Sound Reproduction, Semiotics and Computer Music Composition1



Nicola Bernardini

After tasting the oranges the peasant had offered to him, the King

expressed his approval with a compliment. Happy and proud of his produce, the peasant answered, "Your Majesty! You haven't seen anything yet! With these we feed the pigs." 2


A recent document from IRCAM begins with the following statement: "The problems that Musical Research must solve today are not so much technological as cognitive." (IRCAM - Recherche Musicale, 85/86, p. 1) We feel that this statement summarizes most incisively a situation that at first glance looks very confused. Despite the great technological leaps of the recent past and of the present, computer music -. and, for that matter, music in general - still seems to be, esthetically speaking, at a very critical point. Indeed, there are many ideas circulating, but few of them seem relevant to compositional activity.

The aim of this paper is to penetrate the twists and turns of composition in the Western world today (including the U.S.S.R.) and to try to point out at least some of its relevant instruments - both physical and theoretical. Coming from a computer music composer, this paper might be considered a compositional proposal (though not in the generative/procedural sense,) although it must be clear that: 1) it is not intended to be an absolute in any way; 2) rather, it is a reflection that stems from the compositional activity in the field of computer music; 3) it is not, by any means, an analysis of the author's own compositions. We would, hope that what a composer thinks is quite different from the compositions themselves.

Since the paper will delve into many different fields, prior works will be mentioned only as they help to clarify specific elements in the discourse. Moreover, we will try to convey their meaning and purpose through necessarily short quotations. Of course, the responsibility for any inaccuracy rests entirely with the author, who wishes to encourage all remarks, observations and criticisms that may arise.


Some Reflections on the Composer's Environment

To understand how a compositional model works in its related enviornment, it is first necessary to analyze the reality in which this model exists: that is, post-modern society, in our case. Cultural activity in post-modern society has been abundantly studied: (cf. for example, Hassan 1971, Lyotard 1979, Lyotard 1984, Vattimo 1985) we are therefore relieved of the responsibility of doing it ourselves. So, let us underline what we consider to be its most important characteristics. In post-modern societies "[narrative function] shatters into clusters of narrative, but also denotative, prescriptive, descriptive, etc. linguistic elements, each carrying within itself some sui generis pragmatic valency ... Thus, the derivating society is less dependent on a Newtonian anthropology ... than on the pragmatics of linguistic particles." (Lyotard 1979, p. 8) Lyotard's thesis is that, in this way, this society produces a "crise du recit," a crisis of the narrative device that, up to now, has allowed the legitimization of knowledge (cf. Lyotard 1979). All that remains of language as it disappears is an infinite chain of separate phrases. The uniformity and homogeneity of this condition can be broken up only into that "instant of language in which something that must be expressed in phrases cannot be expressed yet." (Lyotard 1984) This "lag" is the "difrerend" which indicates a verbal surplus in respect to human will and which casts doubts on the concept of "a language naturally at peace with itself, 'communicational' and agitated solely by human will, passion and intention" (Lyotard 1984). Of course, this involves many ideological and political implications which, although important, are beyond the scope of this paper.

Paradoxically, this new nihilism, this "pensiero debole" (cf. Vattimo et al., 1983) produces "a subjectivity without a subject" (cf. Blanchot 1983) which incorporates in itself its own contradiction: a "strong" element of hope and survival. In fact, it is not surprising that hermeneutic philosophies are now claiming a "return to the subject" (cf. the 77th issue of Langages, Paris, March, 1985), by re-evaluating thinkers like Beneviste and Ricoeur and their fight against "the outline of a transcendentalism without a subject" (cf. Ricoeur 1963) operated by structuralism.


The Status of Sounds

In the society described above, sound is trying to establish a new identity after the irreversible transformation undergone via the development of sound reproduction techniques. This transformation has been thoroughly analyzed from the sociological point of view (cf. for example Adorno 1963; Benjamin 1974; Adorno and Eisler 1977; Mayer 1985). The outcome of these studies has produced many considerations which are indeed valuable for the electronic and tape music composer (cf. Stoianova 1983). The loss of the traditional "hic et nunc," the "aura" (cf. Benjamin 1974) of the reproduced work of art, which becomes "more and more the reproduction of a work of art designed to be reproduced" (cf. Benjamin 1974) is something with which most of us deal closely on a day to day basis. On another level, "the influence of the various ramifications of media industries (...) has induced ... a deep change in the 'music' institution as it has been handed down to us through history and of the functions and structures of both old and new music" (Mayer 1985, p. 119). Willingly or not, as musicians we are part of this change and it would be foolish to ignore it.

Still, we find that something in these sociological studies has been neglected, that is, sound itself, along with today's human perception of musical structure in the era of their reproducibility. However, other authors, from not specifically musical fields, have provided appropriate insight into these matters. McLuhan, for one, by analyzing the transformations introduced by typographic technologies (cf. McLuhan 1962) has given us good clues as to what happens during and after media revolutions.

