A Field Theory of Music Semiosis -- Part One

Copyright 2000, by Victor A. Grauer

Music, which, according to Umberto Eco, is "purely syntactic," with no "apparent semantic depth," presents very special problems, both for a semiotics of music per se and a general semiotics capable of including musical "signification" within its scope. One does not have to fully agree with Eco to see the difficulty. Few today would contend that any music can be "pure," totally free of cultural content, context and connotation. Nevertheless, the failure of anything we might want to call "music," in and of itself, without the assistance of verbal language, to clearly, consistently and unequivocally represent (i.e., "denote") some generally agreed upon referent or concept, has time and again posed what seems an insurmountable barrier to any theory of musical semiosis. The apparent lack of a clearly defined musical signified which could, in all musical "languages," be paired with a corresponding, clearly articulated, signifier, has created especially serious problems for those attempting to work from the model outlined by Saussure. This difficulty, coupled with the tendency to associate his approach generally with what has been criticized as "the linguistic model," has discouraged semioticians of music from following his lead.

Back to Linguistics?

If we must insist, as now seems patently clear, that neither a semiotics of music nor semiotics-in-general can be based on one to one correspondences with structural linguistics, we must also acknowledge the serious difficulties involved in any attempt to bypass such methodology altogether. In the words of Goran Sonesson, "numerous exponents of other semiotic domains have marked their distance [from] the linguistic model, but this has often meant a return to a pre structuralist (paradoxically called poststructuralist), and even pre theoretical, stage of reflection . . ."(1)

Thus, while undeniably important work has been done through the application of less formal, less systematic, methods to the investigation of variouis aspects of the "musical sign," the very notion of a comprehensive theory of musical "signification" in general has come to seem increasingly problematic.

In my view, the rush away from the model offering the most promise for the development of such a theory has been both premature and unnecessary. What has been missed is the fact that Saussure's thinking is grounded in a construct which is already quite "musical." I am referring not to his signifier/signified relation, but the notion of "value," as in his description of language as "a system of interdependent terms in which the value of each term results solely from the simultaneous presence of the others."(2)

While the signifier/signified relation is certainly important for any understanding of verbal language, the notion of value is in my opinion both more fundamental and far more broadly applicable. For many Saussure explicators, there is something both difficult to grasp and also problematic about this idea, which, for someone who wants to get right down to signifier/signified basics, can seem rather superfluous. Musicians, however, should have little difficulty in grasping both the meaning and importance of "value." The most obvious point of comparison is, of course, the rhythmic "values" we have learned so early in our careers as to take them for granted. Four quarter notes equal two half notes which equal one whole note. If we happen to have a dotted quarter handy, we can exchange it for three eighth notes because both are equivalent in value.

Something very similar is at work in the realm of pitch, since any scale system can certainly also be described as "a system of interdependent terms in which the value of each term results solely from the simultaneous presence of the others." If we can see that intervals are analogous to rhythmic values, it is not difficult to understand how they too can be "exchanged": a perfect fourth being understood as equivalent in tonal value to a whole step plus a minor third, say, or six half steps to a diminished fifth.

Already in 1932 Roman Jakobson had written "[t]here is . . . exactly the same relationship between a musical value and its realizations as there is in language between a phoneme and the articulated sounds which represent this phoneme in speech."(3) The American Heritage Dictionary defines the phoneme quite simply as "The smallest phonetic unit in a language that is capable of conveying a distinction in meaning." "Meaning" in such a context is usually understood in a strictly semantic sense. Thus a phoneme is usually defined according to distinctions of denotation, e.g., cat is opposed to rat or cab because each of these signifiers stands for a different signified. In my view, however, what gives phonemes the ability to produce such distinctions in the first place is their existence as vocable classes, something which is prior to denotation and far more closely associated with the notion of value. A phoneme can thus more fundamentally be defined as a class of vocables heard, for the purposes of a given language, as essentially the same sound, i.e., having the same value, a definition not necessarily needing to be formulated in semantic terms and thus much more readily applicable to music. Noam Chomsky has made a similar observation, disputing the notion that phonology must necessarily be based on semantic distinctions.(4)

