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If the semantics of music theorizing is broke, let's fix it.

Philosophers of music and music theorists go their separate ways, sometimes disdainfully, ignoring the fact that they occupy common semantic ground: they both speak natural language. This fact acquires remarkable significance in the twentieth century due to the widespread interest in semantics of natural language on the part of scholars in a variety of subject-fields. In this essay I shall recognize this semantic intersection of philosophy of music with music theory (the scholarly discipline which analyzes musical form) by calling them alike: music theorizing.

It is the natural language of music theorizing that I shall discuss in this essay, not the language of music, music not being a natural language. I shall show in Section I that the language of many influential music theorizers contains semantic errors which would be unacceptable in the scholarly literature on semantics,[1] notably a profound error in exemplification that renders generalizations about musical expression invalid. I shall show in Section II that various natural languages of music theorizing presently in widespread use throughout the world contain a profound error in extensional identity that renders knowledge claims about music incoherent. I shall submit, in conclusion, that a drastic semantic reform is needed, namely: the development of a new kind of music theorizing language, capable of giving a valid, coherent account of the world's music.

I

In order to demonstrate that semantic errors do occur and what some of them are, let me consider a recent article by an influential philosopher of music. Malcolm Budd[2] confuses the elementary semantic distinction between object language and object.[3] Confusion over this distinction can be detected in many passages throughout Budd's essay, notably in two sentences which in conclusion summarize his main point.

The first of these, which I shall call sentence (a), is: 'Music . . . can be heard as expressing, not an occurrence of emotion, but a quality of emotion' (p. 137). Earlier, Budd had asserted that 'the notion of the musical expression of emotion' corresponds to the 'sense in which emotion can be communicated by music which expresses it' (p. 131). There is, of course, a semantic relation between communicating and what communicating is about, namely the aboutness relation. Thus, if emotional qualities expressed by music are communicated by music, they are what music is communicating about. Now, the aboutness relation holds between an object language and its objects. Therefore, sentence (a) implies that music is an object language.

The second of the two summary sentences, which I shall call sentence (b), is: 'If this [sentence (a)] is right, the account I have sketched of the nature of our emotional reaction to emotionally expressive music . . . will need to be amended to cover the experience of music heard as related only to a quality or kind of emotion, not to an occurrence of the emotion' (p. 137). If the account will need to be amended, the music theorizing will need to be amended, not the music. By this reasoning, the emotional qualities expressed by music are what music theorizing is communicating about. Therefore, sentence (b) implies that music is the object of an object language.

There is a way to resolve this confusion in order to move on to the substance of Budd's argument. Leave undecided the question whether music communicates; assume only that music theorizing communicates. Then Budd's essay can be summarized as follows in conformity with sentence (b). He finds defective some recent metaphor theories of interpretation, such as those of Donald Davidson, Nelson Goodman and Kendall Walton. By contrast, the make-believe theory of interpretation, also due to Walton, opens up new perspectives on musical expression which intrigue Budd. He gives three versions of the make-believe theory: (1) pretending that the music is a person expressing emotion; (2) pretending that the music is arousing emotion in a person listening; (3) pretending that the music refers impersonally to an emotional state of affairs. Budd finds much merit in the third of these. Even so, he points out, it does not account for the elementary fact that on many occasions we are, indeed, personally moved by music we hear. Therefore, he submits the following revision: 'I experience what melancholy, loneliness, or triumph feels like', but not 'a melancholy, lonely, or triumphant state or condition' (p. 136).[4]

Suppose someone were to object that by ignoring musical communication I distort Budd's argument, because expression without communication would legitimate subjective emotional responses by listeners - just what Budd deplores. To object that my way of correcting Budd's semantic error about communication fails is to imply that there is a semantic error about communication, thereby making my point: semantic confusion discredits his whole argument.

Another semantic error by Budd has consequences reaching far beyond the argument of his article. He states: 'Any account of the value of music - the value of music as music - should do justice to the medium of music, so that neither emotionally expressive music in general, nor any individual musical work, is represented as a mere vehicle for the expression and communication of psychological states' (p. 129). Agreed, music should not be reduced to a message machine. But I have added italics to emphasize something else: the quoted sentence assumes tacitly that every example of emotionally expressive music is a musical work.