Music Notation and Music Reproduction

Referring to the transformations introduced by the phonetic alphabet, McLuhan wrote that "a new kind of processing of problems, one thing at a time, simultaneous mosaic, a dealing with many aspects and levels of meaning in crisp simultaneity. This method will no longer serve in the new (alphabetical and typographical) lineal era" (McLuhan 1962, p. 129). This "linearity" of processing, transposed to the introduction of music printing shortly after typography, has contributed to the sequential development of tonality (a phenomenon that McLuhan himself noticed - cf. McLuhan 1962, p. 61). Here too, some self-evident facts hide a deeper transformation, the influence of which is still being felt (cf. below). The proliferation of the madrigal, of the French polyphonic "chan-son and of lute tablatures are strictly connected to the expanding market directed towards the new bourgeois classes and the urban aristocracy, a market enhanced beyond imagination by the new-born music publishing business. But we are allowed to think that, if music printing changed the target of compositional activity from a religious to a more lay (though not yet entirely bourgeois), it then set the basis for a music in perpetual lineal development. That is, a development based on sequential transgression of the rules set forth in precedence. The tempered tonal system served as an excellent starting point because of its strong grammar, and has lasted for 300 years (a long time considering how weakening each transgression has been). This is the model of music composition evolution we have inherited, and which, as we shall see, is still very much alive.

It is reasonable to consider that the simultaneity between the shattering of the tonal system (and subsequently, of its development model) and the birth of sound reproduction was a mere coincidence. Nevertheless, this simultaneity rendered the crisis which music had been suffering in this century exceedingly profound. Considering digital developments, we may not agree with McLuhan's prediction that "our" world shifts from a visual to an auditory orientation in its electric technology" (McLuhan 1962, p. 26). "On one hand, the oscillation... from visual to auditory space took human consciousness back to a sensorial oneness...: on the other hand, this return was not structured as a simple return to a pre-alphabet past" (McCaffery, 1983, p. 73). This means that the mind is now able to maintain its linear epistemologic habits in a multi-dimensional perceptual world, which brings us back to the post-modern situation we envisioned at the beginning of this paper. And as we suspect that sound reproduction involves far deeper transformations than music printing did, we are bound to think that, instead of synthesizers, digital technology, etc., sound reproduction, as a modifier of our oral, perceptual structures, is really the instrument of a new kind of compositional evolution, which must not be confused with a new kind of composition.

The Musical Sign's Status Today

Goodman (cf. Goodman 1968, p. 99 and also cit. in Eco 1975, p. 241) makes an important distinction between "autographic" and "allographic arts: "the former cannot be notated and does not contemplate performance, while the latter can be translated into conventional notation, and the resulting 'score' can be performed, with a certain freedom of variation (i.e. music)" (in Eco 1975, footnote in p. 241). Eco then specifies that this distinction is derived from the opposition between "dense vs. discrete" signals. A "dense" or continuous" signal is one for which it is difficult to determine generating rules making any kind of replica impossible (i.e. paintings, cf. Goodman 1968, Eco 1975). This is not without consequences, because, in language theories, dense signals have often been considered to constitute symbolic monoplaner systems. That is, they are not interpreted, rather, they tend to be interpretable (cf. Hjelmslev 1943). And even when someone like Eco tries to establish a system for these signals, he is obliged to limit himself to very vague terms like "textual galaxies," "open signals," "propositional structures" and so on (cf. Eco 1975, par. 3.6.6). This is because of the non-segmented nature of these signs which will not allow precise and definite articulation.

Since music has always been "reproduced" by means of conventional notation it is usually considered to be constituted by "discrete" signals. We want to point out that this conception of the musical sign is only partially correct, since it works only because of notation. It would seem, then, that musical signs behave like verbal ones, constituting some sort of dichotomy like that proposed by Saussure (the dichotomy langue-parole; cf. Saussure 1922, chap. III) or that suggested by Pike (the subdivision of emic-etic; cf. Pike 1947, chap. II). Many musicologists and linguists have adopted these schemes to represent music in terms of language (cf. Springer 1956, Buyssens 1967; Bright 1963; Nettl 1971; Chenoweth 1972; Nattiez 1975). Nattiez (Nattiez 1975, pp. 76 and ff.) has foreseen in the adaptation of music to the langue-parole dichotomy some of its limitations, and has tried to demonstrate that this dichotomy automatically generates a trychotomy as in Figure 1 (Nattiez, op. cit. p. 82):



Reference system Composition

Notated Composition                     Particular Interpretation


Figure 1

However, since "the tonal system [among other reference systems] exists only for harmony treatises and manufacturers, for whom 'grammatical' rules are in fact stylistic rules' (Nattiez op. cit. p. 84), our author discovers, "between the single composition and the tonal system, ... an infinity of stylistic levels" (p. 82). But this does not eliminate the affinity between verbal language and musical language since Nattiez himself writes a little later that "it is extremely interesting to establish that it is impossible, in the musical field, to depend on one single pertinence level much in the same way as linguistics have been forced to refine the Sausurrian dichotomy langue-parole" (p. 86, italics ours). Evidently the problem is elsewhere.

The fact is that, from the "notation-as-means-of-reproduction" point of view, rather than a discrete signal, sound behaves like a so-called "dense" signal. Following the definition given by Eco of such signals, "given a perceptual model as a 'dense' representation of a certain experience, assigning to the perceived object x the properties xl, x2, x3, .... , xn, as soon as the cultural experience is carried out the perceptual model originates a semantic model that keeps only a few properties of the 'dense' representation" (Eco 1975, p. 312, italics ours). Which is exactly what happens with music notation.

