Looks with a smile of derision
Upon the magnified efforts of Art
To excel her works
By a continual breach of her laws
- Osborne Russell1
Music Theory and "Meaning"
Although the creations of nature could be seen as perhaps more complex, varied, and beautiful than any creative output of human beings, the goal of developing a theoretical understanding of nature seems a widely acceptable and even highly respected endeavor. Why then should it be any less appropriate to take a similar approach to the creative works of human beings, which could certainly not be said to be above theoretical analysis any more than the works of nature? Indeed, by looking to theories about nature we can perhaps not only find justification for the theoretical endeavor, but might also discover some insights into the nature of what a theory should be. In a field such as physics, we find that there are wide ranging theories that reflect not only observations and insights about the natural world but have great predictive powers as well.
"What is theory?" one might
ask. In music the examination of works
traditionally fallen into what I perceive as three categories: theory,
and criticism. In other fields of art, such as literature or painting,
categories have been outlined. In general, in these other fields,
is traditionally viewed as something that serves analysis and
criticism. In music a
similar situation has existed. However, too often in the academic environment what really amounts to
analysis is presented as theory. This tends to confuse the issue a bit.
Furthermore, the genre of the critical
review that appears in newspapers and magazines is often construed as
criticism, when, in fact, criticism is historically a discipline that primarily concerns itself with elucidating meaning.
In other words, theory concerns itself with the various structures and
processes that lead to the production of
meaning, while criticism is concerned with meaning itself. One can see where the problem with criticism in
music arises, for what does music mean? Or more appropriately perhaps,
In literature the question of meaning does not
seem so problematic. Because literature is based in language, and denotative and
connotative meanings are an apparent appendage
of most literary uses of language, the question of meaning is appropriate and the
role of the critic established. Here
too many theoretical disciplines (i.e., psychoanalytical, Marxist, Philosophical, anthropological) may be
brought to bear on the elucidation of
meaning, since the use of language ties them all together in one network. In music, although the elucidation of
meaning has enjoyed some vogue in the
past, particularly in the 19th century, today it is viewed with a great deal of skepticism. Yet, in
literature too, elucidation of meaning, which was so much a part of what
was commonly called the New Criticism, has
fallen from favor, or at least now has a powerful adversary. The main
reasons for this shift in emphasis are the new ways of looking at language that have developed in the field of
linguistics, new ways of looking at language that have stretched the
definition of what a language is itself. As
Jonathan Culler (1982) points out, "the categories and methods of linguistics, whether applied directly to the
language of literature or used as the
model for a poetics, enable critics to focus not on the meaning of a work
and its implications or value but on the structures that produce the
It took the
insight of Claude-Levi Strauss to see the wider range of application of the insights of linguistics.
Language, he reasoned, was a system
of meaning. Linguistics, in turn, had developed a way of looking at this system of meaning that was not concerned with
meaning itself but rather with the
structures and processes that made it possible for meaning to exist. He
then reasoned that there were other systems of meaning in the cultures of the world that were non-verbal that
could also be approached similarly to
the way that linguists were approaching language. The resulting approach has come to be called
Structuralism and its methodology has
spread to many disciplines and fields of inquiry. As Culler (1982) suggests, "structuralists take
linguistics as a model and attempt to
develop 'grammars' - systematic inventories of elements and their possibilities of combination - that would
account for the form and meaning of literary works,"3 or
works in any field that the structuralist
Music has not been untouched by this structuralist approach, although it has not been in the mainstream of the movement as literature has. This seems inevitable since the role of meaning in music is not so easily accepted as it is in literature. In What is Literature, Jean Paul Sartre states that "literature differs from all the other arts by virtue of its means ‑ language. Words ... signify; they convey meaning."4 Music has always been concerned with structure. Whereas the traditional approach to the teaching of literature has been to elucidate the meaning of works to students and to give them some tools for doing this, in music education the emphasis has always been more on understanding structures and processes. Nevertheless, music theoreticians have looked to the new insights in the field of linguistics and tried to bring some of this methodology to bear on the understanding of music. This contemporary approach to music theory is represented clearly in a recent book entitled Music, Mind and Brain, edited by Manfred Clynes. The opening article by Marvin Minsky, entitled "Music, Mind and Meaning," outlines the territory of the structural theorist and also articulates these theorists' approach to meaning. As we shall see this approach is quite different from that of the New Criticism in literature or of the 19th century theorists in music.
Minsky establishes one axiom of this new approach when he states,
"we must see that
music theory is not only about music, but about how
What can we learn from Minsky? First of all, in music theory we need to distinguish between theories of construction and theories of perception. To describe the way a twelve-tone serial piece is constructed is to give us insight into some part of the compositional process of the composer, to reveal his or her methodology. However, how this methodology relates to the perception of the listener is another matter. The perceptual understanding of the listener may be based on a whole different set of parameters that are not stated in the methodology, yet are understood intuitively by both the composer and the listener. These parameters must allow for the sending and receiving of wholly new information as well as information with which we are familiar. As Jeremy Campbell (1982) says, "a theory is an ordering process, and the order not only connects the known to the known; it also connects the unknown to the known."12 Furthermore, we often tend to think of theory as a simplification. While it is true that a complete description of something simple is often simpler than the thing itself, music is not simple. Music is complex and something complex is likely to be its own simplest description: "...the
relevant context for each element in the composition is the whole."13 Therefore, any attempt at theory must be seen as a reduction of the possibilities that exist in the piece itself, at least in so far as that theory seeks to be quantitative and thereby useful for analysis. Also a theory will either have to try to encompass many different strata, or else concern itself with one particular strata. That is, if we speak of music in grammatical terms, we can say that a theory can be a set of meta-rules that make possible the generation of a specific grammar; or it can be the rules of the specific grammar; or it can be rules about syntactical statements within that grammar. In the first case, we are dealing with the possibilities of all musics, existing and non-existing; in the second case we are dealing with specific musical systems and all the possible pieces in that system; in the third case we are dealing with a specific piece and possible descriptions of its surface structure. In the end, it is only the piece itself that can refer to all levels at once.