This tacit assumption seems, at first impression, no more remarkable than assuming that every example of cloth is a piece of cloth. On second thought, however, one realizes that not every example of music is a piece of music (i.e., a work of music, i.e., a musical composition). For counter-examples spring to mind. (1) The standard repertoire of emotionally expressive classical jazz includes among other examples of music: the 12-bar blues. (2) The standard repertoire of emotionally expressive classical Iranian music includes among other examples of music: gusheh-ha (singular gusheh). (3) The standard repertoire of India's emotionally expressive classical music includes among other examples of music: ragas.[5]

Why is the twelve-bar blues or a gusheh or a raga not a musical work (i.e., a piece of music, i.e., a musical composition)? A musical work has the following conventional property: most of its sounding or silent events at one performance are in the same temporal succession at any other performance. This property is shared not only by those conventional musical examples mentioned in Budd's article, Mahler's Symphony No. 6, Mozart's Masonic Funeral Music, and Elgar's Sospiti, but also by many other conventional musical examples from many other times and places in the world. By contrast, the 12-bar blues (in its instrumental form without words) or a gusheh or a raga has the following conventional property: most of its sounding or silent events at one performance are not in the same temporal succession at any other performance. This property, too, is shared by many other conventional musical examples from many other times and places in the world. The former property, namely invariable temporal succession from performance to performance of most sounding or silent events, can be named succinctly: property I. The latter property, namely variable temporal succession from performance to performance of most sounding or silent events, can be named succinctly: property V. It follows that examples of emotionally expressive classical music having property I are conventional examples of music which are musical works, but examples of emotionally expressive classical music having property V are conventional examples of music which are not musical works. To my knowledge music theorizers have no accurate term for the class of musical examples having property V. The term 'improvisation' is often used, but it is inaccurate, since it often means, as in Quantz, ornamentation by the performer of musical examples having property I.[6]

(N.B. The distinction between properties I and V raises a question about musical identity: can an example of music be identified as two or more musical performances of the same music? This and other questions of musical identity are complex and controversial, meriting extended discussion. Nevertheless, one brief comment can be inserted here: music having property V lacks a conventional score. That is, such music is not denoted by some notations inscribed on some surface in some spatial ordering (combining left to right ordering or vice versa with top to bottom ordering or vice versa) according to the convention that all such spatial orderings denote one and the same temporal ordering: invariable succession of sounding and silent events at every performance. Thus, Goodman's claim that a musical work is identified by a conventional score[7] is irrelevant to much of the world's music.)

I think I hear a roar coming from various directions including Budd's: 'Who needs all this jargon - gusheh, gusheh-ha raga? All you need is one paradigm example of what is music, and obviously a work of Mozart fills the bill'. The paradigm example argument, often invoked tacitly or vaguely, is explicitly defined by Parry and Hacker. 'A definition of a genus by paradigm species is a definition in which the genus is defined by reference to a species which clearly and non-controversially illustrates the conventional intension of the definiendum-term'.[8] Try to apply this definition to the species, works of music, thus: a definition of the genus, emotionally expressive classical music, by paradigm species is a definition in which the genus, emotionally expressive classical music, is defined by reference to a species, works of music, which clearly and non-controversially illustrates the conventional intension of the definiendum-term, 'emotionally expressive classical music'. The attempt fails. Musical works do not illustrate clearly and non-controversially the conventional intension of the term 'emotionally expressive classical music', since musical works clearly lack a conventional property that many examples of emotionally expressive classical music possess, namely property V. Furthermore, the raga simhendra madhyama[9] and the gusheh which is the daramad of dastgah Shur[10] are not paradigm examples of the genus, emotionally expressive classical music, either, since they clearly lack a conventional property that many examples of that genus possess, namely property I. In that raga the augmented melodic interval between lowered ga and raised ma (third and fourth scale step) does recur repeatedly at every performance, according to a conventional rule, but by another conventional rule this interval is preceded or succeeded by sounding or silent events varying at every performance. Similarly, in that gusheh a melodic interval of a neutral second between scale steps 7 and 1 as well as between scale steps 6 and 7 does recur repeatedly at every performance, according to a conventional rule, but by another conventional rule this interval is preceded or succeeded by sounding or silent events varying at every performance. To my knowledge, music theorizers have no term for a paradigm species of the genus, emotionally expressive classical music.

Budd's paradigm example error is a semantic error involving the intension of the term 'emotionally expressive classical music', as pointed out in the previous paragraph. Another semantic error of exemplification made by Budd involves the extension of that term (i.e., its reference).[11] Budd uses the term 'emotionally expressive classical music' as a mass term which refers identically to any and all examples of emotionally expressive classical music. He would appear to be in distinguished company. Quine states that a mass term may identify its reference, as the mass term 'water' may refer to one and the same object scattered about at various places. However, he adds, a mass term may also divide its reference: 'Treating "water" as a name of a single scattered object is not intended to enable us to dispense with general terms and plurality of reference'.[12] For example, the general term 'lake' may refer to that part of the collective whole, water, which is exemplified by the water in Loch Lomond, and the general term 'pool' may refer to that part of the same whole which is exemplified by the water in Franklin Delano Roosevelt's swimming pool, and so on.

