. See also my email exchange with Nicola Bernadini last November. return

Footnote 11

Part 2: While I presented diagrams very much like these in Santa Barbara, I extemporised their explanation. The lecture in Santa Barbara was filmed, so it is possible to reconstruct what I actually said. The explanations here describe the state of these ideas in March 2002, and are more or less what I said on February 28th. return

Footnote 12

The following changes have been made to this diagram in March 2002 (after my return from Santa Barbara): return

Footnote 13

Changes corresponding to those in Footnote 12 have been made to this diagram (also after my return from Santa Barbara). return

Footnote 14

In Santa Barbara, I was asked about the future performance of music from paper. I think it is so practical for performers to use paper, that this will continue. It is both unnecessary and prohibitively expensive for performers to read computer screens. I expect it will be possible to define one of the symbolic levels to be printable for performers, but composers and editors dont have to work at that level all the time... return