Since the third example, the syntactical theory, is only concerned with the immediate ordering of surface structure elements and, as Minsky has suggested, of only superficial interest, I will not go into details of such a system here. The second category, however, that of the grammar is a more interesting one and has spawned a fair amount of thought as well as a few
clearly articulated systems and useful tools. Heinrich Schenker's graphic analysis approach is an early example of work in this area. The key ingredient in his system is a hierarchical approach that allows the music to be divided into gestural strata that become increasingly more simple and yet correspond to the reality of the hearing process of the listener. He showed the time-span importance of larger formal gestures and also gave a preeminent role to the actual act of listening to the music. This brought the menagerie of former techniques, particularly harmonic analysis and formal analysis, under the rubric of one hierarchical system representable by a graphic display that, while at times a bit difficult to penetrate, is nevertheless elegant and revealing. His work established the goal of the so-called generative music theory as trying to provide an account of the musical intuitions of the listener. (For Schenker this meant the experienced listener in the tonal idiom.) While revealing structural features of the music he was guided by the apparent psychological reaction of the listener to the music. Although he did not label it such, he was apparently focusing on the evidence provided by the difference detectors in the brain.
Furthermore, Schenker and his disciples, such as Felix Salzer, by introducing the concept of prolongation into music theory, succeeded in accounting for the importance of musical memory, while also moving beyond the syntactical nature of previous harmonic analysis. They looked at the totality of a piece of music, where each chord structure could be seen in its overall context, thereby exploding the theory of constantly shifting modulations which chord syntactics implies. By defining the notion of contrapuntal chords as the structures of prolongation, they reserved the term harmony for those chords that are the essential framework of the piece and are therefore the structural guideposts that the contrapuntal chords move between and within. This established a hierarchical framework that would allow the notion of harmonic prolongation as well, where a structural harmony could contain within it a modulatory substructure, without losing its main structural identity, even when the substructure has, in some cases, a fairly lengthy time-span. By building upon the language of previous harmonic analysis they put a new emphasis on progressionalism and created what for them is a very clear notion of harmony.
Ray Jackendoff and Fred Lerdahl have attempted to extend the grammatical approach. They have isolated four distinct hierarchical structures for describing music: grouping structure, metrical structure, time-span reduction, and prolongation reduction. Grouping structure deals with motive, phrases and sections. Metrical structure is concerned with beat patterns. Time-span reduction is concerned with the relative importance of events within discrete durational parameters. And prolongation reduction is concerned with the hierarchy of pitch stability, emphasizing connections among pitch-events and their movement towards tension and relaxation. Like Schenker, they attempted to bring apparently disparate parameters into the hierarchical relationships of one system and to represent those relationships graphically so their connections can be easily grasped. Like Schenker they emphasize structural simplification and the importance of being responsive to the intuitions of the listener. They go beyond Schenker in attempting to account for temporal patterning and to represent human cognitive abilities. Overall they have presented some useful analytic tools. Yet they too have confined themselves to the particular grammar of the tonal idiom.
To step outside the tonal idiom we can turn to James Tenney. In his article "John Cage and the Theory of Harmony," Tenney settled on the notion of harmony as an area of valid concern for theoretical approaches. However, he feels that the definition of harmony has become too narrowly constricted to the specific language of the triadic system. Instead, he feels it should be expanded again to include a broader notion of vertical organization in music. Pointing to the work of John Cage as emphasizing the multi-dimensional character of sound space, with pitch as just one of its dimensions, Tenney has pointed to the multi-dimensional nature of pitch perception itself. This multi-dimensional space he calls harmonic space. With this spatial notion in mind he maps a network of harmonic distance based on a city-block metric, also adding the notion of tolerance range to the overall concept. This leads him to define pitches as a lattice work of points, while allowing for the reality of a continuum. Tenney (1984) states, "an interval is represented by the simplest ratio within the tolerance range around its actual relative frequencies, and any measure on the interval is the measure on that simplest ratio."14 Tenney's approach allows for an expanded notion of harmony beyond the three-dimensional harmonic space of triadic/tonal music (which is based only on the prime numbers 2, 3, and 5). As he says, "new compositional approaches to harmony will almost certainly involve new microtonal scales and tuning systems, as well as for the analysis of the old ones."15 Tenney expands the notion of harmony beyond the triadic progressionalism of Schenker to include that aspect of musical perception which depends on harmonic relations between pitches - i.e., relations other than higher or lower. Furthermore, he establishes what he sees as the important first principle for a new theory of harmony: "that there is some (set of) specifically harmonic relation(s)
between any two salient and relatively stable pitches.16 Also, Tenney is wise enough to see that there are limitations to any theory of harmony. He suggests that "a theory of harmony can only be one component in a more general theory of musical perception, and that the more general theory must begin...with the primary dimension common to all music: time."17 Although Tenney is still dealing with points and intervals, he has opened the door to Cage's notion of sound as, not "one of a series of discrete
stops, but as the transmission in all directions from the field's center."18 He has given us tools for establishing a multi-dimensional lattice-work defining such a field, while at the same time showing the field centers (as defined by whatever number of dimensions we wish to operate in) and the spatial relationships among these centers within the context of the complete field under consideration.