Could not Budd reason analogously about emotionally expressive classical music? The analogy would run as follows: treating 'emotionally expressive classical music' as a name of a single scattered object is not intended to enable us to dispense with general terms and plurality of reference. On this analogy, the general term 'symphony' would refer to that part of the collective whole, emotionally expressive classical music, which is exemplified by the emotionally expressive classical music in Mahler's Symphony No. 6; the general term 'gusheh' would refer to that part of the same whole which is exemplified by the emotionally expressive classical music in the daramad of dastgah Shur; and so on. The analogy is false. All examples of water have the same essential formula, [H.sub.2]O, whether in a lake or a swimming pool, but all examples of emotionally expressive classical music don't have the same essential formula, whether in a symphony or a gusheh. An essential formula of a symphony is I'e (invariable succession of events), whereas an essential formula of a gusheh is V'e (variable succession of events). The reference of these two formulas is not one and the same. In other words, the analogy falsely identifies the class of examples to which the mass term 'emotionally expressive classical music' refers and thereby falsely identifies the extension of that term.

Budd's semantic errors in exemplification, both intensional and extensional, are typical of music theorizers, present and past. Consider, for example, a selection by Alperson of fourteen philosophers of music and music theorists representative of late twentieth-century music theorizing in the Anglo-American tradition.[13] None of these theorizers betrays the slightest doubt that 'example of emotionally expressive classical music' is synonymous with 'work of emotionally expressive classical music'. Consider, too, a selection by Lippman of fifty-eight philosophers of music and music theorists representative of the Western cultural tradition.[14] Lippman points out that, although in antiquity there was some recognition of improvisation as a mark of genius and inspiration, yet the ancients' main emphasis was on composition as a craft (editor's introduction, volume I); he points out that in the nineteenth century there developed the concept of the work of art as an autonomous and self-contained world (editor's introduction, volume II); and he points out that in the twentieth century there has been an overwhelming interest in the analysis of compositions (editor's introduction, volume III). Furthermore, in the Damschroder-Williams selection of several hundred music theorists representative of the Western music-theoretic tradition,[15] the same point is illustrated: generalizations about emotionally expressive classical music are typically generalizations about musical works (i.e., musical compositions, i.e., pieces of music).

To summarize Section I: not only do some music theorizers flounder in elementary semantic errors, such as confusing object language with object, but also many music theorizers (whether music theorists or philosophers of music) make a profound semantic error by assuming that emotionally expressive classical music is exemplified solely by musical examples having property I, or that the term 'emotionally expressive classical music' refers solely to such examples. In other words, they assume that such examples, usually called musical works, exemplify all emotionally expressive classical music, whether by paradigm species (intensionally) or by mass term reference (extensionally). This is a semantic error in exemplification. It is a semantic error in exemplification in the natural language of music theorizing not exemplification in the language of music, the latter being Goodman's topic.[16]

I would not be surprised were some reader to retort that neither music theory nor philosophy of music can be reduced to branches of ethnomusicology. Such an objection would miss the point. Section I has not urged music theorizers to travel to Polynesia or Senegal to do field research - as though additional data from non-Western cultures would automatically solve all problems of exemplification. The point is semantic: generalizations about the partial intension or extension of the term 'emotionally expressive classical music' lack validity. They lack validity because a generalization about emotionally expressive classical music cannot be valid unless it is true of all examples thereof, not just some. What Section I deplores is that widespread acceptance of these invalid generalizations shrivels the concept of emotionally expressive classical music.

II

However, I am aware of an epistemic objection which would be to the point, namely: we do not know what the intension or extension of any term is unless we know how to use that term idiomatically in natural language.

Kennick once remarked that we know 'how to separate those objects that are works of art from those that are not because we know English'.[17] His witticism encapsulated an epistemic doctrine typical of ordinary language philosophy. As Rorty wrote at about that time, 'It is almost a cliche of recent analytic philosophy that to have knowledge of a universal is simply to know the meaning of a word'.[18] At first impression, these two quotations appear to support the objection I have just anticipated, since they link the semantic with the epistemic. On second thought, they furnish only superficial support, since they do not distinguish intension from extension. Although ordinary language philosophy has waned, this oversimplification is one of its errors from which music theorizers have not profited. For example, six influential music theorizers representative of the last three decades of the twentieth century[19] fail to distinguish the intension (or connotation or meaning) of the term 'music' from its extension (or denotation or reference). As a result, I find no precedent for responding to the epistemic objection I have anticipated. Therefore, I have decided to restrict my response within the remainder of this brief essay to just one of the myriad questions which the objection raises, namely this question: do we know what the extension of the term 'music' is, only if we know how to use that term idiomatically in natural language?

