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       M U S I C          T H E O R Y         O N L I N E

                     A Publication of the
                   Society for Music Theory
          Copyright (c) 1995 Society for Music Theory
| Volume 1, Number 1     January, 1995     ISSN:  1067-3040   |

  All queries to: mto-editor@husc.harvard.edu
AUTHOR: Cochrane, Richard, J.
TITLE: The Phases of Fire
KEYWORDS:  Meyer, Deleuze, Heraclitus, postmodernism ontology

Richard J. Cochrane
University of Wales College of Cardiff
Department of Philosophy

ABSTRACT: The present paper begins by discussing Meyer's conception 
of musical conformancy in terms of the Platonic model which is implied 
in his *Explaining Music*. It goes on to argue, with reference to 
Deleuze and Heraclitus, that Meyer himself cannot base musical 
ontology on this model as he wishes, but is forced to base it on the 
very concept which the model attempts to exclude: the simulacrum. 

[1] Musical analysis has often relied on a concept which Leonard 
Meyer has called "conformancy." The importance of this notion can 
hardly be overestimated. The idea of similarity, and of a pattern 
which governs such relations of similitude, is crucial to it.  As 
Meyer defines it:

     By conformant relationships I mean simply those in which 
     one (more or less) identifiable, discrete musical element 
     is related to another such event by similarity.(1)  

A little later, Meyer gives a fuller summary of his idea of 
conformancy by means of the following "formula":

     C =  ---------

I have abbreviated the formula for easy reference (2).  "C" 
represents the strength of the conformant relationship, while the 
combined terms on the right-hand side of the formula are considered 
to be in direct proportion to it.  Regarding the right-hand side, the 
following symbols are used.  "R" denotes the regularity of the pattern. 
This is the most ill-defined of the terms, but it seems to mean simply 
that a pattern which is very complex will not be easily recognizable 
when it reappears.  "I" denotes the "individuality of profile," 
meaning that the pattern must not be too like the surrounding music.
"S" denotes similarity between the different copies of this model. 
These factors all enhance the effect of conformancy. Underneath the 
bar, "V" denotes the variety of events which comes between successive 
copies, while "T" denotes the time period between them. This way of 
looking at music would seem to work by means of model and copy. The 
model, which must be regular and individual (R.I), is reproduced in 
the copies, which must be similar to one another (S). I will now
briefly examine the implications of some of Meyer's conclusions 
about this view.

1. Meyer, Leonard, *Explaining Music* (Chicago: University of Chicago 
Press, 1973), p. 44.
2. The full formula is given in Meyer, p. 49. I have changed it only by 
abbreviating each term in his equation to a single letter.

[2] Meyer sets up two possible modes of conformancy relations 
between copies:  repetition and return (3). In repetition,
copies change processively with little or no other musical material 
between them.  Repetitive conformancy is therefore "developmental." 
In the case of the returning copy, however, much other material 
separates the two copies; the relationship is formal or structural. 
In the former case, the copy circles around the model (which is an 
abstract idea, not a musical object), picking up various of its facets.  
Repetition is thus about disclosure of the model through successive 
variations  of the copy: it is like building up a three-dimensional 
view of an object by combining a number of perspectival views. 
Return is more about the reappearance of the recognizable copy of 
the familiar model, after a period during which either the copies 
of another model were in evidence, or no model was discernable behind 
the music at all. (Meyer does not draw this distinction, but that is 
not a serious problem for his argument.) Repetition emphasizes the 
difference between copies of the same model, while return emphasizes 
the verisimilitude of copy to model.

3. Meyer, p. 49.

[3] With the distinction between repetitive and returning conformant 
relationships, Meyer hints, perhaps, at a view of music as a dialectic. 
This is a view which, as it turns out, he does indeed hold. Later (4), 
when speaking about hierarchic structures in general (which may or 
may not be made up primarily of conformant relationships), he lists 
five factors necessary for coherent musical structure. To be fair, he 
recognizes that he is talking about a very specific kind of music -- 
what we might, without very serious reservations, call Classical 
(and Romantic) music -- but he acknowledges this fact, and feels that 
his ideas might be more widely applicable if adapted.