In his own work, Tenney has seen the desirability of moving beyond the specific grammar approach of someone like Schenker to a consideration of all musics. This has led him to what I earlier established as the first strata of my triumvirate of grammatical approaches, that of meta-rules. In his classic work Meta + Hodos, Tenney begins to develop the rules and methodology of a meta-system for examining music. He attempts to free his analytical tools from the language of any specific musical grammar. The key to his approach is what he calls the TG or temporal gestalt-unit. This idea is similar to that of the time-span in Jackendoff and Lerdahl. Like Jackendoff and Lerdahl, Tenney arrays this temporal gestalt into a tree graph showing a hierarchical relationship between what he calls element, clang, sequence, and the piece as a whole. These categories define the territory of temporal succession. Next he uses the terms monophonic and polyphonic to define the relationships that can exist among elements, clangs and sequences. He describes these possible relationships as simple-monophonic, simple-polyphonic, compound-monophonic, and compound-polyphonic. He then addresses the need to account for listener perception by pointing to factors of cohesion and segregation, the most important of which he calls proximity and similarity and their opposites, separation and difference.
Tenney continues by outlining the salient musical parameters that one must consider in analysis, being careful to define these as perceptual parameters and hence the need to consider their multi-dimensional nature. In relation to pitch, Tenney takes the notion of pitch height and pitch croma. With timbre he points further to spectrum, modulation, and envelopes; and with time he defines the sub-parameters of epoch, duration, and temporal density. Interestingly, tempo is seen as a special case of temporal density. This is significant, I think, because it relegates the perception of tempo, which is often neglected in analysis, to a place of importance where it can be understood as more than just speed. (Tenney's notion of temporal density is closer to the Javanese idea of irama than to our normal idea of tempo.) Finally, Tenney defines pitch-height (log-frequency) and epoch (real time occurrence) as distributive parameters "because a difference in at least one of these is necessary for two sounds to be perceived as separate."19 All other parameters he labels attributive parameters. Next, Tenney outlines the parameters of formal perception as state, shape and structure. "State refers to the statistical and other 'global' properties of a TG [temporal gestalt],...Shape refers to the 'profile' of a TG in some parameter, determined by changes in that parameter with respect to either of the distributive parameters, epoch and pitch-height...Structure refers to relations between subordinate parts of a TG."20 He sees the notion of shape as being time-dependent while he describes state and structure as "out-of-time" characteristics. He also points out that at certain levels of the hierarchy (i.e., element) these parameters may not be perceivable under normal conditions. He expands his idea of structure to include three sub-categories: statistical structure (relations between states), morphological structure (relations between shapes) and cascaded structure (relations between lower level structures). Finally, he points out that there is still another possible structure: "one involving relations between relations, rather than relations between (various aspects of) the TG's themselves."21 This type of structure he labels relational and defines three sub-categories: state-relational structure, shape-relational structure, and structure-relational structure.
After establishing these perceptual parameters he divides them into two categories. Those parameters whose variation focuses attention on shape he calls formative, and those parameters whose constancy create a sense of unity he calls cohesive. Considering parameters with respect to time he then defines the categories of ergodic (same state), non-ergodic (different states), isomorphic (same shape), heteromorphic (different shapes), and metamorphic (changing shapes, i.e., related by some process of transformation). Finally, Tenney points to the perception of variation (essentially difference detection) as perhaps the most important aspect of musical experience and he utilizes the notion of entropy as a measure of variation that can be applied to any type of structure.
Meta-Theory and Information Theory
Although primarily a structuralist, Tenney has seen the need for approaching music as a field of perception, while at the same time realizing that we must have quantitative mapping tools to use in the process of analysis. His search for meta-rules to delineate variation as a variable in relation to entropy reflects the recent insights of information theory. Claude Shannon first published his papers on information theory in 1948 while working at the Bell Telephone Laboratories. Although the theorems of information theory were directed specifically at problems faced by radio and television engineers, they turned out to have a much broader implication because they expanded the definition of what can be called a message. "By treating information in clearly defined but wholly abstract terms, Shannon was able to generalize it, establishing laws that hold good not for a few types of information, but for all kinds, everywhere."22 Whereas Noam Chomsky might ask, properly speaking, is music a language, it seems a little harder to question whether music is information. Jeremy Campbell sees such power in the theorems of Shannon that he suggests they have added a third component to the explanation of the world: "To the powerful theories of chemistry and physics must be added a late arrival: a theory of information. Nature must be interpreted as matter, energy, and information."23 The key ingredient in this new theory is the concept of entropy. Entropy measures a physical property, the transformation of energy from an accessible to an inaccessible state. "It has to do with probability, since the most probable state of a system in constant random motion is for all its contrasts to be smoothed out."24 In Tenney's system entropy is used as a measure of difference. Significantly, entropy is both subjective and objective. "The human observer cannot be excluded completely because the idea of order is inextricably linked to the mind's awareness."25 So human perception is a key ingredient in information theory, just as it must be in a theory of music. Also, in thermodynamics, entropy is an irreversible process. For this reason, it has often been seen as an index of the one-way flow of time. Since Tenney has suggested (via Cage) that time is the single most important ingredient in an understanding of music, entropy would seem to be relevant since it can be taken as a measure of time.