Given the above, it is not difficult to understand how a pitch class can be regarded as in some sense analogous to a vocable class, or phoneme. But we must proceed with caution at this point or we will find ourselves back where we started, with the now bankrupt "linguistics model." What should be meaningful for us about the notion of value is not that it helps to link pitch classes with phonemes, but that it suggests the existence of a more fundamental principle at work in both music and verbal language, a principle which gives rise to value and ultimately, in my opinion, meaning itself, in the most basic sense of the word, a sense that must be regarded as pre-semantic. Pitch classes and phonemes are analogous to one another. They are not exactly equivalent. Each works in a different way to produce very different effects. Music is not speech. But both can be understood as "language", both are, in some sense, "meaningful." The strong similarities and analogies suggest a common ground.

The Musical Field

In my paper "Toward a Unified Theory of the Arts," I present a theoretical framework within which the system of class identities behind things like phonemes and pitch classes can be situated. What I call "Principle 1" is crucial, as it provides us with an approach to the notion of "meaning" totally independent of semantic considerations: "any object of perception can signify (take on meaning) only in relation to a controlling syntactic field." Such a field can be understood in Saussurian terms as a value based "differential field." It is also a Gestalt field, perceptible in terms of figure against ground, in which the whole can be regarded as greater than the sum of its parts. It can be regarded also as a "vector field," in which each element must be understood as in some sense "pointing" in a certain direction. Above all, it is a "syntactic field," in the very broadly defined sense of a structure ("tax") which brings together, or unifies ("syn"). In this context we could associate "meaning," not with the co-ordination of a signified with a signifier, but with the sense of orientation within a field which makes the signifier/ signified relation possible.(5)

Adopting a field approach, we are more easily able to understand issues pertaining to meaning in relation with issues pertaining to space and time which have been (since Kant's "transcendental aesthetic") also associated with sensory experience. Thus we can more effectively treat questions regarding the affects of perception on signification (and vice versa).

In the "common practice" of 18th and 19th Century Western concert music, we find two such fundamental syntactic fields, the space-like "tonal field" and the fundamentally temporal "metric field," which, when coordinated, unite to form a more basic "tonal-metric" field of tonal "dynamics" or "motion." I have chosen the common practice "major-minor" system as the focus of this paper because 1. I can be reasonably sure everyone present has more than a passing acquaintance with the repertoire, and 2. this particular musical "language" embodies the principles I wish to discuss in a highly developed and clear manner, relatively easy to explicate. In principle, any traditional musical "language" from any society anywhere in the world ought to be analyzable in more or less equivalent terms.

As stated above, a syntactic field can be understood as, at one and the same time, a value field, a gestalt field, and a vector field. As value fields, the tonal and metric fields are clearly articulated and coordinated by systems of difference, such as tunings, scales, meters, which produce various "phoneme-like" classes, such as pitch classes, interval classes, time point classes, duration classes, etc. Since the pioneering work of Leonard Meyer,(6) the interpretation of common practice music in gestalt terms should present no problems. For example, melodies are heard as "figures" against a "ground" of harmonic progressions and tonal relationships, musical lines emerge via gestalt principles such as "the law of good continuation," musical structures are perceived as wholes "greater than the sum of their parts," etc. The field idea itself is, of course, fundamental to gestalt theory.

The third "dimension" of the syntactic field, intimately associated with the other two, its vector aspect, should be equally familiar to musicians via certain basic notions such as chord progression, tendency tone, etc. Within a given key or chord, certain notes are less stable than others, "point" toward others. The leading tone "wants" to move upward to the tonic, suspensions are heard as "needing" to resolve to the note a step below. Chord progressions "move" in a certain tonal "direction," dominant seventh chords "want" to resolve to their respective tonics. In purely rhythmic terms, up-beats "move" toward downbeats, unaccented notes incline toward accented notes, etc. It is my contention that all such phenomena are produced and controlled by the dynamics of the tonal-metric field as a whole, a hierarchical vector-based force field in which, at any given moment, we can posit an "arrow" pointing in a certain direction within tonal-metric "space." It is this vector aspect which enables us to continually "orient" and "re-orient" ourselves within "musical space" as we are listening.