There are some musical terms in natural language whose idiomatic use presupposes knowledge claims. Consider, for example, that in Great Britain and America today music theorizers use terms that are in natural language but not in ordinary language, as when they say 'in the key of C major'. When the term 'key' is used by such music theorizers, it does not cease to be a term in the natural language of English. However, it does cease to be an ordinary language term in the natural language of English with rich ambiguity, illustrated by such expressions as 'the key to the lock', 'the Florida keys', and 'key me in'. It becomes a technical language term in the natural language of English. (Gilbert Ryle distinguished technical language from ordinary language but failed to acknowledge that a technical term can be in natural language.[20]) Although this technical term was adumbrated vaguely in treatises written during several centuries in diverse languages, such as Greek, Latin, Italian, French, Spanish, and German, as well as English, ultimately its application became unambiguous: today 'key' (italicized as a technical term) applies to a definitive system of intervallic relations among tones. This semantic fact is usually taken for granted, but a certain epistemic presupposition of it is usually ignored, namely: when theorizing about art music in Europe during several centuries before the twentieth, one knows that any sound is musical only if it is in a key.[21]

This is not the only instance of a knowledge claim presupposed in music theorizing. When the term 'maqam' is used in music theorizing in the Arab Middle East today, it ceases to be an ordinary language term in the natural language of Arabic, translatable into ordinary English ambiguously as 'position' or 'place'[22] or 'status' or 'system'.[23] It becomes a technical language term in the natural language of Arabic. Despite its gradual evolution out of treatises written in diverse languages, Farsi and Greek as well as Arabic, today 'maqam' (italicized as a technical term) applies unambiguously to a definitive system of intervallic relations among tones which differs from a key. Whereas the term 'key' applies to music with harmonic progressions (sometimes implicitly, as in the suites for solo instruments by Telemann, J. S. Bach, C. P. E. Bach, and others of that era), the term 'maqam' applies to music without harmonic progressions. For this reason the two terms 'maqam' and 'key' apply to mutually exclusive classes of musical examples. Nevertheless, the idiomatic use of 'maqam' implies a knowledge claim similar to that of 'key': when theorizing about art music in the Arab Middle East during several centuries before the twentieth, one knows that any sound is musical only if it is in a maqam (translating 'it is in a maqam' phonetically as: wehua fi'l maqam; transliterating it as: whw' by 'l-m'q'm).[24]

Consider a third instance of the same sort. In north India today, when music theorizers use the term 'that', this term ceases to be an ordinary language term in the natural language of Hindi translatable into ordinary English ambiguously as 'framework'[25] or 'luxury'.[26] It becomes a technical language term in the natural language of Hindi, even though centuries elapsed before this technical meaning emerged from treatises in various languages, such as Sanskrit, Tamil, and Urdu, as well as Hindi. Today, 'that' (italicized as a technical term) applies unambiguously to a definitive system of intervallic relations among tones which is neither a key nor a maqam.[27] The term 'that' applies to music without harmonic progressions, unlike music in a key, and to music with drone tone(s), unlike music in a maqam. For this reason the three terms 'that', 'key', and 'maqam' apply to three mutually exclusive classes of musical examples. However, the epistemic point remains: when theorizing about art music in the Hindustani tradition of north India during several centuries before the twentieth, one knows that any sound is musical only if it is in a that.

Here is substantial evidence that natural language idiomatically used in music theorizing is not natural language simpliciter. Rather, it is a special kind of natural language. This special kind of natural language mixes together, even in a single sentence, ordinary language (such as the noun phrases 'anything sounding', 'an example of music', and so on) with technical language (such as the verb phrases 'is in a key', 'is in a maqam', and so on).

Let me call any such language mix an LM.

Many such language mixes are in use. European music theorizers use one LM (or set of LM's if sub-cultures and historical eras are distinguished); Arab Middle East music theorizers use another LM (or set of LM's); those in north India use another; and so on.

Now, it is a fact that some LM's have terms applying to mutually exclusive classes of musical examples, as already noted. In view of this fact we cannot claim that we know what class it is to which all musical examples belong. On the contrary, we have reason to ask. Accordingly, we must revise the initial question thus: do we know what the extension of all incompatible LM's is, only if we know how to use them idiomatically?