It is interesting, that around the same time Shannon was publishing his theories on information, Cage was laying the groundwork for his experiments with chance, which would surface in his compositions by 1951. Cage's work would seem to throw into a turmoil any possibility of arriving at an all encompassing theory of music that might elucidate the structural mechanisms that carry meaning. What could randomness and structure have in common? It is precisely this relationship that information theory addresses and as a result has brought about a re-thinking of the nature of probability. This newer interpretation of probability begins with the premise that:
a theory of probability is simply a method of encoding partial knowledge. In other words, it encodes 'missing information.' According to this view, probability, which is at the root of information theory, is inextricably connected with the amount and type of knowledge we possess about any given event or series of events whose outcome is uncertain. Serious difficulties arise when scientists try to separate the idea of probability from the idea of information, because the first cannot be defined
without the help of the second. In Shannon's theory, entropy is a probability distribution, assigning various probabilities to a set of possible messages. But entropy is also a measure of what the person receiving a message does not know about it before it arrives. Entropy is an index of his
uncertainty as to what to expect.26
So probability is a measure of both knowledge and ignorance, and since the purpose of communication is to send messages which are not fully predictable (whether the message be music, language, or something else), it must share properties in common with any process whose outcome is uncertain. Cage's music must be understood in such a context because in any given piece there are many elements about which we have a great deal of knowledge. By introducing chance into areas that normally attract our attention, he forces us to examine the other elements that have gone relatively unnoticed and to find the message that is there. Any music theory that hopes to account for the problems that Cage has presented must deal with the concept of entropy (as Tenney has) and the dynamic relationship between knowledge and ignorance that we find in probability.
Information theory would seem to be a fruitful area for the musician to examine when attempting to come to an understanding of music that would encompass all music. As Campbell says, "information is in essence
a theory about making the possible actual."27 That means it must account for the potential as well as the actual. A successful music theory must do this very thing, so that form can be treated as an "active, inherent principle
of change [that] takes part in the becoming of things."28 At the meta-level of understanding we are dealing with information rather than causality. And information is the result of a code, a set of rules that restrict the amount of choice by introducing a certain amount of redundancy, thereby making some possibilities more probable than others. The code strikes a bargain with freedom because too much freedom would result in high entropy and sameness, while the code, if it is a good one, makes possible unlimited creativity.
We must account for this dialogue between structure and freedom, between redundancy and entropy, if we are to describe the creative works of men and women, or of nature. With entropy, for the first time scientists were forced to face the possibility that not only did they not know everything about the world (or the behavior of gas in a container for that matter), but that it was not possible to know everything about anything. In order to grasp the nature of reality they would have to give up their particle or atomistic view of things and their Newtonian notion of causality. Information theory should help make this transition more palatable. Uncertainty upset scientists as much as it did musicians. Gradually, we are all getting used to the idea.
In Asphodel, That Greeny Flower, William Carlos Williams writes,
For there had been kindled
than that of the discoverers
and set dancing
to a measure,
a new measure!
The measure itself
has been lost
and we suffer for it.
We come to our deaths
The bomb speaks.29
By measure, Williams does not mean our contemporary notion of the word measure, which has come to denote a process of comparison of something with an external standard. Williams means measure, I think, in the original sense of the word. The Greeks saw outward comparison merely as a display of a deeper inner measure. Physical health was regarded as the result of the "right inward measure of all parts and process of the body. Measure is a form of insight into the essence of everything."30 Significantly, Protagorus said "Man is the measure of all things." In other words, measure does not exist independently from human beings and their perceptions. Furthermore, the physicist, David Bohm, points out that "measure is to be expressed through proportion or ratio....Of course, this ratio is not necessarily merely a numerical proportion (though it does, of course, include such proportion). Rather, it is in general a qualitative sort of universal proportion or relationship."31 Theory then is an exemplification of this notion of ratio, "in the sense of implying that as various aspects are related in our idea, so they are related in the thing that the idea is about. The essential reason or ratio of a thing is then the totality of inner proportions in its structure, and in the process in which it forms, maintains itself, and ultimately dissolves. In this view, to understand such ratio is to understand the 'innermost being' of that thing."32 So the measure that William Carlos Williams says we have lost is this inner measure, and he is pretty clear where he feels our more constricted notion of measure is leading. We are fragmenting our view of the world until we are on the verge of blowing it to bits.