We believe that the mistake of considering sound a 'discrete' more than a 'dense' signal is due to the fact that we think of music in an old fashioned way, while experiencing it through the contemporary world of reproduction and media. This mistake has given rise to many inconsistencies in the study of musical signs. To begin with, we think that the difficulties encountered in establishing pertininence levels by means of the classical operation of commutation (cf. Hjelmslev 1961), among others, has led many musicologists to think of music as a monoplanar language (cf. for example, Imberty 1975, p. 70; Jakob-son 1983, p. 14; Delalande 1953, p. 53) as do the exponents of the traditional formalist theory (cf. Hanslick 1893; Stravinsky 1942; Langer 1951, etc.). This, in turn, has led the theorists who believed in a musical language not purely syntactical but provided with a semantic depth, to think of the semantic connotations of music in terms of referential connotation exclusively (cf. the extreme example of Cook 1962; but also Meyer 1956; Osmond-Smith 1972; Imberty 1976; and to a certain extent Lissa 1976; Stefani 1976). It is worth noting, however, that the problem of a semantic level of music has been debated for more than a century now, and it is still very confused.

Once again, sound reproduction comes in very handy, because of its ability to subdivide the sound continuum into segments as small as desired. It is clear that sound reproduction is an innovation comparable to that of the phonetic alphabet and of movable type, while the representation of sound and music given by music notation is, at best, comparable to the representation a good photograph can give of a work of art. The lack of a means of segmentation in music has oriented its perception in the past towards a purely denotative system of signs (except in the case of program music in which, although the referents were coded quite artificially, some semantic capability of music was thus demonstrated). Sound reproduction (and its corollaries, such as music diffusion etc.) has allowed our perception to grasp new connotational levels that were simply inconceivable before. Of course, it is the appearance of digital technology that clarifies beyond doubt the potential of segmentation, falsification, and of connotation production inherent to sound reproduction. Other problems raised by musicologists during the time of analog sound reproduction, such as the problem of a scientific analysis of musical interpretation (cf. Ruwet 1975, p. 34, just to make an example of a problem clearly dictated by the new status of musical sign), can now be solved with digital means (cf. Clynes 1984). In this frame of ideas, it is not surprising that the computer music community has spent a lot of is time trying to establish if a certain technique or a certain machine is able to reproduce natural sounds, insisting on the fact that this is not done for a musical reason but for an experimental one. There are very good musical reasons to do it, and computer music composers are starting to become aware of them (cf. Barriere 1984, p. 182).


Possible Models of Compositional Development

It is evident now that our traditional lineal compositional models need to be revised under this new light. The ambiguity and depth of the new poetic message in music will not be described by lineal development of, for example, a new musical variable to be serialized or some new more or less designed stochastic process (cf. Thomson 1983). It should be clear that, after 4'33" by John Cage, there can no longer be any lineal "transgression of rules" in music (significantly enough, Cage begins his book Silence with the following sentences (cf. Cage, 1973, p. xii):

nothing is accomplished by writing a piece of music          our ears are now

nothing is accomplished by hearing a piece of music         now in excellent condition

nothing is accomplished by playing a piece of music

Rather, the poetic spark of music might be created, today, by the connotational ambiguity of the present time multi-dimensional musical language. That is, music is getting closer and closer to the mechanisms of poetry. Which means, in short, that music has finally acquired the possibility of becoming its own meta-language. This possibility was forseen by a few perspicacious investigators (cf. Levi-Strauss 1964; Court 1971; Eco 1975) and composers (among others Mahler, Berg, Ives, Nancarrow, Berio, Schnitke). But, due to technological and theoretical limitations, the full potential of this model is far from being realized. The authors we have just mentioned do not push themselves much further than sophisticated quodlibet and quotation techniques.

A general model for semantic representation which works quite well in music is the MSR model elaborated by Eco (cf. Eco 1975, par. 2.11 - MSR stands for Semantically Reformulated Model) and adapted to specific musical examples by Stefani (cf. Stefani 1976, pp. 220 and ff.). Up to now, however, it has served to demonstrate specific referential connotation capabilities of functional music. It is particularly meaningful that in Stefani's study, the examples used are jingles for advertisement, a genre closely dependent on sound reproduction. The model is represented in Figure 2. MS (marche sintattiche) represent the syntactical marks that allow the signifier to be combined "with other signifiers so as to produce well formed and grammatically acceptable phrases even though they are anomalous ... and therefore to define as unacceptable other phrases that would instead make sense from a semantical point of view" (Eco op. cit p. 133; " the d's and the c's are denotations and connotations ... (" denotative ... marks ...constitute ... the cultural unit to which the signifier is primarily related and on which successive connotations are based. ... connotative ... marks ... contribute to one or more cultural units expressed by the sign function previously constituted" Eco op. cit p. 123); "(cont)'s are contextual selections, which give instructions of the type 'finding (conta) use the following d's and c's when the sememe is contextually associated with an <<a >> sememe' (circ)'s are circumstantial selections, which give instructions of the type 'finding (circ);s use the following d's and c's when the signifier that corresponds to the sememe is accompanied situationally by the event or object 11=11 which must be intended as a signifier pertaining to another semiotic system*" (Eco 1975, p. 153). "The contextual selections file other sememes selections file other signifiers ... which belong to different semiotic systems, or objects and events gathered as ostensive signs, usually occurring with the corresponding signifier of the represented sememe" (Eco 1975, ibid.).