Let us put this question in its starkest terms. Let '[LM.sub.1]' denote any language mix which defines a necessary condition for knowing whether any sound is musical. Then [LM.sub.1] says:

Anything sounding is musical only if p

The letter p here is a schematic letter which can be replaced by 'it is in a key' or 'it is in a maqam' or 'it is in a that' or some other such open sentence.[28] Let '[LM.sub.2]' denote any other language mix whose condition for knowing whether any sound is musical is incompatible with p. Then [LM.sub.2] says:

Anything sounding is musical only if q

The letter q here is a schematic letter which can be replaced by one or another open sentence incompatible with the replacement for p (as 'it is in a maqam' is incompatible with 'it is in a key'). Ultimately, then, the epistemic question at issue will boil down to this: do we know what the extension of [LM.sub.1] and [LM.sub.2] jointly is, only if we know how to use them idiomatically?

Confronted with incompatible concepts of music in diverse cultural traditions, many turn to multiculturalism or cultural pluralism or cultural relativism for an explanation. One version of cultural pluralism, widely accepted, uses the plural term 'musics' to refer to music in diverse cultural traditions.[29] This solution to the epistemic question at issue would seem to be simplicity itself: take incompatible statements about music to be alternatives. That is, simply assume that we know that:

anything sounding is musical only if p, or anything sounding is musical only if q.

Unfortunately, the appearance of simplicity is deceptive. To talk about anything musical is to talk about any and all examples of music, i.e., to talk about the extension of any mass term for music. But, clearly, whatever the extension of some mass term for music in [LM.sub.1] is interpreted to be, it cannot be identified with the extension of some mass term for music in [LM.sub.2], since any sound which is musical only if p cannot be one and the same sound which is musical only if q, due to the incompatibility of p and q. What is really being assumed is more complex, namely that we know that:

Any sounding x is musical x only if p, or any sounding y is musical y only if q

In other words, what is really being assumed is that the values of x comprise the universe of discourse of [LM.sub.1] and the values of y comprise the universe of discourse of [LM.sub.2]. Thus unmasked, this version of cultural pluralism turns out not to solve a semantic problem but to create one, namely untranslatability (not indeterminate translation, which is Quine's topic).[30] That is, the term for musical x in [LM.sub.1] could not be translated into the term for musical y in [LM.sub.2] at all. Even if it happens to be the case that some such terms are similar, as the English term 'music' resembles the Arabic term 'musiqi',[31] nevertheless any such similarities only obscure the underlying semantic dilemma, namely: if any and all musical examples were taken to comprise the values of x, then no musical examples at all could be included among the values of y; and vice versa. By this reasoning English speakers could not give the name 'music' to any examples of musiqi, and Arab speakers could not give the name 'musiqi' to any examples of music. This version of cultural pluralism makes a semantic error in extensional identity: mistaking mutually exclusive universes of discourse called musics for one and the same universe of discourse called music.

I can think of at least three cultural relativists who eschew plural universes of discourse. Without pretending to give a complete. account of their views, let me show the relevance of their views to the epistemic question at issue: do we know what the extension of [LM.sub.1] and [LM.sub.2] jointly is, only if we know how to use them idiomatically? Danto submits that what is art (including music) is determined by transfiguration. A commonplace object o is transfigured into a work of art W by means of some interpretation I in some historico-cultural context (such as a metaphorical interpretation or an expressional interpretation or a stylistic interpretation); another interpretation I of the same commonplace object in some other historico-cultural context transfigures it into another work of art; and so on. Such transfiguration, says Danto, is a kind of function such that I(o) = W.[32] Margolis submits that what is art (including music) is determined by culturally emergent properties. One set of properties embodied in physical objects (but not physical properties of those objects) emerges only when the physical objects are in a certain historico-cultural context; another set of properties, likewise embodied in physical objects though not physical properties, emerges only in another historico-cultural context; and so on.[33] Wolterstorff submits that what is art (including music) is determined by norm-kinds. One norm-kind of art is established by the practices of artists (e.g., the performance practices of musicians) in one historico-cultural context; another norm-kind of art is established by other practices of artists (e.g., other performance practices of musicians) in another historico-cultural context; and so on.[34]

Now, each of these three philosophers theorizes cross-culturally within a single universe of discourse. This universe comprises commonplace objects (for Danto) or physical objects (for Margolis) or performed objects such as violins (for Wolterstorff). Furthermore, each of these three philosophers uses an LM, since each mixes ordinary English phrases, such as 'it is' or 'it has', with technical English terms, such as 'a musical work', 'atonal', 'measures', or 'notated'. Using an LM implies that the necessary conditions for knowing whether any sound is musical can be stated in [LM.sub.1] or [LM.sub.2]. Therefore, all three philosophers imply that the epistemic question at issue should be answered as follows: we know that

any sounding x is musical x only if p or q

This amounts to saying that any member of the sounding class is identical with any member of the musical class, only if p or q - an implicit identification of a universe of discourse. Explicitly stated, we know that any object x, whether a commonplace or physical or performed object, is sounding if and only if it is musical on condition that p or q. That is, the epistemic question at issue can be answered as follows: we know that