Science as a Theoretical Paradigm
As I suggested at the outset, science, and particularly physics, provides us with a paradigm of what a theoretical approach should be. So even though science seems to have led us into the fragmentary corner in which we now find ourselves, current thought in physics might give us a clue to what theory should be in the coming cycle. In Wholeness and the Implicate Order, David Bohm addresses the problems that physics is faced with in the post-relativity, post-quantum mechanics period. First of all, he suggests that "all theories are insights, which are neither true nor false but, rather, clear in certain domains and unclear when extended beyond these domains....there is evidently no reason to suppose that there is or will be a final form of insight (corresponding to absolute truth) or even a steady series of approximations to this."33 We must realize that "experience and knowledge are one process, rather than to think that our knowledge is about some sort of separate experience."34 It seems, as Bohm suggests, that "nature will respond in accordance with the theory with which it is approached."35 Furthermore, relativity and quantum mechanics seem to imply "the need to look on the world as an undivided whole, in which all parts of the universe, including the observer and his instruments, merge and unite in one totality. In this totality, the atomistic form of insight is a simplification and an abstraction, valid.only in some limited context."36 While such a view might seem to spell the demise of theory, in fact, it simply redefines once more what a theory should be and places the theoretical in the open-ended realm of creativity where it belongs. With this in mind, David Bohm has defined what he calls "Undivided Wholeness in Flowing Movement." What he means is simply to imply that "flow is, in some sense, prior to...the 'things' that can be seen to form and dissolve in this flow."37 This means that in theoretical endeavors we need to look at "forming activities," not just forms, and not persist in holding to a truth beyond its proper limits. In the quantum domain, the procedure by which things are analyzed into interacting parts breaks down, "for whenever two entities combine to form a single system the process by which they do this is not divisible."38 In other words, our normal idea about the indefinite analyzability of each process into various parts breaks down.
In response. to these implications of quantum theory, Bohm creates a new description of reality which he calls the holomovement. This holomovement is unbroken and undivided totality and is undefinable and immeasurable. Contained within the holomovement is what Bohm calls the implicate and explicate order. This implicate order is an order that is enfolded into the whole and as such is indistinguishable from the whole. Under certain conditions an implicate order may become explicate. As Bohm says, "the word 'electron' should be regarded as no more than a name by which we call attention to a certain aspect of theholomovement."39 The electron is a theory that allows us to bring that particular aspect of the implicate order into focus. Therefore, things may seem to behave with a certain amount of autonomy, but this autonomy should not be seen as fundamental but rather as relative and limited in degree. In reality, "everything is enfolded into everything."40
It would seem that in Bohm's theory then, perceptive mechanisms are basically devices for unfolding the implicate order. A hologram, for example, is an instrument whose function is to make a static record of this order. So is our eye. The actual order is the complex movement of fields in which any point (just as in a hologram) contains information about the whole. Instead of a hierarchical ordering in which there is a point by point correspondence between the actual order and the image of it (as in a photograph), there is instead an implicate order in which one point contains information about all other points and is not just related to these other points by some measure of space and time. It seems to me that this analogy can be applied directly to our experience of music, where we must consider hearing as a process in which every element contains information about the whole: the experience of the whole is a constant unfolding (a "flowing movement") and not the gradual construction of some hierarchical model (holography not photography). In trying to develop an understanding of the "enfolded" nature of memory in the brain, Bohm turns to the act of listening to music as an example.
At a given moment a certain note is being played but a number of the previous notes are still 'reverberating' in consciousness. Close attention will show that it is the simultaneous presence and activity of all these reverberations that is responsible for the direct and immediately felt sense of movement, flow and continuity ... one does not experience the actuality of this whole movement by 'holding on' to the past, with the aid of memory of the sequence of notes, and comparing this past with the present. Rather, as one can discover by further attention, the 'reverberations' that make such an experience possible are not memories but rather active transformations of what came earlier, in which are to be found not only a generally diffused sense of the original sounds, with an intensity that falls off, according to the time elapsed since they were picked up by the ear, but also various emotional responses, bodily sensations, incipient muscular movements, and the evocation of a wide range of yet further meanings, often of great subtlety. One can thus obtain a direct sense of how a sequence of notes is enfolded into many levels of consciousness, and how at any given moment, the transformations flowing out of many such enfolded notes interpenetrate and intermingle to give rise to an immediate and primary feeling of movement.41
It seems that in music the enfolded order is "sensed immediately as the presence together of many different but interrelated degrees of transformations of notes and sounds."42 From such an observation Bohm concludes that "in listening to music, one is therefore directly perceiving an implicate order."43
Since we have lost the old measure, Bohm attempts to define a new measure that can guide us in our understanding of structure. "Evidently, we have here a new notion of structure, for we no longer build structures solely as ordered and measured arrangements on which we join separate things, all of which are explicate together. Rather we can now consider structures in which aspects of different degrees of implication can be arranged in a certain order."44 The new measure that Bohm introduces he calls the implication parameter (Tn), which would define the relationship between the total structure and its series of substructures. This measure would determine the degree of implication of the various substructures and would hence point to those aspects that would emerge from the holomovement at any moment. The picture present at any given moment would consist only of aspects that can be explicated together (i.e., aspects corresponding to a certain value of the implication parameter T). As events happening at the same time are said to be synchronous, so aspects that can be explicated together may be called synordinate, while those that cannot be explicated together may be called asynordinate. The more explicate an aspect, the more we tend to give it a separate identity. In turn, aspects that become explicate together (i.e, synordinate aspects), we tend to give separate identities but also relate them in some way. It is at this point that we begin to build hierarchies of relationships.