A roughly similar type of field can be posited for verbal syntax, where adjectives "point" to nouns, adverbs to verbs, transitive verbs to their objects, subsidiary clauses to principle clauses, etc. In the realm of the visual arts, a strong analogy to the common practice tonal-metric field is the perspective system, also a combined value, gestalt and vector field, in which every represented object must be "seen" as clearly oriented within an illusory three-dimensional space.

The representation of such a field for music poses far more of a challenge than it would for verbal language or perspective, however, and I must confess I have not yet succeeded in constructing a model that satisfies me completely. What I do have, at this point, can be visualized as a kind of clock. For any given musical "event," whether a single beat or an entire phrase or section, we can construct two such clocks. The tonal "vector" of each note would be represented by a clock "hand" in the form of an arrow, inclined in the direction of that position in the circle of fifths toward which the note seems to be "pointing." The strength of the tonal "pull" would be represented by the length of the arrow. Something analogous could be constructed to represent the metric vector of each note. Instead of the circle of fifths, we might want to have the principle beats of the measure represented, with the note's vector arrow pointing at the beat representing either the position or the "goal" of that note. The vectors of all the notes of that section of the piece could then be summed to produce resultant vectors for both the tonal and metric fields. And these vectors could, in turn, be coordinated to produce a single "master" vector pointing in a particular direction in tonal-metric "space," with a particular degree of force. In principle, at least, this is vaguely how something like this might work. To actually put it into practice would, I must acknowledge, be replete with all sorts of difficulties.

While such an exercise might seem both cumbersome and artificial, an awareness of the workings of the tonal-metric field in some such terms can help us to grasp one of the most important and also neglected aspects of music theory and analysis -- the manner in which the interplay of tonal and metric forces simultaneously 1. controls the way we "hear" a piece of music from moment to moment and as a whole; 2. gives meaning to every detail as well as to the whole, and 3. opens each musical formation up to the possibility of serving as a signifier for some signified. I would like to briefly discuss each of these aspects:

1. As is well known, any given pitch class will sound different when heard in a different key. What may not be so well understood is the manner in which the tonal-metric field can produce a wide range of such sonic "colorations," to produce extraordinarily subtle effects. For example, comparing the opening measures of two apparently very different sounding works, the prelude to Tristan and the Prelude to the Afternoon of a Faun, we discover that, in purely harmonic terms, they are actually quite similar. In both, the first chord we hear is the half-diminished seventh, or "Tristan chord," which then resolves quite smoothly to a dominant seventh. There is, to my knowledge, no theoretical framework which enables us to understand why the effect of these chords is so dramatically different (even when both passages are reduced for piano, so orchestration will not be a factor). It is only when we consider the field effect of the very different melodic materials preceding the opening chord of each that we can adequately explain why both the Tristan chord and the following dominant seventh chords sound so radically different, despite both their essentially identical tonal content and their similar function according to traditional theoretical principles. Heard within any given tonal-metric field, any musical gestalt will have a certain "value" determined by its orientation within the total field, not simply its function within some given key. What we hear, from moment to moment, therefore, is not the acoustically determined sounds, but their field determined value, which is always associated with a vector "pointing" in a certain direction within the field.

2. As should now be clear, what we understand as musical "meaning" is intimately associated with the notion of value, as discussed above. It is possible thus to claim that orientation within a syntactic vector field is what gives music its meaning. When we become disoriented, and can no longer relate what we are hearing to such a field, and are thus unable to assign it a value, then what we are hearing becomes "meaningless."(7)

3. We can therefore go on to claim that the identification of particular musical gestalts, as oriented within a tonal-metric field, tends to set up certain semiotic expectations in the mind of the listener. This is due, in my opinion, to an intimate relationship between perception in terms of such a field and semiosis: any figure perceived within a syntactic field "wants" in some sense to signify and, as a corollary, any sign, in order to function as such, must be perceptible within a syntactic field. Thus musical figures will have a strong tendency to be heard as signs, easily attaching themselves to verbal texts, or inducing the listener to produce some sort of imaginary signified in order to fulfill a semiotic expectation. Though traditional music is not necessarily semantic in the sense that language is, it therefore possesses semantic valence nevertheless. In more general terms, where there are no particular conventions turning particular gestalts into particular signifier/signified pairs, the mind will tend to manufacture signifieds of its own, according to more loosely defined conventions.