(x) (Sx [equivalent to] Mx .only if. p or q)

Does this version of cultural relativism answer the epistemic question at issue? Do we know what the extension of [LM.sub.1] and [LM.sub.2] jointly is, only if we know how to state idiomatically in one or the other a necessary condition for any sound to be musical?

Let us consider one particular case, the case when a commonplace or physical or performed object x is musical only if sounding in a key. In this particular case a musical sound is not in a maqam, of course, since the two open sentences, 'it is in a key' and 'it is in a maqam', are mutually exclusive, as explained earlier. This is a case of p and not q:

(x) (Sx [equivalent to] Mx .only if. pq)

By contrast, let us consider another particular case, the case when object x is musical only if sounding in a maqam. In this particular case a musical sound is not in a key, of course - for the same reason. This is a case of q and not p:

(x) (Sx [equivalent to] Mx .only if. qp)

These two cases offer a choice, namely: identify any and all values of x as musical sounds in a key but not in a maqam, or vice versa. That is:

(x) (Sx [equivalent to] Mx .only if. pq or qp)

Notice that this choice is exclusive. If any and all values of sounding x are musical conditional on pq, none can be conditional on qp; but if any and all are musical conditional on qp, none can be conditional on pq. That is to say, x is in a key if and only if not in a maqam, in a that if and only if not in a maqam, in a key if and only if not in a that, and so on for other cultural traditions. For this reason the expression 'pq or qp' can be replaced by the expression 'p if and only if not q':[35]

(x) (Sx [equivalent to] Mx .only if. p [equivalent to] q)

In the final analysis, then, this version of cultural relativism harbours a contradiction. It says that the members of the sounding class and the members of the musical class all belong to one and the same class, only if they belong to two mutually exclusive classes. This incoherence results from mistaking the exclusive 'or' between p or q for a non-exclusive 'or' - more fully, from assuming that all historico-cultural conditions for knowing whether any sound is musical are non-exclusive conditions, whereas in fact some are exclusive. Thus occurs an error in extensional identity, namely the claim that the extension of the term 'musical sounds' is identified (Sx [equivalent to] Mx), only if it isn't (p [equivalent to] q).

To summarize Section II: music theorizers (whether music theorists or philosophers of music) typically make profound semantic errors in extensional identity by assuming that mutually exclusive universes of discourse about music have one and the same extension, or that in a single universe of discourse mutually exclusive terms for musical conditions have one and the same extension. Exposing these errors has shown that the answer to the epistemic question at issue is: no. We do not know what the extension of [LM.sub.1] and [LM.sub.2] jointly is, only if we know how to use them idiomatically.

I would not be surprised were some reader to retort that epistemology has nothing to do with cultural relativism in the first place. Such an objection would miss the point. Section II doesn't advocate epistemic relativity - as though contradictory knowledge claims about music of diverse cultures could possibly constitute a single coherent body of knowledge. The point is semantic: we know that incompatible LM's cannot possibly have one and the same extension. We know this because we know that mutually exclusive classes of musical examples cannot possibly have the same members. What Section II deplores is that this widespread error in extensional identity has turned much cross-cultural generalizing into gibberish.

CONCLUSION

Sections I and II have exposed some serious semantic errors in the kind of music theorizing language in widespread use. At first thought the solution might seem simple: just repair this linguistic vehicle which has carried us along so far. On second thought the question arises: would this be trying to make a bus out of a bike?

For, as Section I showed, to assume that every example of music is in the same temporal succession at every performance is to make a semantic error in exemplification, because not every example of music is; but, as Section II showed, attempting to correct this error by means of conventional music theorizing languages (LM's) leads to an incoherent conclusion: all musical examples belong to one and the same class, the musical class, only if they belong to mutually exclusive musical classes. Clearly, Sections I and II jointly not only raise the question whether music theorizing is handicapped by the kind of theorizing language it uses (the LM kind) but also answer that question in the affirmative.

As matters stand at present, then, the semantics of music theorizing is broke in two senses of the word, being both bankrupt and dysfunctional. It needs fixin'. The need is severe. Nothing less than drastic reform will do. If the diverse music theorizing languages presently in widespread use cannot even identify the class of examples they are all talking about, then we need to develop a new kind of music theorizing language which can.