In his apocalyptic poem, Third Psalm: The September Vision, W. S. Merwin says, "0 objects come and talk with us while you can."45 Separated from the natural world and on a road to Armageddon, he is asking the world to reveal itself before it is too late. In modern poetry there has emerged a kind of poem known as the object poem. As Robert Bly
says, "the senses long to experience objects and things on their own."46 The object poem is a result of what Bly calls second stage art. The poet Novalis spoke of two stages in an artist's life: the first stage is one of introspection, the second stage is one of observation. What the poet is really concerned with in this second stage is seeing, what Bohm calls attention. In what I think was a strange misreading of the object poem, Roland Barthes says that "in it, Nature becomes a fragmented space, made of objects solitary and terrible, because the links between them are only
potential."47 While it is true that object poems often have a kind of existential feel to them, the real object poem could be described in Bohm's terms as an attempt to sense the implicate order and to partake in the holomovement as a uniting of experience and knowledge, of mind and matter. (Scientists are often engaged in observation as their primary activity. Perhaps for them the second stage is introspection.)
Some of Cage's music could be said to fall into this second stage, in the sense that it is concerned primarily with hearing, in the same way that the poet might be concerned with seeing. In fact, this kind of hearing is also a kind of seeing because one begins to see one's self hearing. That is, we become conscious of how we hear, conscious of the nature of hearing itself. And this is precisely what we must do to create a meaningful theory of music today. But this means more than just a structuralist analysis of the mechanisms of hearing. We must keep in mind too what the deconstructionists call the moment when logic fails. We have seen in quantum theory that something as logical as cause and effect does not have meaning in some contexts. Philosophically, the notion of causality was called into question by Nietzsche in his deconstruction of causality in The Will to Reason. Nietzsche demonstrates that it is our perception of the effect that causes us to perceive the so-called cause. As Nietzsche says,"the cause gets imagined after the effect has occurred."48 The principle of causality asserts the logical and temporal priority of cause to effect. Nietzsche demonstrates that it is really the effect that causes the cause. By doing so he does not eliminated the idea of cause, but rather he disrupts the hierarchy of the causal scheme and thereby the notion of origin. The question of origination cannot be resolved, for at the moment when one is about to do so it reverses itself (the particle becomes a wave, so to speak) and leaves us empty-handed.
Perhaps empty-headed would be a more appropriate image, since we still have what we had, causality, but our notion of it has been disrupted. There is a point at which any hierarchy will break down or reverse itself. This does not decry their usefulness. It only demands that we be conscious of their limitations. Newton's laws still have great usefulness in physics. So too, historical theoretical approaches still have usefulness in music. Barthes' distinction between the classical and the modern in literature is a valid one for music also, I think. The classical follows the order of an ancient ritual, it perfects the symmetry of an established relation. The modern forces our attention back on the basic materials, on the things themselves. "Not Ideas about the Thing but the Thing Itself,"49 as the poet Wallace Stevens says. Perhaps it is such a notion that led James Tenney to say, "Cage's most radical earlier innovations had involved extensions of materials and these may one day have more profound implications for theory than his investigations of method."50 William Carlos Williams' later dictum, "no ideas but in things," does not contradict Stevens. Rather it reminds us that our perception of things is an act of seeing and, as such, is a union of mind and materials. Modern art will always cause a re-thinking of theory while classical art will reaffirm the validity of a theory that is already established.
Tenney has pointed the way to a theoretical understanding that will encompass the broader range of musics that we are experiencing today. His concept of ergodic structures and the role of entropy are important insights that reflect the thrust of information theory and quantum mechanics. To further the structuralist approach we need to take a harder look at the notion of code, keeping in mind that we will never be able to distinguish the encoding as a material or perceptual phenomenon because, in the implicate order, these two are united. The notion of the implicate order sheds an interesting light on the concept and importance of time, too. David Bohm points out, "the whole implicate order is present at any moment, in such a way that the entire structure growing out of this implicate order can be described without giving any primary role to time. The law of structure will then just be a law relating aspects with various degrees of implication. Such a law will, of course, not be deterministic in time."51 If we relate such a notion to music we would have to question Tenney's admonition (via Cage) that the primary parameter, the one which all aspects of music have in common, is time. Instead, we would have to say that time is a secondary parameter, not having any bearing on the implicate order and therefore on the wholeness or potentiality of something, but rather only having bearing on the explicate order and a particular manifestation of that potentiality. Time could be seen, in this light, as the governing parameter on the explicate level and, as such, one which in some way controls or affects relationships only between what Bohm calls synordinate aspects, but not between asynordinate aspects. Perhaps we may consider Bohm's implication parameter Tn as a possible tool in analyzing the relationship between the implicate and the explicate, where T equals the aspects of different degrees of implication, and n equals the action required to explicate something from the implicate order. The concept of time itself is so integral to life yet so little understood that we might be better off to consider the notion of timeliness rather than time. Time implies, too often, an inexorable forward flow, while timeliness implies the appropriateness of something to a given context. In perception, time and memory are somehow interlocked. Consider the image of Orpheus, a great musician who can out-play the sirens, but can save what he loves only by renouncing it. He is moving ahead but at the same time is filled with the desire to look back. The "arrow of time"52 is the moving ahead, while the "looking back" is memory. Significantly, the desire to look back is a combination of the two: like T. S. Eliot's The Wasteland where "April is the cruelest month, breeding/Lilacs out of the dead land, mixing/Memory and desire."53