4. Meyer, p. 83.

[4] The first factor is the requirement of both "similarity and 
difference." Copies, since they are copies of the same model, must 
be similar to one another. They must also, however, differ from one 
another, so as to create tension (or "stability-instability 
relationships"). Without difference, the same copy would be repeated 
again and again; even in minimalist music, this does not happen for 
very long.  The second factor is that copies must be clearly 
separated.  Thus, they must be separable units, or poses (5). 

5. I have discussed some of the problems which this raises in "The 
Ontology of Music," *Inside Out*, forthcoming. Basically, the problem 
arises with the attempt to derive movement from a set of instants. 
Zeno's paradox of the arrow is the classic case in point.

[5] Third, repetition is an essential element of the copy.  A copy 
is not heard as such (i.e. as different in kind from a passing phrase 
which is of little structural importance) until it is repeated. The
formal, returning relationships are thus founded on an initial 
repetition or series of repetitions.  This proviso must be 
supplemented, however, by the fourth factor:  that implications are there 
to be realized.  As I said above, a model is not a musical but an ideal 
entity, and represents more a series of potentialities than a melodic 
contour or rhythmic motive. Potentialities are not yet implications; yet 
some potentialities will find themselves "virtualized" in a specific 
musical context. At this point, we refer to them, as Meyer does, as 
"implications". These implications remain fairly abstract, however, until 
they are realized in the music itself. Returning conformancy can do this. 
The fifth factor is "harmonic cadence and tonal stability": the arrival at a 
point of rest, having actualized all those potentialities that were set up as 
implications by the initial repetition of the copy.  All this points 
to the return of the one (the first copy or, perhaps, its first 
repetition) as the Absolute, the aggregate of copies which realizes 
all of its own implications. Of course other potentialities within 
the model might have been turned into implications:  hence the 
tradition of writing variations on a theme invented by another 

[6] Meyer's analyses show a development of large-scale, or macro- 
dialectics (such as the movement of the whole piece, or a single 
movement) out of smaller dialectically constructed units, down to 
the micro-dialectical copy itself.  At each level, there is a sense 
of the virtualization of implications which are then fulfilled and 
bring the dialectic to a close.  As the dialectics become smaller, 
approaching their critical point in the copy, the sense of closure 
becomes less decisive, since less of the implications are fulfilled 
at that level.  Even at the level of the copy, however, a certain 
amount of closure is necessary in order to constitute the copy as 
a unit.  "Closure, then, is an aspect of patterning" (6). The idea 
of a hierarchy of closed blocks of musical sound, composed 
ultimately of copies and forming at the highest level the macro-
dialectical structure of the piece itself, is crucial to Meyer's 
conception of (at least Western tonal) music as a whole:

     A motive, phrase or period is defined by some degree of 
     closure.  On the level of its closure -- the level on which 
     it is understood as a separable event -- it is a relatively 
     stable, formal entity. Though it contains and is defined by 
     internal processes, once closed, it is not a process but a 
     palpable 'thing'. When in turn it combines with other events 
     at the same level and thereby becomes part of a higher-level 
     event, it again functions in a processive way. (7)

It should be clear from the above that Meyer's very subtle notion 
of musical structure rests on the idea of a hierarchic system of 
dialectics, functioning by the logic of model and copy. 

