John Paynter

Music as the art of the possible

Teaching from what is offered

The teacher's task is, first and foremost, to awaken in young composing pupils a spirit of inquiry so that they can offer back the products of their imagination. However, this should not be interpreted as a "free" or "discovery" method which leaves children to find out for themselves what they need to learn.
The teacher's influence is paramount in
Primarily, the teacher teaches by drawing from the pupils' compositions musical principles which can be discussed and from which everyone can learn. When a piece has been heard, something of musical significance must be said about it, wherever possible calling attention to parallels between the pupils' music and that of established composers. This last point is especially important. "Teaching from what is offered" does not mean restricting the scope of learning to what the pupils themselves produce. They must be given the opportunity to understand their own work in the context of the best that musical tradition has to offer. Only by becoming aware of a core of music which is widely accepted as significant can any of us sensibly experiment with other possibilities. It follows that
Here we are not speaking of simple musical theory but rather of understanding what music is for, why it functions as it does, and how aesthetic judgements are made. A deep knowledge of musical possibility (what is music, and how it is music) is essential as a basis from which to discuss pupils' compositions, to help them to explore unfamiliar musical territory, to sharpen their critical faculties, and to develop independence of mind.
There are no formulae for composing. Music is not created by rules or recipes. Even if it is derivative it will have some special meaning for whoever has made it. "Making a borrowed idea your own" is a well-established aspect of originality, one that was cultivated by baroque composers -- notably Handel -- to great effect. It is also worth remembering that, traditionally, jazz musicians begin by imitating players they admire, and from there develop their own styles. Every piece of music is unique, and in its own way -- however naive or untutored -- reveals something of the ideal wholeness to which human nature aspires. Music models that ideality in sound-worlds which have no need of verbal explanation: it is made to be heard, not analysed.
That being so, how can we say anything at all about the music our pupils create? If they like what they have done, does it matter what anyone else thinks? With regard to music's purpose generally, it does not matter at all; it is enough that the music is made. After all, when we listen to an acknowledged masterpiece, we do not ask what was its conceptual basis! We accept it and delight in it for what it is, and we recognise that it is an acknowledged masterpiece precisely because we can learn from it something of lasting and humanising value. All art educates, but it is as art that it educates: and we learn most from the most successful art.
Learning how to learn from music itself should be the main business of musical education. By composing, and by developing a sense of adventure about how individual pieces of music work, pupils can begin to see why some pieces "succeed" and others, apparently, do not. From that they may come to understand what is interesting or exciting -- or, perhaps, disappointing! -- in the many different kinds of music they encounter. Obviously, it is important to consider what makes music successful. We all know that some pieces are "better" than others, but how are such judgements made? These are matters for discussion. When we have just performed or listened to a piece, if we feel that it is not completely satisfactory, or that it does not match our expectations, can we discover why that should be so? Questions about the "language" of a piece and about why it works as it does go to the heart of musical experience, and therefore we must educate our pupils to ask, about the music they create and also about other music, "is it as good as it can be?" and to have some idea of what "good" means in that context.

"Le charme des impossibilités"

With this now famous phrase Messiaen introduced the driving force of his musical language1: a fascination with "certaines impossibilités mathématiques des domaines modal et rhytmique".
For him, the "barriers" of modes of limited transposition and non-retrogradable rhythm patterns presented a challenge to the imagination, compelling him to expand his thinking by extracting more and more structural opportunities from unalterable resources. Others have written about the process of composition in somewhat similar terms: Stravinsky, for example, in Poétique musicale (1942):

My freedom will be so much greater and more meaningful the more narrowly I limit my field of action and the more I surround myself with obstacles.
In fact, the challenge of impossibility is endemic in musical endeavour; it includes the kind of technical obstacles which fascinated Messiaen, but also it extends far beyond them. The time-form of music is the supreme "impossibility".
Almost anything in human experience may become the inspiration for a composition. The stimulus is transformed into Idea (an essentially musical concept of how the piece will sound overall), and then the composer faces the challenge of creating a form which will fulfil the Idea in time. That is to say, if the piece is to succeed, the content of the music in performance must quite literally "fully fill" listeners' perceptions of the time which the music appears to take. Of course, if music were completely successful it would go on for ever, fully filling all Time and (presumably) ending the need for further musical forms as substitutes. Hence, the paradox that, whilst we strive -- albeit unconsciously -- for the ultimate, every piece we make is but a model of "all-time" form; therefore it starts, goes on, and stops, because only in that way can it characterize the completeness that the human mind, stimulated perhaps by the limitations of a temporal existence, desires above all else2.

