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sound-waves, all stand to one another in the same internal relation of depicting that holds between language and the world"" (paragraph 4.014). Although subsequently he abandoned the picture theory, the joint study continued.
The proposal appears repeatedly in his Blue and Brown Books (1931/ 1958)-thought to be the notes for his last work, Philosophical Investigations (1953)-and in other places. In the Investigations, he a.s.serts: ""Understanding a sentence lies nearer than one thinks to what is ordi-narily called understanding a musical theme"" (1953, paragraph 527).
This engagement throughout his philosophical career suggests that Wittgenstein might have had something deeper in mind than merely using music as a handy a.n.a.logy for his remarks on language. Keeping to his later works, it seems that the suggested parallel between music and language involved two broad but related steps: rejection of ""emotive"" theory of music, and emphasis on internal significance of music.
6.2.2.1.
Music and Emotions Wittgenstein rejected what is generally held to be the most salient aspect of music: music ""represents emotions in a way that can be recognized by listeners"" (Dowling and Harwood, cited in Raman 1993, 42). Raman proceeds to cite Roger Scruton: it is ""one of the given facts of musical culture"" that the hearing of music is ""the occasion for sympathy."" For Scruton, if someone finds the last movement of The Jupiter Symphony ""as morose and life-negating,"" he would be ""wrong"" (see also Boghossian 2007).
Thus the literature on the emotional significance of music includes items such as being merry, joyous, sad, pathetic, spiritual, lofty, dignified, dreamy, tender, dramatic; it also includes reference to feelings of utter hopelessness, foreboding, sea of anxiety, terrified gesture, and the like.
Jackendo and Lerdahl (2006) suggest the following list: gentle, forceful, awkward, abrupt, static, earnest, opening up, shutting down, mysterious, sinister, forthright, n.o.ble, reverent, transcendent, tender, ecstatic, senti-mental, longing, striving, resolute, depressive, playful, witty, ironic, tense, unsettled, heroic, or wild.12 Following Jackendo 1992 and Jackendo and Lerdahl 2006, I would call these things collectively as ""musical aect.""
Wittgenstein dismissed the whole thing: ""It has sometimes been said that what music conveys to us are feelings of joyfulness, melancholy, tri-umph etc., etc. and what repels us in this account is that it seems to say that music is an instrument for producing in us sequences of feelings.""
Elaborating on why he is ""repelled,"" he says that it is a ""strange illusion""
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that possesses us when ""we say "This tune says something," and it is as though I have to find what it says"" (1958, 178). In the absence of supporting arguments and evidence from Wittgenstein, we may interpret these remarks as follows.
Let us ask why emotions are seen to be so strongly a.s.sociated with the expressive content of music. Music seems to pose the dilemma that it both conveys and does not convey ""thoughts;"" appeal to emotions seems to solve the dilemma. To appreciate the dilemma, for anyone even marginally engaged with music, it seems that ""music is not understood in a vacu-um, as a pure structure of sounds fallen from the stars, one which we receive via some pure faculty of musical perception"" (Levinson 2003). In that sense, a tune seems to ""say"" something.
In the paper cited, Jerrold Levinson supports the thoughtful nature of music with a range of musical examples.13 Thus, we can think of music as drawing a conclusion (Beethoven"s Piano Sonata, op. 110, Dvorak"s Sev-enth Symphony), coming to a close (minuet movements from Mozart"s 40th or 41st), a.s.serting (the opening of Schubert"s Piano Trio No. 2, op. 100), questioning (the opening phrases of Beethoven"s Piano Sonata No. 18, op. 31, no. 3), imploring (the flute introduction to Bellini"s aria Casta Diva), defying (the opening of Beethoven"s Fifth Symphony), disapproving (the orchestral interjections in the first part of the finale of Beethoven"s Ninth Symphony), and so on. Levinson asks: ""Can a medium capable of summoning up such a range of mindful actions be a domain in which thought is absent?""