The "Cost" of Semiosis

The semiotic effects discussed above are not achieved without cost. Because of the gestalt nature of the syntactic field it functions in and through repression. This can be made evident through a closer look at the way rhythmic values operate within the metric field. Each value is supposed to represent a relative duration, but in fact rhythmic values have a double function. If a dotted half is followed by quarter note and a whole note, in two measures of 4/4, this tells us two very different things: 1. the duration of each note with respect to the beat; 2. the exact point in the measure that each note should be attacked. That these are not by any means equivalent will be evident if we imagine this sequence played at a very slow tempo on the piano. Since the piano cannot give each note its full value, the duration of the dotted half and the whole will probably be identical. What is especially interesting about this situation is that it doesn't seem to matter. The "native listener" will not be bothered by this because the difference in duration has no bearing on the musical meaning of the passage. Semiotically, then, it seems evident that, for common practice music, where piano arrangements of just about anything are considered appropriate, the durational aspect of the rhythmic values can be regarded as lacking "pertinence." Their function in determining the exact position of attack points, is, on the other hand, essential. Clearly, the metric field of common practice music is based on attack points, not durations. Duration is certainly important, but its importance must be regarded as strictly supplemental. Changes of duration will not threaten the meaning of a musical passage (assuming a common practice Western traditional context) -- repositioning of attack points will.

This is only one example of a principle very easy to state, but rather difficult to fully explain: all syntactic fields are virtual fields. What we "hear" when we listen to traditional music is not really the "notes themselves" as acoustic entities, since duration is, in fact, pertinent to our understanding of what acoustic entities are. Thanks to the workings of the syntactic field, where duration has been robbed of its pertinence, notes are heard, in some very important sense, merely as impulses. Their existence as what we might want to call "raw sounds" (i.e., acoustically measurable entities) has been repressed by the field.

Therefore, as essential as the syntactic field is in the determination of meaning, in music and elsewhere, a theory of this field alone cannot account for everything of importance. It cannot account for what the field represses and it cannot account for the reasons why such repression might be necessary. It cannot account for the manner in which the actions of the field might be, and in fact have been, resisted, as, for example, in certain types of modernist music. Finally, it cannot account for the dependence of the syntactic field on that which it represses. For this, we must rely on the theory of a very different type of field, what I have called the "antactic" field.

End of Part One

1. from "The Linguistic Model Fallacy," in Paul Bouissac, Encyclopedia of Semiotics, edited by Paul Bouissac, in collaboration with Göran Sonesson, Paul Thibault, & Terry Threadgold, Oxford University Press, 1998.
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2. Ferdinand de Saussure, Course in General Linguistics, trans. Wade Baskin, Peter Owen Limited, 1959, p. 114.
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3. "Musicology and Linguistics," in Roman Jakobson, Language in Literature, Harvard Univ. Press, 1987, p. 456.
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4. See Noam Chomsky, Syntactic Structures, Mouton, 1975, chapter 9, "Syntax and Semantics," pp. 96-98.
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5. Victor Grauer, "Toward a Unified Theory of the Arts," in Semiotica, 94-3/4(1993), pp. 237-238. This essay has been reissued, with extensive additional materials dealing with music, in Music Theory Online and is accessible at the following Internet address:"
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6. see especially, his classic work, Emotion and Meaning in Music, University of Chicago Press, 1956
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7. Here too my conclusions have been anticipated by Jakobson: ". . .in music as opposed to language it is the tone system itself that bears meaning...," op. Cit. p. 457.
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