Form and Event

It is important, at the outset, to distinguish between these two aspects of musical process. Elsewhere I have attempted to show that the actuality of music is as occurrence (Event) rather than continuant (Object)3. We cannot speak of a piece of music as an "art object": even in the apparently fixed formats of printed notation or digital storage the information is no more than an indication of potential music. A composition or an improvisation is only truly music when it is heard: that is to say, when it is received by performers and listeners as an Event occurring in time: and it is only in that existence that judgements about the music, as music, can be made. Therefore, the central task of composition is to anticipate listeners' perceptions of time passing, and to satisfy those perceptions through a continuity induced from the Idea by means of interaction between musical materials and structural devices. If we express this diagrammatically, we should be able to see at a glance how the whole process works. For example, in the following, where is the listener's experience of the Event, which is the presentation (the "making present") of the completed form , which, in turn, is the outcome of carefully organized relationships between Idea , materials -- tones, rhythm patterns, vocal and instrumental timbres -- , structure , and function -- recollection of the original inspiration or other reason for the existence of the piece, such as a commission for particular players -- within a duration which is felt to be "right"4:

Immediately, the diagram raises questions about the relative status of its elements, and by trying to answer those questions we can hope to arrive at a clearer view of what is being attempted in the process we call "composing". For example, the proposed notation "= " could cause confusion between a required performance time (e.g. for a section of film music) and a listener's perception of how long the music lasts. But even without the potential for confusion, the positioning of these symbols in the diagram might suggest that the duration is an outcome of the what happens to the other elements. Merely by altering the sign "=" to "x", duration can be shown, not as an outcome of the process but as an influence upon it: something to be borne in mind:

However, is now equivalent in status to , which cannot be changed because it is in the past; a memory of the original stimulus, exerting influence upon the invented materials but not itself capable of being modified by the action. Is duration really like that? of the action but not in it? This is a matter of some importance, because however memorable the materials and motifs are in themselves (a plaintive melody; a stirring rhythmic figure; an unusual combination of instrumental timbres or techniques), they have little meaning independently: their musical significance derives principally from the structural role they play in creating the wholeness of the form, and that depends crucially upon how long it appears to take. It might almost be said that when things happen in music is more important than what happens. Certainly it is as important; and that suggests that duration is an element of the core interaction:

Here the perception of duration can change throughout the process of composition: in no sense is it even partially a goal towards which the composer is working. This makes more sense. For, "rightness" is whatever is felt to be the most satisfactory continuity of the musical materials in relation to the overall passage of time as that is perceived when the completed work is performed. But how is this achieved? Of all the things that must be considered during the course of making a piece of music, the relationship between perceived virtual time and chronometric playing time is the most difficult to imagine. Is "success", then, due entirely to the composer's ingenuity, or do the musical elements themselves play a part?

What makes music possible?

Such is its extent and variety, both historically and geographically, that there would seem to be no end to ways of making music. Does this mean that anything is possible? -- that music is whatever anyone chooses to think of as "music"? " That which is capable of being conceived in thought" would be an acceptable definition of "the possible": and we could equate that with the musical Idea. However, as the process develops, the interactions and combinations of the materials generate further characters that were not foreseen: they did not form part of the earlier notion of what would be possible' and are, therefore, opponent to it, making the continuation of the original conception impossible5.
Ignelzi (1995) has argued that continuity in a musical work is the result, not of working towards a final cadence which will restore the state of rest out of which all music grows, but of the composer's attempts to avoid that return to homeostasis6. In a related paper, Fulvio Delli Pizzi identifies "swerves" which frustrate closure by creating, in the listener's mind, "expectations of further information"7. These swerves are also responsible for the essentially dramatic properties of music, which, as in any other dramatic context, characterise on the one hand
and on the other hand,
Composing technique is, then, the management of protagonistic and antagonistic structural devices, allowing the music to go on or drawing it back. Ultimately, the activity that has evolved from the Idea returns to stasis: the form must be completed -- or rather, be allowed to complete itself, perhaps? --. In order that the final recession should occur only when it is inevitable (at the precisely "right" moment), we have to learn to assess carefully the strength of tendency to closure in the opponent characters which arise, unforeseen, during the composing process. Thus, it is the impossibility of continuing along the original path that makes musical continuity possible.
The primary questions are, how much music will the Idea yield? and how far can the form be extended?8 Clearly, what is "possible" is much more than simply "that which can be conceived in thought": it is extended thought, the composer taking crucial decisions at key points throughout the process in order to sustain the flow of music. Beethoven's notebooks reveal just such a mechanism in his struggles to organize musical materials successfully, and to fashion, by many small changes, the "right" character of themes and motifs. Similarly, Schubert's unfinished piano sonata movements show him failing to find satisfactory ways of maintaining the formal impetus. All of which would seem to accord with Ignelzi's view that the composer's strategies are designed to avoid closure, and that it is the eventual reversal of the possible/impossible duality, whereby it becomes impossible any longer to avoid complete finality, which makes acceptable the death of the continuity and, thereby, the possibility of the time-model which we recognize as a completed piece of music9.