However, the most obvious candidate for what-is-said, namely, a proposition with truth value, simply does not apply to music. In other words, music does not seem to correlate with extramusical objects which either do or do not satisfy a given musical expression: ""I know that [a tune]
doesn"t say anything such that I might express in words or pictures what it says"" (Wittgenstein 1931/1958, 166). What then do musical thoughts express or signify?
The widespread intuition that music is intimately a.s.sociated with aects helps address the problem. Given the ""strange illusion"" that the sayability of music needs to be captured in some or other extramusical terms, people find it natural to a.s.sume that music expresses aects; perhaps one could even say that (specific) aects are what given pieces of music mean.14 In fact, a closer look at Levinson"s defense of Wittgenstein"s claim that music is a thoughtful activity does not preclude that these thoughts basically produce aects. For example, apart from the instances of musical ""thought"" cited above, Levinson also includes the 204
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following: angrily despairing, menacing, cajoling, comforting, bemoaning, heaven-storming, and so on. It is hard to make sense of these things without some notion of aect. These and the earlier examples suggest that Levinson is more interested in the ""pragmatic"" aspects of musical thought than its ""semantic"" aspects; that is, he is more interested in what music does (to people) than in what music is. It is also instructive that, despite his frequent citations from Blue and Brown Books, Levinson fails to discuss the crucial remark at (178) that recommends disa.s.sociating music from its aects, as we saw.
Notwithstanding its intuitive appeal, there is also a growing body of literature that questions the idea that musical understanding can be suciently explained in terms of musical aects, although the ""a.s.sociation""
between them is never denied. For brevity, I will mention just two related objections to the idea (for more, see Mukherji 2000, chapter 4; Vijaykrishnan 2007, chapter 7, for objections to Mukherji). It seems that ascription of specific aects to given pieces of music is not stable: the first movement of Mozart"s G minor symphony, now considered tragic, was viewed by nineteenth-century critics as cheerful. Further, two very dierent pieces of music from the same or dierent genres can both be viewed as cheerful: Mozart"s Ein Kleine Nachtmusik and the medium-tempo parts of performances of, say, raagas Jayjawanti or Bilaval. If the ""cheerfulness"" is traced to the tempi, then the tonal structure of music becomes irrelevant, apart from the implausible consequence that all music in a certain tempo would have to be viewed as cheerful.
Keeping to the tonal structure, suppose we think of the Beatle"s song Mich.e.l.le as generally sad. Ignoring the (palpably sad) words, could the sadness be traced to the fact that much of the melody in Mich.e.l.le ""moves in a relatively small range in the mid-to-low vocal range, with a generally descending contour,"" as Jackendo and Lerdahl (2006, 63) seem to suggest? Unless sadness is a.s.sociated with this range by definition, I can easily cite sad music that ""wails"" as the notes ascend in the mid-to-high range. In contrast, (the early part of ) the slow movement ""in a relatively small range in the mid-to-low vocal range"" of the so-called morning raaga aahir bhairav is meant to evoke not sadness, but spirituality tinged with joy as the ""dawn breaks.""
This leads to the problem-hardly mentioned in the otherwise ma.s.sive literature on the topic to my knowledge-that, even if we are able to ascribe specific aects to given pieces of music to some degree of agreement between people hearing it, aects can only be global properties of (large) chunks of music; typically, aects are a.s.signed to an entire piece of music, Language and Music 205.
as we saw. But, informally speaking, music is a complex organization of tones which we hear on a tone by tone basis, forming larger and larger groups as we proceed. It is hard to see how the global (aective) property of the piece is computationally reached from its smaller parts.