6. Meyer, p. 83.
7. Meyer, p. 90.

[7] In the second part of this paper, I would like to consider Meyer's 
position in the light of two statements. The first is that of Heraclitus: 
"The phases of fire are need and satiety" (8). The second is what Deleuze 
calls a "Platonic Dualism," which we must elucidate here.  He defines it 

     a subterranean dualism between that which receives the 
     action of the Idea and that which eludes this action. It is 
     not the distinction between the model and the copy, but 
     rather between copies and simulacra. Pure becoming, the 
     unlimited, is the matter of the simulacrum insofar as it 
     eludes the action of the idea and insofar as it contests both 
     model and copy at once. (9)  

What must be understood about this dualism is that it involves a 
difference in kind (10) between the Ideal model/copy system and the 
material simulacrum. It is not a difference in degree, such that "If 
we say of the simulacrum that it is a copy of a copy... then we miss 
the essential, that is, the difference in nature between simulacrum 
and copy" (11) . A favorite example: The idea of a table (model), the 
table (copy) and a sculpture of the table (simulacrum). The table 
"receives the action of the Idea" -- i.e., it corresponds to the idea of what 
a table is. The sculpture, however, is not judged by the same standards. 
We do not say the sculpture is good because it is comfortable to sit at, or 
has nice spacious drawers. The sculpture is judged exactly insofar as it is 
*not* a table -- in spite of its being, indubitably, a sculpture of a table.

8. Mackirahan, R.D., *Philosophy Before Socrates* (Indianapolis: 
Hackett, 1994), Heraclitus fragment DK22B65. I am using the most 
commonly known translation of the fragment, rather than that given in 
this volume.
9. Deleuze, Gilles, *The Logic of Sense* (London: Athlone, 1990)
10. On this term, see Deleuze, Gilles, *Bergsonism* (New York: Zone, 
1991), pp.21-29.
11. Deleuze (1990), p. 257.

[8] It is not that the simulacrum resembles the copy which 
resembles the model, the first thus being nothing more than an 
inferior copy of the model (like a recording of a recording of a 
performance). The copy resembles the model, but the simulacrum 
resembles nothing, or rather:  "If the simulacrum still has a 
model, it is another model, a model of the Other from which there 
flows an internalized dissemblance."(12)  If the copy is like 
a recording of a performance, the simulacrum is like a recording 
without a performance, perhaps finding an analog in some tape 
or computer musics. It can be seen that this is by no means a 
mere difference in degree. Let us assume that, when Heraclitus 
writes of the "phases of fire," he seems to be speaking of becoming 
(need) and Being (satiety). It would appear on the face of it that 
fire in fact involves only need:  when fully sated, the fire goes 
out.  Let us also place another pair of oppositions alongside 
these:  the simulacrum and the model/copy dyad. By fire, 
Heracleitus appears to mean change, a continual and primordial 
temporality.  Meyer, as we have seen, views a whole piece of music 
as governed by the logic of model and copy.  The development of a 
pattern in its copies, its variations and linking passages are all 
implicative: processive (repetitive) at their own level, formal 
(returning) at the next level up. Does this mean that Meyer rejects 
the dualism pointed to by Deleuze, preferring instead a kind of 
monism: a structurality based on the single Ideal model, and the 
similarities and differences which the copies bear to it?

12. Deleuze (1990), p. 258. This is in direct contrast with Plato's own 
view of the simulacrum, and of artworks in general; that they are 
nothing more than second-degree copies of the material world, and are 
therefore worthless.

[9] First, it must be recognized that Meyer's view cannot be 
reconciled with Deleuze's. The difference in kind between pattern-
based music and music formed of simulacra would upset his entire 
position. It is essential for him to exclude all relations in 
music which are not relations of similarity or difference vis a vis 
the Model. Indeed, Meyer even argues that certain musics do not 
conform to his notion of musical structurality:  

    nonhierarchic music -- that of John Cage, for instance, 
    moves, like the ocean, in undulating or sporadic waves of 
    activity in which we attend to, but can scarcely remember, 
    the particular events. (13)  

He seems to be arguing here that his almost ontological privileging of 
the model/copy system is not only specific to a particular sort of 
music, but serves to define an opposition between hierarchic and 
nonhierarchic musical styles. Need and satiety are therefore kept 
rigorously apart: the musics of Being (or approaching-Being, the 
partial copy) and becoming (which eludes the logic of patterning 
altogether) are said to be different sorts of music, and 
incompatible (even incompossible). Meyer characterizes the music 
of need as homogeneous, while the hierarchized music of satiety 
is based, as he points out, on similarity and difference (see 

     Only in the music of transcendentalism -- the music of 
     Cage, Earl Brown, Pousseur etc. -- is there complete homogeneity 
     and nondifferentiation.  Such music cannot be analyzed, only 
     described (14).  