A path through a network

The finalized form is not so much a record of the composer's thoughts as a manifestation of the thought itself, transmuted into the flow of music from start to finish. This suggests a further refinement to our diagram; one which will show flow as an element of the core interaction which is interpreting Idea10:

To examine closely what happens in it may be helpful to borrow terms from physics and mathematics where it is also necessary to be able to demonstrate how processes operate. "News Function" defines the point of change when a normally static system does something that generates gravitational waves. This provides us with a useful analogy of the moment when a musical Idea comes alive (from a quasi-infinite stasis). The News Function begins the interaction which generates waves of interrelationships to form a Network through which an Optimal Path that is, the most satisfactory way to sustain the form until total closure can no longer be avoided is determined by means of choices taken at nodal points (Fig. 1).

Art does not imitate nature, but nature provides some interesting parallels with art. In this connection, Kant argued that the quality of wholeness which artists strive to produce by with their materials occurs in mature natural forms "by chance"11. Thus, a seed is complete in itself: it contains all that is necessary to project the Idea of "the plant". Once the seed is germinated (News Function), growth starts simultaneously below and above ground. Roots, stem, and shoots extend into a Network, and, by responding to every opportunity for continued existence, twisting this way and that way for just as long as is necessary to reach the available light or moisture, the plant avoids the demise of its form. When it reaches maturity (an Optimal Shape, perhaps?), the plant is characterized by a "form of finality" which makes it possible for us to recognise it as typical of its species.
There are parallels between nature and art also in matters of proportion, notably the incidence of the so-called proportio aurea [Golden Section]: those points of organic significance along the path of creation: points where things expand, join, bifurcate, rise or fall, and in so doing influence the stability in the form12. This is no less potent in music than it is in architecture, sculpture, or painting; but in music proportion is also the link between virtual time and measured time.
Numerous pieces of music appear to reach their points of greatest tension a little short of two-thirds of the way through -- that is, at the principal "aurea"[GS1] point: 0.618. Other structurally powerful features may occur at comparable nodes of the Network, and a sense of impending finality is likely to become evident at, or shortly after, GS3.

Such instants are not calculated; they are felt. Even in the spontaneous music of small children we can detect crucial "markers" occurring at, or very close to, the "aurea" points13. It is doubtful that a successful musical form could be achieved merely by calculating those points in advance in order deliberately to make them "significant"; nevertheless, both composers and performers need to cultivate a sensitivity to these time relationships.

What do we learn from this?

More than any other attribute, it is the ability to think about thinking that distinguishes us as human beings. It seems self-evident that such an important quality should be given prominence in education and in musical education no less than in other studies. Fundamentally, musical activity is intuitive: and we must cultivate musical intuition, especially in very young children. However, in world culture music has developed, over some thousands of years, as a manifestation of thought. In that context, "understanding music" means being able to hold on to the intuitive, felt, aspects of musical experience whilst at the same time exploring the musical thought on its own terms. This is why, in musical education, we need opportunities for teachers and pupils to examine together the language of music in relevant musical circumstances, and to discover how different pieces achieve their effect by strategies and "grammar" appropriate to Ideas.
This cannot be accomplished with mechanical exercises. Rather, it is by their thoughtfulness, displayed in the clarity and effectiveness of their playing and of the music they create, that our pupils' understanding will become apparent. This can be aided and encouraged: by careful questioning and discussion as we listen to pupils' composing in progress and to the completed pieces.