Figure 2: after Eco, U. 1975, Tratto de Semiotica Generale, Bompiani,Milano. (Reproduced with the permission of the author and the publisher.)

This model is a good starting point of understanding music as it is perceived in our era. Even by using an approach limited to strongly programmatic music (jingles), Stefani can demonstrate that "the MSR allows the integration in a homogeneous manner on one single level, of sign occurrences that are usually considered 'special', if not anomalous, by musicologists, as in the case of quotation ... As a matter of fact, quotation is reduced in the MSR to a mark like any other, simply decoded on the basis of a given selection" (Stefani 1976, p. 210). We add to this that the MSR can also describe connotations that do not have external referrents. Rough examples of verbally expressed connotations could be: "pointillistic" or "sounds like Debussy" or " pianistic articulation," etc. - expressions which serve to show how much rougher verbal language is when speaking of music than are the connotations themselves.

Another important feature of the MSR is that it can explain why the same composition can be "heard" in many different, even opposite ways, by different people. Itdepends on the different amount of selections that each listener can perform (for a similar approach, cf. Nattiez 1975, p. 74). This means that the MSR model is able to explain different cultural approaches (cf. Stefani 1976, ibid). However, the MSR model is not perfect. Eco himself underlines its deficiencies, noting that "every mark constitutes ..., inside a sememe, some sort of embedded sememe that generates its own branching and so on ad infinitum. ...How is it possible to represent such a semantic universe, especially when it is exactly the semantic universe in which human beings live?" (Eco ibid, p. 174). This problem is particularly felt in music, where syntactic marks and semantic marks of signifiers of different nature (i.e. pitch, rhythm, synchronic and diachronic form, timbre, instrument, techniques, spatial relationships, etc.) are often tightly intermingled together to give very specific and meaningful results (this has also been noticed by Stefani; cf. Stefani 1976, p. 209). For example, it is as if, on top of enumerating strict denotations and connotations, we tried to specify all the paralinguistic activity (i.e. facial expressions, intonation. gestures, etc.) that occurs when someone speaks (a manipulation of these parameters, as a matter of fact, has already taken place in some musical pieces, such as Amirkhanian's The Real Perpetuum Mobile or some of Charles Dodge's compositions).

As a possible solution to this problem, Eco mentions the Q model, named after its creator M. Ross Quillian (cf. Quillian 1968). The Q model is a model of semantic memory that allows a certain degree of analysis of semantic processes of understanding. Unlike the MSR model, in which the structure is based upon a number of different elements and all elements are in the same dimension, the principal characteristic of the Q model resides in its two basic elements and seven linking categories in which elements are in n dimensions (or planes) n being the number of elements that the model includes. It is a model essentially based on defining "linking types" as opposed to the earlier one based on defining

element types" (however, some rough similarities between the two models can be found -as we will see further on). "The memory model consists basically of a mass of nodes interconnected by different kinds of associative links. Each node may be thought of as named by an English word, but by far the most important feature of the model is that a node may be related to the meaning (concept) of its name word in one of two ways. The first relates directly: i.e., its associative links may lead directly into a configuration of other nodes that represent the meaning of its name word. A node that does this is called a type node. In contrast, the second kind of node in the memory refers indirectly to a word concept by having one special kind of associative link that points to that concept's type node. Such a node is referred to as a token node, or simply a token" (Quillian op. cit, p. 234). The similarity between type node and denotation and token node and connotation is noticeable. "In the memory model, ingredients used to build up a concept are represented by the token nodes naming other concepts, while the configurational meaning of the concept is represented by the particular structure of interlinkages connecting those token nodes to each other. It will be useful to think of the configuration of interlinked token nodes that represents a single concept as comprising one plane in the memory. Each and every token node in the entire memory lies in some such plane and has both its special associative links pointing within the plane to other token nodes comprising the configuration. In short, token nodes make it possible for a word's meaning to be built up from other word's meaning as ingredients and at the same time to modify and recombine these ingredients into a new configuration (ibid.). Figure 3 is an example concerning the representation of the three meanings of "plant" as they are described in a dictionary. "The three circled words, of the three planes, represent type nodes; every other work shown in Figure 3 represents a token node.