The story of Orpheus is a myth, but theory too is a myth. According to Claude Levi-Strauss, myths are "logical techniques for resolving basic • antinomies in thought and social existence....all explanatory models for fundamental states of affairs, whether sophisticated or primitive are myths."54 This does not mean that we should stop creating these models. Those who would hold with what the poet Donald Hall calls the theory of no theory are not, in fact, reacting against theory at all. What they are reacting against is the notion that thought and action are one, that mind and spirit are one. Instead, they cling to a fragmented view of the world that separates the human dimensions into islands in the stream, rather than combining them into one flowing movement that is the stream itself. But the overly analytical approach will not suffice either. As Anthony Braxton states in his Tri-Axium Writings:
I recognize that the extremities of a given analysis can reveal different aspects of how to view a particular essence, and certainly I accept the notion that the extremities of analysis can help differentiate the cynamics of what procedures can be understood and utilized, but I disagree as to what this phenomenon ultimately means. My point is that - there can be no new music unless there is a new reality, and unless there is a new vibrational and spiritual basis from which investigation can be made to express not only the empirical surface laws surrounding how a given phenomenon seems to work but also including the spiritual position of that phenomenon.55
So we should continue to pursue the structural examination of music, looking to information theory, linguistics, spectral analysis, the theory of complex systems, physics, and other places for new tools, keeping our eyes open for forming activities and not just forms. Grammatical models of music will be very useful to composers who are attempting to apply computers to music, as long as they are used to identify or manipulate those parameters that can be handled more efficiently by the linear processing of the computer, or to isolate new parameters or approaches that come from the nature of the machine itself. However, as Curtis Roads points out, "a weak or trivial grammar model of a composition
is probably less effective than a strong, non-grammar model."56 The composer must beware of defining computer driven algorithms that make decisions based on such a trivial model or that might be better handled by the more sophisticated, multi-dimensional network of the brain. We should continue to make "systematic inventories of elements and their possibilities of combination - that would account for form and meaning..."57 But we should recognize, too, that the tables have not yet turned, that the awareness that I have spoken about in this paper is not yet common. Therefore the responsibility of the post-structuralist in music theory, if I may paraphrase Jonathan Culler, must be the same one that has emerged in the other arts: to investigate the way that the structuralist project is subverted by the workings of the pieces themselves, and thereby reveal the moment when logic fails. John Cage's idea of the Promised Land is a world of no music, where all sound is heard as music. We should take this not as a goal, but rather as a kind of eschatology that will lead us to open new doors. And perhaps we should think of theory as William Carlos Williams thought of friendship, as something "dangerous - uncertain -made of many questionable cross ties, I think, that might fail. But while they last, give it a good cellular structure - paths, private connections between the members - full of versatility."58
Barthes, Rolan Barthes, Roland, Le Degre Zero de L'Ecriture, Editions du Seuil, 1953. Writing Degree Zero, trans. Annette Lavers and Colin Smith, Hill and Wang, 1983.
Bly, Robert, News of the Universe, Sierra Club Books, San Francisco, 1980.
Bohm, David, Wholeness and the Implicate Order, Ark, Boston, 1980.
Boretz, Boretz Benjamin and Cone, Edward T., Perspectives on Contemporary Theory, Norton, New York, 1972.
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Cage, John, Silence, Wesleyan University Press, Middletown, CT, 1961.
___________ , A Year From Monday, Wesleyan University Press, Middletown, CT, 1963.
__________ , M, Wesleyan University Press, Middletown, CT, 1974. Campbell, Jeremy, Grammatical Man, Simon & Schuster, New York, 1982.
Chomsky, Noam, Selected Readings, ed. J. P. B. Allen and Paul Van Buren, Oxford University Press, London, 1971.
Cogan, Robert, New Images of Musical Sound, Harvard University Press, Cambridge, 1984.
Culler, Jonathan, On Deconstruction, Cornell University Press, Ithaca, NY, 1982.
Eliot, T. S., The Waste Land and Other Poems, Harcourt, Brace & World, New York, 1934.
Jackendoff, Ray and Lerdahl, Fred, "A Grammatical Parallel Between Music and Language," Music, Mind and Brain, ed. Manfred Clynes, Plenum Press, New York, 1982, pp. 83117.
Lidov, David and Gabura, Jim, "A Melody Writing Algorithm Using a Formal Language Model," Computer Studies, lv - 3/4, 1973, pp. 138-48.
Mervin, W. S., The Carrier of Ladders, Atheneum, New York, 1974.
Minsky, Marvin, "Music, Mind, and Meaning," Music, Mind and Brain, ed. Manfred Clynes, Plenum Press, New York, 1982.
Morris, Richard, Time's Arrows, Simon & Schuster, New York, 1982.