1. Stimulus (e.g. the music's function: its reason for existing: a title, a story, an assignment -- such as "make a piece for flute and violin", or "make a piece which explores...[a technical point: e.g. thirds]"). How did the composer(s) use it as a starting point? How was is discussed, and what led to the Idea?
2. Idea -- the overall musical concept derived from the stimulus. Can the composer(s) describe this? (Or play its principal features?)
3. Materials -- melodic and/or rhythmic motifs, extended rhythmic patterns, particular combinations of instruments and/or voices. How do these elements relate to the Idea? How were they derived from it? How might they be expanded (developed)?
4. Quality of invention (i.e. of Idea and Materials). How distinctive are the musical materials? Are they interesting and do they stir the imagination? Could they, perhaps, be more adventurous (more exciting and interesting)? -- and would that offer greater scope for transformation and development?
5. Interaction: what happens and when does it happens. Are there moments of particular significance? Is there sufficient repetition? Too much? Too little?
6. Perceived duration: is it about right for the Idea? Too long? Too short? What, in the music, suggests "rightness"? (or tells us that it is not "right"?)
7. Chronometric duration: what can we discover about the proportional relationships between the time taken by the piece as a whole and points where significant things happen in the music?
8. Degree of success: is the piece successful -- why?
Not as successful as it might be -- why?
Unsuccessful -- why? (Is it worth working at? Or should the composer(s) leave it and try a different approach to the same Idea or even a different Idea?
9. Context: what other music should these pupils now listen to? (Comparable Idea; similar structural procedures; similar instrumentation or way of playing a particular instrument.)


1 Olivier Messiaen, Technique de mon langage musical. Paris: Leduc, 1944, p. 5.
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2 Cf. Antony Storr, "Man's quest for integration and unity seems to be an inescapable part of the human is the art which most aptly symbolizes this quest." ('Music in relation to self'. In Music and the Cycle of Life. London: British Society of Music Therapy, 1988, p. 13).
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3 John Paynter, 'The form of finality: a context for musical education'. In British Journal of Music Education vol. 14. Cambridge: Cambridge University Press, 1997, pp. 5-21.
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4 Cf. Basil de Selincourt, "The beginning and ending of a composition are only one if the music has possessed itself of the interval between them and wholly filled it. For this reason there is no more crucial test of a composition that the test of its length. The piece that seems long is the piece that has failed to suspend our consciousness of real time". ('Music and Duration'. In Music and Letters, vol. 1. London: Oxford University Press, 1920).
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5 Cf. W.E. Johnson, Logic Part III: the logical foundation of science. Cambridge: Cambridge University Press, 1924, pp. 6-7.
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6 Michele Ignelzi, 'Homeostasis as Negative'. In Fulvio Delli Pizzi, Michele Ignelzi and Paolo Rosato, Rhetoric without a Rhetor. Three studies on the meaning of music in memory of Firmino Sifonia (1917-1995).
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7 "Various behaviours...dissonances, deceptive cadences, modulating processes, and so on" (F. Delli Pizzi, 'Musical Rhetoric is not a Will-o'-the-Wisp'. In F. Delli Pizzi, M. Ignelzi and P. Rosato op. cit.).
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8 The history of western music reveals composers striving continuously to create ever more extensive works of greater complexity and longer duration. This tendency reached a peak in the late nineteenth century and the first years of the twentieth century, and is still evident in that style which is (somewhat incongruously) called "minimalist".
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9 Every form, from the moment when it begins, is destined to conclude. Cf. the hour-glass as a symbol of "a life" (and, by association, with a musical form), in Visconti's film version of Thomas Mann's Death in Venice: "The opening through which the sand passes is so narrow that at first it seems that the level of the greater part is hardly changing at all. To our eyes it seems that the sand passes through only at the very end, and until that happens, it [the end] is not worth thinking about".
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10 Cf. Elliot Carter: "Music is the only world in which you can really manipulate time in rather a free way so that how you make the stream flow and what obstacles you put in to modify the flow, and so on, become fundamental." (Allen Edwards, Flawed Words and Stubborn Sounds, New York: W.W. Norton, 1972, p. 37).
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11 Immanuel Kant, The Critique of Judgement (1790).
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12 Cf. M. Ignelzi, op. cit.
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13 See Coral Davis, 'Listen to my song: a study of songs invented by children aged 5 to 7 years'. British Journal of Music Education, vol. 9 (1992), pp. 19-48. Also, for a more detailed discussion of the Golden Section in music see E. Lendvai, Béla Bartók: an analysis of his music, London: Kahn & Averill, 1971.
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© Copyright 1997 John PAYNTER