The non-terminated arrows from tokens indicate that each has its special pointer leading out of its plane to its type definition, i.e., to a type node standing at the head of its own plane somewhere else in the memory. Each of these planes, in turn, is itself entirely made up of tokens, except for the type word that heads it (...) Therefore, the over-all structure of the complete memory forms an enormous aggregation of planes each consisting entirely of token nodes except for its 'head' node, which is always a type node" (Quillian, op. cit, p. 242 and ff.). "As to the nature of the nodes themselves, it will be assumed that these correspond not in fact to words, to sentences, or to visual pictures, but instead to what we ordinarily call 'properties' ... Representing a property requires the name of something that is a variable, an attribute, plus some values or range of values of that attribute. This feature is achieved in the memory model by the fact that every token is considered to have appended to it a specification of the appropriate amount or intensity in the particular concept being defined .... These values allow encoding restrictions to a fineness of nine gradations, i.e., permit nine degrees of 'absolute discrimination' to be represented" (Quillian, op. cit. p. 242). This means that "the model's range readings on tags [appended to each node], together with its ability to form disjunctive sets of attributes, provide it with a ready facility for representing information having a great deal of vagueness. This is essential. It is the very vagueness of the meaning of most language terms that makes them useful" (Quillian, op. cit., p. 245, italics ours).





1.    Living structure which is not an animal, frequently with leaves getting

  its food from air, water earth.

2.   Apparatus used for any process in industry.

3.   Put (seed, plant, etc.) in earth for growth.

Figure 3: after Quillian, M.R. 1968 "Semantic Memory", in Semantic Information Processing, (Minsky, M., ed., MIT Press, p. 236).Reproduced with the permission of the author and the publisher.

This fairly detailed description of the Q model is necessary in order to clarify potentialities and problems concerning the use of this model in music. The Q model proves to be a good analysis method because, not being a generative but a semantic model, it provides the following features: 1) it embodies, as we have seen, meaning ambiguity and vagueness; 2) it is possible for the system to make inferences (described as 'plane-hopping': cf. Quillian, op. cit. p. 251); 3) the system can operate structure modifications by itself; 4) finally, it is n-dimensional, allowing the different semiotic planes of music (or of any other language) to be linked together. Actually, the possibility of adaptation of this model to music seems to be dependent mainly on the possibility of expressing links in terms of musical objects, an operation that, at first, sounds quite remote. However, speaking of visual memory, Quillian states that " it seems at least as reasonable to suppose that a single store of information underlies both 'semantic' memory and 'spatio-visual' memory; their difference being not in the structure of the information sorter, but rather in the way that the static information of that store is used' (Quillian, op. cit. p. 239). Once again, segmentation of a continuum (in this case, the visual one) is the conclusive condition for semantic proliferation; this condition is now possible in music by means of sound reproduction.

There were a few problems in the 1968 version of the Q model, some of which were more of a technical nature and may well have been solved by now (Quillian, op. cit. par. 4.5). But one of a more structural nature undermined many of its possibilities: it was, basically a deterministic model. The idea of memory as a huge dictionary, derived from the Katz-Postal model (cf. Katz and Postal 1964, a model that Quillian himself criticized: cf. Quillian, op. cit p. 265), inflates the Q model into " an enormous aggregation of plans" (Quillian, op. cit p. 237) which seems to have little relation to a normal human memory (as Minsky wrote in the introduction of the same book, "I have never heard of any instance that seriously suggests that a person can hold many millions of independent facts" (cf. Minsky 1968, p. 25). In his book, Eco asserts that the competence of a subject is more similar to an encyclopedia than to a dictionary (sf. Eco 1975, par. 2.10.2) and that "the fact that, ..., the encyclopedia looks more like a Speculum Mundi than an Encyclopaedia Britannica, suggests the idea that the natural language universe is very far from the universe of formal languages and has instead a lot in common with a 'primitive' universe" (Eco, p. 162). A model that we believe comes even closer to the target is the memory model of ancient rhetoric: a non-infinite "container" (a "building" ) in which every "content" ("memory images" and "symbols" ) occupies discrete definite spaces. The container is "filled-up" with contents whenever a memory search is needed and the mind " takes a walk" into the "edifices" to find what it was looking for (cf. on this subject see Yates 1966).

             At any rate, a possible way to solve this problem of the Q model could well be inside the model itself. It resides in the range tags that are appended to each token node these tags determine the preferential and secondary meaning paths that might explain both the functioning of human memory and that of ambiguity in signification.