Nietzsche, Friedrich, Werke, Vol 3, ed. Karl Schlechta, Hanser, Munich, 1966.
Roads, Curtis, "Grammars as Representations for Music," Computer Music Journal, Vol III, no. 1, 1979, pp. 48-55.
Rudyar, Dane, The Magic of Tone and the Art of Music, Shambhala, Boulder, 1982.
Russell, Osborne, Journal of a Trapper, 1834 -1843, ed. Aubrey L. Haines, Lincoln, 1955.
Salzer, Felix, Structural Hearing, Dover, New York, 1952.
Sartre, Jean Paul, Qu' est-ce que la Litterature?, Gallimard, Paris, 1948. English translation, What is Literature?, Methuen, London, 1950.
Stevens, Wallace, The Palm at the End of the Mind, ed. Holly Stevens, Vintage, New York, 1972.
Tenney, James, Meta + Hodos and META Meta + Hodos, Frog Peak Music, Oakland, CA, 1986.
__________ , "John Cage and the Theory of Harmony," Musicworks, 27, 1984, pp. 13-17.
Williams, William Carlos, Selected Poems, ed. Charles Tomlinson, New Directions, New York, 1985.Williams, William Carlos
__________ , Autobiography, New Directions, New York, 1967.
1 Osborne Russell, Journal of a Trapper, 1834-1843, ed. Aubrey L. Haines, Lincoln, 1955.
2Jonathan Culler, Theory and Criticism after Structuralism, Cornell University Press, Ithaca, NY, 1982, p. 21.
3ibid., p. 22.
4Susan Sontag, preface to Le Degre do L'Ecriture, by Roland Barthes, Editions du Seuil, 1953. Writing Degree Zero, trans. Annette Lavers and Colin Smith, Hill and Wang, New York, 1983, p. xi.
5 Marvin Minsky, "Music, Mind and Meaning," from Music Mind and Brain, ed. Manfred Clynes, Plenum Press, New York, 1982, p. 29.
8ibid., p. 35.
10 ibid. p. 40.
11ibid., p. 44.
I2 Jeremy Campbell, Grammatic Man, Simon and Schuster, New York, 1982, p. 230.
13 David Lidov, and Jim Gabura, "A Melody Writing Algorithm Using a Formal Language Model," Computer Studies, IV - 3/4, 1973, p. 146.
14James Tenney, "John Cage and the Theory of Harmony," Musicworks, 27, Spring 1984, p. 14.
16 ibid., p. 17.
18 James Tenney, "John Cage and the Theory of Harmony," Musicworks, 27, Spring 1984, p. 14.
19James Tenney, Meta + Hodos and META Meta + Hodos, Frog Peak Music, Oakland, CA., 1986, p. 106.
20 ibid.,p. 107.
21 ibid.,p. 110.
22James Campbell, op. cit., p. 17.
23 ibid., p. 16.
24 ibid., p. 54.
25 ibid., p. 32.
26 ibid., p. 62.
27 ibid., p. 269.
29 William Carlos Williams, Selected Poems, ed., Charles Tomlinson, New Directions, New York, 1985, p. 231.
30 David Bohm, Wholeness and the Implicate Order, Ark, Boston, 1980, p. 21.
31Ibid., p. 30.
33 ibid, pp. 4-5.
34 ibid., p. 6.
36 ibid., p. 11.
38 ibid., p. 73.
39 ibid., p. 155.
40 ibid., p. 177.
41 ibid., p. 199.
43 ibid., p. 400.
44 ibid., p. 153.
45 W. S. Merwin, "Third Psalm: The September Vision," A Carrier of Ladders, Atheneum, New York, 1974, pp. 106-107.
46 Robert Bly, News of the Universe, Sierra Club Books, San Francisco, 1980, p. 211.
47 Roland Barthes, Le Degre Zero de L'Ecriture, Editions du Seuil, 1953. Writing Down Zero, trans. by Lavers, Annette and Smith, Colin, Hill and Wang, New York, 1983, p. 50.
48 Friedrich Nietzsche, Werke, Vol. 3, ed. Schlechta, Karl, Hauser, Munich, 1966, p. 804.
49 Wallace Stevens, The Palm at the End of the Mind, ed. Stevens, Holly, Vintage, New York, 1972, p. 387.
50 James Tenney, "John Cage and the Theory of Harmony," Musicworks, 27, Spring 1984, p. 14.
51 David Bohm, op. cit., p. 154.
52 The arrow of time' is a metaphor invented by Sir Arthur Eddington to express the idea that there exists a purely physical distinction between past and future, independent of consciousness. Such a distinction is based on the entropy principle, which asserts that as time goes on energy tends to be transformed from an orderly into a less orderly form." (Jeremy Campbell, op. cit., p. 83.)
53 T. S. Eliot, The Wasteland and Other Poems, Harcourt, Brace & World, New York, 1934, p. 29.
54 Susan Sontag, op. cit., p. xx.
55 Anthony Braxton, Tri-Axium Writings, Vol. 1, Synthesis Music, 1985, p. 353.
56 Curtis Roads, "Grammars as Representations for Music," Computer Music Journal, Vol. III, no. 1, 1979, p. 49.
57 Jonathan Culler, op. cit., p. 22.
58 Williams, William Carlos, Autobiography, New Directions, New York, 1967.