REFERENCES

1 See, e.g., A. W. Moore, ed., Meaning and Reference (Oxford U. P., 1993); C.-T. James Huang and Robert May, eds., Logical Structure and Linguistic Structure: Cross-cultural Perspectives (Dordrecht: Kluwer, 1991); Emmon W. Bach, Informal Lectures on Formal Semantics (New York: SUNY Press, 1989); John Passmore, Recent Philosophers (LaSalle, Illinois: Open Court, 1985) chapters 3, 4; William G. Lycan, Logical Form in Natural Language (Cambridge, Massachusetts: MIT Press, 1984); S. D. Guttenplan, ed., Mind and Language (Oxford U. P., 1975); M. Munitz and P. Unger, eds., Semantics and Philosophy (New York U. P., 1974); D. Davidson and G. Harman, eds., Semantics of Natural Language (Dordrecht: Reidel, 1972).

2 'Music and the Communication of Emotion', The Journal of Aesthetics and Art Criticism vol. 47, no. 2 (Spring 1989), pp. 129-38.

3 The locus classicus of this distinction is in Rudolf Carnap, The Logical Syntax of Language, trans. Smeaton, sixth ed. (with corrections) (London: Routledge and Kegan Paul Ltd., 1964; orig. pub. 1934), ch. 1, p. 11.

4 This theory of musical expression clarifies and augments ideas originally advanced in Budd's book, Music and the Emotions (London: Routledge and Kegan Paul, 1985).

5 See, e.g., Stanley Sadie, ed., The New Grove Dictionary of Music and Musicians (London: Macmillan, 1980) containing extensive articles on African, African-American, American, Near East, and Far East classical traditions, such as 'Blues', vol. 2, pp. 812-19; 'Iran', vol. 9, pp. 292-309; and 'India', vol. 9, pp. 69-166. Also William P. Malm, Music Cultures of the Pacific, the Near East, and Asia, 2nd ed. rev. (Englewood Cliffs, New Jersey: Prentice-Hall, 1987) containing the statement on p. 213 of the epilogue: 'three of the four major written music-theory systems of the modern world [are]: the Arab-Persian, Indian, and Chinese'.

6 See, e.g., David Damschroder and David Russell Williams, 'Improvisation' (heading in topic index) in Music Theory from Zarlino to Schenker: a bibliography and guide (Stuyvesant, New York: Pendragon, 1990).

7 Nelson Goodman, Languages of Art, 2d ed. (Indianapolis: Hackett, 1976) ch. V.

8 William T. Parry and Edward A. Hacker, Aristotelian Logic (Albany: SUNY Press, 1991) ch. 5, sec. 5D1c, def. 27, p. 106.

9 See, e.g., Walter Kaufman, The Ragas of South India (Bloomington: University of Indiana Press, 1967) pp. 599-600; Three Ragas: Ravi Shaukar (Hollywood: Capitol DT 2720, n.d., probably late 1960s) side 1, band 2 - not side 2 as the jacket notes erroneously say.

10 See, e.g., Hormoz Farhat, 'Art Music, intervals and scales', section I of 'Iran' in Sadie, ed., The New Grove vol. 9, p. 296, Ex. 1; Classical Music of Iran (New York: Nonesuch, H-72060, 1974) side 1, band 1; Ella Zonis, Classical Persian Music: an Introduction (Cambridge, Massachusetts: Harvard U. P., 1973) p. 14, n. 20; p.49, fig. 3; B. Nettl with Bela Foltin, Jr., Daramad of Chaharga: A Study in the Performance Practice of Persian Music (Detroit: Information Coordinators, Inc., 1972) pp. 32-3.

11 For the rough distinction between intension (meaning, connotation) on the one hand and extension (reference, denotation) on the other hand see, e.g., Irving G. Copi, Introduction to Logic, 5th ed. (New York: Macmillan, 1978) section 4.4, pp. 142-7. For finer distinctions among these six terms, see, e.g., Donald Kalish, 'Semantics', in P. Edwards, ed. The Encyclopedia of Philosophy (New York: Macmillan, 1967) pp. 348-58; and Norman Kretzmann, 'Semantics, History of', in the same encyclopedia, vol. 7, pp. 358-406, notably in the fourth section on the nineteenth and twentieth centuries, pp. 391-404.