The token nodes and their tags constitute what is known as a fuzzy set, that a "class of objects with a continuum of grades of membership" (Zadeh 1965, p. 338, cf. also Zadeh 1971a, 1971b, 1968; Zadeh, Sun Fu, Tanaka and Shimura 1975; Mamdani and Gaines 1981; Gupta and Sanchez 1982; Schmucker 1983; Wange 1983; Pal 1985; Skala, Termini and Trillas 1984; Kaufmann 1973). The formal definition of it is "a fuzzy set (class) A in X is characterized by a membership (characteristic) function f suba (x ) which associates with each point in X a real number in the interval [0,1], with the value of f suba (x ) with x representing the 'grade of membership' of x to A. Thus, the closer the value of I suba (x ) to unity, the higher the (Zadeh 1965, p. 339). "Intuitively, a fuzzy set is a class with unsharp 'boundaries,' that is, a class in which the transition form membership to non-membership may be gradual rather than abrupt" (Zadeh 1968, footnote p. 161). " f suba can be defined in a variety of ways; in particular, (a) by a formula, (b) by a table, (c) by an algorithm (recursively), and (d) in terms of other membership functions (as in a dictionary)" (Zadeh 1968, p. 161). Due to the lack of space, it will suffice here to indicate that fuzzy sets can, as other kinds of sets, undergo a number of operations such as identity, complementation, containment, union, intersection, algebraic product and sum, absolute difference, (fuzzy) relation, and can be convex, nonconvex, bounded or unbounded (cf. Zadeh 1965). The union, intersection and complementation operations follow De Morgan's laws as well as distributional laws; union and intersection operations can be represented by networks of sieves (analogous to the switch networks of ordinary sets: cf. Zadeh 1965, pp. 342 and ff). It is evident that the wealth of operations on these sets allow for quantitative formalization of such things as meaning (" a fuzzy subset of [a universe of discourse] U" cf. Zadeh 1968, pp. 164 and ff) and language (" a fuzzy binary relation from a set of terms T, to a universe of discourse U: cf. Zadeh 1968, pp. 168 and ff). Though "completely nonstatistical in nature" (Zadeh 1965, p. 340) fuzzy sets provide the necessary tools for extremely "complex or ... ill-defined problems" (Zadeh 1969, p. 469). The implementation of a time-dependent fuzzy set theory (cf. Lientz 1972, p. 367) could suit some syntagmatic aspect of music particularly well. In general, fuzzy set theory can complement the Q model to provide planing schemes often needed in music composition.

Music Theory References of These Models

Semiology of music would seem the appropriate field in which to develop these conceptions. A semiotic musicological discipline began developing in the sixties and became quite popular in the seventies together with all other semiotic studies. Given the wide disintegration into small groups which followed, we will avoid a detailed description, since several fairly accurate ones are already in existence (Nattiez 1971; Nattiez 1973: Nattiez 1975). Many musicological tools have been elaborated, following different linguistic approaches: we have already mentioned above the ones that seem relevant to us as compositional models. However, towards the middle of the seventies musical semiotics seemed to lose momentum. The movement was undermined by contrasts among different currents (cf., for example Nattiez 1975; Ruwet 1975; Avron 1975, etc.) and changing times in general (cf., for examples the desemiotization and deconstruction theories of Lotman 1971; Restivo 1985; Vattimo et al., 1983, etc.).

What is worth considering, though, is that most of these approaches were designed by musicologists and, of course, work in a musicological context: they are only marginally useful to composers (except during their apprenticeship). This does not mean that musicological semiotics or musicology per se is useless: on the contrary, the role of musicologists is to develop the discourse about music, a thing that could never be accomplished by composers (with a few notable exceptions). Nevertheless, when we attempt to use the type of knowledge found in semiotic musicology in the context of our compositional model, we run into problems. Let us rapidly analyze a few of them.

The first one is that some musicologists and linguists believe that music cannot be its own meta-language, and tend to designate verbal language as the appropriate metalanguage for music (cf. for example Nattiez 1975, p. 45; Stefani 1976, p. 33; Nattiez 1976, p. 3; Jakobson 1983, p. 14). Others, it is true, do not trust the verbal language as musical meta-language, but nonetheless use it - not finding anything better suited to the purpose (cf., for example, Baroni 1980, p. 35; Imberty 1975, p. 90; Osmond-Smith 1972, p. 32). A third group asserts that the verbal language is absolutely incapable of conveying musical meanings, thus denying the possibility of existence of musicology itself (cf. for example, Harweg 1972: Barthes 1972; Rosset 1979; Levi-Strauss 1971). But nobody thinks that music will ever become a meta-language (an exception is constituted by Barthes, who believes that the speaking and singing voice can be used in the meta-musical sense; cf. Barthes 1972).

The second problem is the absolute faith these scholars have towards musical graphic lineal notation, conventional and non-conventional (cf. for example Nattiez 1975; Molino 1975) when we know too well how problematic such an aspect is today (cf. Manoury 1984). By relying on notation, it is clear that analyses, even the most precise and detailed ones (cf. for example, the distributional analyses proposed by Ruwet 1972; Nattiez 1975, etc.) are bound to be limited to some particular aspects (i.e. formal aspects, melodic contours and redundancy, subdivided rhythm and meter, etc.) while ignoring others (i.e., the connotational aspects and, in general all metamusical aspects) which are often noticed instead by much criticized and "non-scientific" music critics (cf., for example, Ivaskin 1985). A different approach to the subject has been given by Cogan who has made spectrograms of entire compositions and of specific passages (cf. Cogan 1984). This approach works in the opposite way: it does not reduce information in the notational process, so that the reader can freely select which aspect to look for at any given time. The reduction of parameters, necessary for controlling the process, is subjective, much as it is when listening to a piece of music.

The third problem is "scientific legitimacy" . True, in the past it often seemed as if anything goes" had become the motto of musical analysis and criticism. As a reaction to this, an all too understandable tendency to stricter formalization occurred (cf. Stefani 1976; Nattiez 1973; Nattiez 1975). But, with all the problems we have listed, it should be clear that a "scientific" approach in musical analysis can be claimed only by people who do not have a very precise idea of what "science" is, laying themselves open to strong criticism from authoritative figures in the field (cf. for example, Ruwet 1975; Groddeck 1972). Therefore, it is questionable whether " scientific legitimacy" is useful at all.