While the term "transcendentalism" is probably not to be taken too 
seriously here, the terms "homogeneity" and "nondifferentiation" are. It 
is evident that Meyer sees hierarchic music as founded on differences, 
not similitude, which founds the avant-garde music to which he opposes 
it. It is also clear that the "analyzability" of the music is of great 
importance. The book, after all, is called *Explaining Music*, and 
begins with the following statement:  

     Experienced naively ... the world, as William James observed, 
     is a buzzing, booming confusion of discrete, unrelated sense 
     impressions....One may, of course, try to experience existence 
     in this way: unmediated by classes, concepts or relationships. 
     And a number of artists and writers -- for example, John Cage, 
     Norman O. Brown and Alain Robbe-Grillet -- have urged such 
     mindless innocence upon us... But [their] world... cannot 
     be understood. It has neither process nor form, meaning nor 
     value (15).  

The music which affirms the simulacrum -- i.e., that which 
denies the "action of the Idea," which is neither model nor copy -- 
would seem to be not just another form of music but a "naive" form, 
a childish receptiveness to the world of sound which is not open 
to analysis.

13. Meyer, p. 80.
14. Meyer, p. 6.
15. Meyer, p. 3.
[10] The music as he now describes is homogeneous only inasmuch 
as it is composed of absolute differentiation: "a... confusion of 
discrete, unrelated sense impressions."  What analysis requires, as 
Meyer rightly observes, is an object which can be broken down into 
"concepts, classes, or relationships." It is this kind of 
differentiation which is needed, a difference based on similarity, 
which operates hierarchically according to the notion of both 
similarity and difference within the copy. It is difference of 
degree of similitude which is to be measured, which can measured. 
Differences in kind cannot be quantified, since they are pure 
qualities. The music of Cage, therefore, is vilified for its childish 
refusal to enter the adult world of quantification, and its desire 
to affirm differences in kind absolutely. The problem is that 
Meyer happily acknowledges that the world "experienced naively -- 
without any psychological predispositions or cultural preconceptions 
whatever" is a world of the Cageian sort: homogeneous difference in 
kind, not differences in degree. "To understand [this] world, we 
must abstract from the ineffable uniqueness of stimuli by selecting 
and grouping, classifying and analyzing." Thus, the analyzable 
system is formed by an abstraction from the object, which is a 
simulacrum. The model/copy system is logically and chronologically 
posterior to the simulacrum, which is the object in its raw, 
unanalyzed state. If Meyer succeeds in "explaining music,"  he does 
so by creating an abstract, hierarchic system from the object, 
which is concrete and nonhierarchic. This he admits from the very 
beginning of his project, and he is right to do so.

[11] If the phases of fire are need and satiety, the logic of fire 
extends across both: the compulsion of need which sustains it and 
the cessating effect of satiety together form its dual dynamic. 
If Heracleitus is right, one without the other would be meaningless,  
and an analysis of one without the other would also prove 
philosophically inadequate.  Meyer's approach, too, would be 
ineffectual, hierarchizing as it does the two terms:  first, by 
arguing that nonhierarchized music destroys the natural dialectic 
of music, and second by arguing that it is prior to the analysis, 
which imposes the hierarchic structures onto nonhierarchized 
phenomena. The confusion about the epistemic status of hierarchies 
within Meyer's text requires an understanding of the logic of 
fire -- that is, the nature of temporality -- in order to move 
beyond it.


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