12 W. V. Quine, Word and Object (Cambridge, Massachusetts: MIT Press, 1960) ch. III, sec. 20, p. 99.

13 Philip Alperson, ed., What Is Music? (New York: Haven, 1987).

14 Edward A. Lippman, Musical Aesthetics: A Historical Reader (Stuyvesant, New York: Pendragon, 1990).

15 Music Theory from Zarlino to Schenker.

16 Languages of Art, ch. II.

17 W. E. Kennick, 'Does Traditional Aesthetics Rest on a Mistake?' Mind vol. 67 (1958) pp. 317-34; reprinted in F. J. Coleman, ed., Contemporary Studies in Aesthetics (New York: McGraw Hill, 1968) pp. 411-27; quoted sentence in Coleman, p. 415.

18 Richard Rorty, 'Relations, Internal and External' in Edwards, The Encyclopedia of Philosophy, vol. 7, pp. 125-33; quoted sentence p. 129.

19 Jerrold Levinson, Music, Art, and Metaphysics (Ithaca: Cornell U. P., 1990); Jean-Jacques Nattiez, Music and discourse: toward a semiology of music, Eng. trans. by C. Abbate (Princeton U. P., 1990) - a complete rewriting of Nattiez, Fortdements d'une semiologie de la musique (Paris: Union generale d'editions, 1975); Peter Kivy, Sound and Semblance (Princeton U. P., 1984); Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, Massachusetts: MIT Press, 1983); Wilson Coker, Music and Meaning (New York: Free Press, 1972); Leonard B. Meyer, Explaining Music: Essays and Explorations (Berkeley and Los Angeles: University of California Press, 1973).

20 Joseph Oliva pointed this out to me in a conversation concerning Gilbert Ryle, 'Ordinary Language' in Collected Papers (New York: Barnes and Noble, 1971) vol. II, essay 23, pp. 301-18.

21 See, e.g., Thomas Christensen's review of two books, one by Carl Dahlhaus, Studies on the Origin of Tonality, trans. Gjerdingen (Princeton U. P., 1990) and the other by Joel Lester, Between Mode and Keys: German Theory 1592-1802 (Stuyvesant, New York: Pendragon, 1989) in Music Theory Spectrum v. 15, no. 1 (Spring, 1993) pp. 94-111.

22 Harold Powers, 'Mode as a Musicological Concept', in Sadie, The New Grove vol. 12, pp. 422-50; quoted terms pp. 423, 429.

23 Alan Podet, Arabist, College at Buffalo, State University of New York, USA.

24 Podet.

25 Malm, Music Cultures, ch. 4, p. 99.

26 Mamta Bhargava, Hindu Cultural Center, Buffalo, New York, USA.

27 A succinct summary of the point is in Bonnie Wade, 'Classification of Ragas' in Music in India: The Classical Traditions (Englewood Cliffs, New Jersey: Prentice-Hall, 1979) ch. 3, p. 79.

28 This concept of a schematic letter follows W. V. Quine, Methods of Logic, 3d ed. (New York: Holt, Rinehart, and Winston, 1972) ch. 22, p. 121.

29 E.g., Helen Myers, ed., Ethnomusicology: An Introduction (New York: Norton, 1992) pp. 7, 9, 14; Bruno Nettl, 'Musics and Cultures', topic heading, p. 377 of Myers; Joseph Kerman, Contemplating Music (Cambridge, Massachusetts: Harvard U. P., 1985), pp. 174, 175, 228; Elizabeth May, ed., Musics of Many Cultures (Los Angeles: University of California Press, 1980).

30 Quine, Word and Object, ch. II.

31 A traditional term appearing as early as the tenth century AD in the title of Al-farabi's treatise, Kitab al-musiqi al-kabir. See, e.g., Henry G. Farmer, Al-farabi's Arabic-Latin Writings on Music (Glasgow: the Civic Press, 1934).

32 Arthur Danto, The Transfiguration of the Commonplace (Cambridge, Massachusetts: Harvard U. P., 1980) ch. 5, p. 125.

33 Joseph Margolis, Art and Philosophy (Brighton: Harvester, 1980) intro. and ch. 1.

34 Nicholas Wolterstorff, Worlds and Works of Art (New York: Oxford U. P., 1980) intro., wherein artistic practices are declared fundamental, and p. 58, where works of art are defined as norm-kinds.

35 Quine, Methods of Logic, ch. 3, first exercise, p. 23.

For constructive criticisms of earlier drafts of this essay I am indebted to Ronald Roblin, Joseph Oliva, Hilde Hein, an anonymous referee for this journal, and participants in the 1990 meeting of the eastern division of the American Society for Aesthetics at Fredericksburg, Virginia, notably Morris Grossman.

Robert B. Cantrick, Performing Arts Department, Buffalo State College, Buffalo, New York 14222-1095, U.S.A.
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Publication:The British Journal of Aesthetics
Date:Jul 1, 1995
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