Actually, these problems do not exist in musical composition. As in composition, music is its own meta-language. Using semiotic principles and methods can only enhance the insight and control of musical processes by the composer. Just to make an example of how different this approach is, it is possible to show that something like the "double articulation" of language as expressed by Martinet (that is the subdivision of language in a first level of natural segmentation and a second level of cultural segmentation - the 'semantic units': cf. Martinet 1960), a theory very much criticized by musicologists, could be very useful in establishing the actual meta-linguistic capabilities of music precisely.


Early Uses of the Computer as a Musical Instrument

It is evident from what we have said so far that the typical instrument to allow the development of music in the era of its reproduction is the computer. The ultimate segmentation abilities a digital system can operate on the sound continuum need no further demonstration. Furthermore these abilities can provide such a control on musical connotative selections that it is possible to anticipate the definite stabilization of a perceptual articulation system (cf. above and Martinet 1960), the multiplicity of musical language particles constituting the first level while the second level is built upon the articulation of the connotations established by the particles. This preference towards the computer does not mean that other, traditional instruments cannot be used as well, but simply that some of them will adapt to this model better than others (i.e., voice, percussion, string orchestra vs. piano, organ, saxophone, etc.). As we mentioned in the beginning, digital signal processing technologies and all computer related issues are fairly advanced as far as music is concerned. Still, a lot of progress can be made, but the basics (i.e. synthesis techniques, hardware, etc.) are quite well under way. The main problem in the use of computers in music resides with the conceptions most composers have of what to do with them.

In general, our tendency is to take the model of analog electronic music, and expand it to digital technology; in other words, a certain unlimited "faith-in-the-machine" tempered only by the difficulty, for a musician, to enter the digital world. A description referring to digital techniques such as: " the electronic material, the synthesized sound gives - in theory - the possibility of creating a decisively new universe, liberated from the limits imposed before" (Boulez 1975, p. 28) sounds awfully similar to another one which twenty years earlier was related to analog technology (" we are on the lookout for an unheard world of sounds, rich of possibilities and practically unexplored" -. Boulez 1954, p. 34). While enthusiastic comments about the possibilities of the computer are not uncommon, it is interesting to notice that meager results in computer music are often explained in terms once clearly stated by Xenakis (Xenakis 1981, p. 17):

a) Musicians that use the computer ignore general theories, especially mathematical, physical and acoustical theories [why not language theories?]. Their talent, when they have it, is not capable of penetrating the virgin spaces where only abstraction can guide their experience...

b) scientists who have access to computer technology feel a sort of inferiority complex in the face of musical aesthetics ... They lack experience in an aesthetic field and do not know which direction to take at all.

Xenakis then proceeds to outline various directions stating that a fusion between macro-composition and micro-composition are based on particular geometrical and mathematical properties (cf. Xenakis 1981, p. 18 and fr.) These have strictly nothing to do with musical semantics, which indicates a certain contempt of the composer for the empirical data of " how is his composition going to-sound." It must be clear the we are not criticizing Xenakis' music, which can be intriguing and beautiful, nor the use of mathematics in music (of which we just gave an example cf. above in discussing "fuzzy sets" ). All we are trying to say is that the semantical aspects of that music are either based on the very empirical "taste of the composer" (referred to as "talent" by Xenakis in selecting the output of his algorithms), or completely coincidental (which is fine as far as music is concerned). In the same vein, it is easy to show that integral serialism, more than " ... method for pitch [rhythm, dynamics, attack, timbre etc.] structuring" (Boulez 1966, p. 151-152), semantically speaking represents the absolute supremacy of timbre over all other semiotic systems that act in music.3

These are just two very rough examples of the lineal romantic ideal of music development that composers have inherited from strong non-fragmented languages, along with the ideas of "talent," "genius," etc. We think these conceptions are quite outdated, just as we believe that Bach was regarded by his contemporaries (in the beginning of the era of music printing) as we now might consider an excellent film music composer more than a genius in the romantic sense. These same conceptions have led to a questionable speculation operated by some composers with respect to psychoacoustics.

These composers have considered psychoacoustics as the new "art of orchestration." We would like to invert this statement: there is a very little theory produced by psychoacoustics that cannot be found in explicit musical terms in good old orchestration manuals. Of course, the immense effort of explaining orchestration (among other things) in terms of psychophysical sciences need not be underestimated, but it is clear to psychoacousticians themselves that this theory lies in an infra-semiotic field, very close to natural phenomena (that means, in rough terms, that psychoacoustical research stops a few inches inside the aural system). Just to quote the most obvious example, the fact that the very limited timbral semantic segmentation provided by certain models (cf. McAdams 1982) has been sufficient for some composers to base compositional processes on it gives testimony of our still strongly traditional way of thinking (that is, tied to old lineal schemes of composition evolution, such as looking for algorithmically created timbres as some "new" compositional tool to be exploited). What we want to stress here is that psychoacoustical knowledge will be extremely useful (i.e. to clarify syntactical marks and physical properties of " musical monemes" ) once we have found the way to link it to the field of musical semiotics. As far as we know, this has not been attempted.

Considering the situation exposed in this paragraph, it is not surprising that results in computer music are generally rather meager. Another good excuse for this - and a strange one at that - is that the whole field of contemporary music is at a critical stage. While this is not absolutely true, what is indefensible is that computer music has a very strong general connotation already. That is, we can easily define a computer music genre, an unpardonable flaw when we think that computers are instruments with really potentially unlimited capabilities in sound synthesis and reproduction.


The Computer a New Musical Instrument for a New Musical Thought

Considering the change of perspective proposed in this paper, we will briefly proceed to outline a few possibilities for immediate direction. The first and, most important one is the study of the computer music instrument under the profile of what we could call transparency (or neutrality). Transparency is a non-quality; it is the lack of linguistic and cultural connotations of an expressive medium (the absence of "noise" ; cf. Shannon 1949). The piano is a clear example of a non-transparent instrument (" opaque" ). Any sound from a piano keyboard will not fail to recall to us at least one of the different universes of language" represented by piano literature. Therefore, we can see that total transparency is practically impossible to attain. Transparency means, in this sense, the access the composer has to the manipulation of the micro-structures of the synthesized sounds (i.e. single sample or group of samples) in terms of how many parameters he/she must define for them.

For example, hardware-defined machines are not transparent. They will force the composer to use the same synthesis technique over and over, a great problem considering that synthesis techniques themselves are, as we will see, "opaque." Thus, micro-programmable machines (cf. for example DiGiugno and Kott 1981; Samson 1980) have constituted a real breakthrough. The problem with them is that, even when they are extremely powerful, they are still not powerful enough (in a sense, they imitate the structural limitations of traditional instruments) and they are quite difficult to use (a factor of *opacity" , indeed, for most composers). However, the great technological leaps Operated by VLSI technology (cf. for example, the TMS 32020 chip, the WORDSLICE technology, the 68020 general purpose chip, the dedicated semi-customs, etc.) will presumably solve these problems in the not too distant future. Nevertheless, we do not think it will be possible to solve the transparency problem completely. An "efficient" technique will always tend to be connoted because of its data reduction schemes ("opaque" in its results), while a "flexible" one will never be easy to handle because of the number of parameters involved (' opaque" in its control). This cannot be avoided, but an attempt to measure the transparency" should be made in order to select and realize more "musically powerful" synthesis techniques.

A proposal in this direction could be the analysis of the various synthesis techniques we already possess (cf. Risset 1969; Rabiner and Gold 1974; Crochiere and Rabiner 1983) to establish a quantitative "transparency" factor based on some kind of a "sample flexibility/number of control parameters" ratio (in relation, maybe, to the Lagrange linear approximation method or non-linear approximations like spline functions. etc.). This could be particularly useful in the evaluation of synthesis-by-model techniques or synthesis technique aggregations. Artificial Intelligence could be used to provide " intelligent" automated parameter controls to improve " transparency" on non-efficient techniques. Following the general trend of convergence of methods between synthesis and composition tool structuring (cf. for example the CHANT/FORMES project in Rodet, Potard and Barriere 1984; Rodet and Cointe 1984) some new methods for quantitative musical analysis could be devised, in the path of the theories of information shaped more than two decades ago (cf. Shannon and Weaver 1963; Meyer 1967; Coons and Krahenbuehl 1958; Moles 1960). Other problems that should be solved concern loudspeaker "opacities" , which play an important role in all loudspeaker-produced music (and, of course, all reproduced music as well). These problems are basically divided into two categories, which we could call sound localization" and " instrument vs. loudspeaker irradiation." To our knowledge, these two categories of problems are presently being studied separately (the first one, cf. Kendall and Martens 1984a. 1984b; Bennett, Barker and Edeko 1985; Borish 1985; the second one cf. Benade 1985). In our opinion it is very important, in the perspective indicated in this paper, that these two fields be brought together in order to provide a general theory on loudspeaker "transparency" (a theory we realize has a long way to go yet).


There are many topics that could still be discussed widely under the point of view proposed here. The return of subjectivity, new concepts of " tonality" and " atonality" in the sound reproduction era, the generative approach to analysis and composition, artificial intelligence, non-deterministic systems, cross-synthesis techniques, the notion of structural coherence and that of "materials" in this perspective, etc.; these and other arguments will not find a space in this paper. In any case, it is important to re-assert now what has already been pointed out in the beginning. We hope this paper has presented a new way of thinking about music, and some (by no means all) of its most important aspects and strategies. Once again, we wish to make it clear that it is not the usefulness of systems and theories that we are questioning (in composition, anything is useful) but how they are used.


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1 Paper presented at the 1986 International Computer Music Conference, Vancouver, Canada.

2 From a joke my grandfather often used to tell; also in C. Bernardini "Che cose una legge fisica" , p. 77, Ed. Riuniti Rome, 1983.

3 This is explained by the obvious supremacy which natural structures, i.e. timbres, have even with a weak second-level articulation over abstract, second articulation structures that do not possess first articulation foundations - the serialized parameters (cf. on this subject the enlightening, provocative and much criticized Ouverture in Levi-Strauss 1964, pp. 22-38; and also Martinet 1960).