To me, the problem seems pretty overwhelming. If a cheerful music is cheerful in each of its parts-an implausible a.s.sumption in any case-then the compositionality of the global property of cheerfulness is trivial; that is, the music as a whole is not saying anything dierent from its parts. If a (globally) cheerful music is not cheerful in its parts, then cheerfulness is not a compositional property of the piece of music allowing Ein Kleine Nachtmusik and Jayjawanti to have identical global properties, as noted; aects just do not compute in the desired sense. In sum, the notion of musical aect makes the deeply complex and significant internal structure of music essentially irrelevant for understanding of music. It is interesting that Jackendo and Lerdahl (2006, 61) note, almost in pa.s.sing, that ""musical meaning"" is ""the aects that the listener a.s.sociates with the piece by virtue of understanding it."" So, the ""a.s.sociation"" of aect with the piece follows its understanding; the a.s.sociated aect, therefore, does not explain what it is to understand a piece of music. The dilemma, posed above, persists.
None of this is meant to deny that musicians and their audiences are often aected by music-as reflected, in part, in their complex facial responses. The point is that the fact need not to be traced to the internal structure of music itself. Jackendo (1992, chapter 7) shows that it is possible to explain why we want to hear the same music from the properties of musical processing alone, not because the piece invokes-although it may-pictures of reality, desires, and the like, that we wish to revisit.
From a dierent direction, Ma.s.simo Piattelli-Palmarini (personal communication) suggests that, even if opera shows that certain emotions (ha-bitually) go with certain kinds of melodies, it could be that representations are not involved. If these suggestions hold, then, it should be possible to explain the undoubtedly intimate relationship between music and human aects without tracing the relationship to the internal structure of music.
As songs attest, outputs of both language and music certainly access aects. Perhaps music accesses aects more directly and definitively because music has nothing else to access.
6.2.2.2.
Internal Significance Given the salience of the notion of musical thought, and the total absence of anything extramusical to correlate these thoughts with, Wittgenstein (1931/1958, 166) proposed perhaps the only 206
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option left: ""Given that what a tune "says" cannot be said in words, this would mean no more than saying "It expresses itself." To bring out the sense of a melody then "is to whistle it in a particular way." "" As noted, he extends the claim to language as well-to the understanding of a sentence, for example. He suggests that what we call ""understanding a sentence"" has, in many cases, a much greater similarity to understanding a musical theme ""than we might be inclined to think."" The point is that we already know that understanding a musical theme cannot involve invoking of ""pictures."" Now the suggested similarity between music and language is meant to promote a similar view of language as well, that is, no ""pictures"" are made even in understanding a sentence. ""Understanding a sentence,"" he says, ""means getting hold of its content; and the content of the sentence is in the sentence"" (p. 167).
The remarks quoted from Wittgenstein suggest that they comprise of three ideas: that music expresses itself, what the music expresses can only be shown by whistling it in a particular way, and that understanding sentences of a language is much like understanding pieces of music. Is there a way of giving a coherent shape to these apparently disjoint claims? To emphasize, we are aiming for a scheme in which each of these ideas play significant roles.
The idea that music expresses itself is the natural place to start since it signals the point of departure from ""externalist"" understanding of music.
Roger Scruton (2004) supports Wittgenstein in questioning the prevalent idea that musical meaning is a relation between music and something else such as emotions. Scruton holds that, for Wittgenstein, it is either not a relation at all, or, at best an ""internal relation"" in the ""idealist"s sense"" that ""denies the separateness of the things it joins."" In line with this thought, Scruton suggests that ""the connection has to be made in the understanding of those who use the sign."" However, for Scruton, the ""idealist"s sense"" is best understood in terms of the a.n.a.logy of (gestalt properties of ) facial expressions and ""first-person ascriptions."" But then Scruton also holds that Wittgenstein"s reference to language is ""no more than an a.n.a.logy"" since linguistic understanding, unlike musical understanding, involves ""semantic properties"" governed by a generative grammar.15 No doubt, in some scattered remarks, Wittgenstein did toy with the a.n.a.logy of facial expressions (I am setting aside the first-person issue).
But he explored it-without much success in my opinion-primarily for language, especially for word meanings, to study what may be involved in ""semantic interpretation."" So, by Scruton"s own account, if the study of Language and Music 207.
musical understanding is like the study of facial expressions, then the similarities with language cannot just be ""no more than an a.n.a.logy."" In any case, appeals to such a.n.a.logies just shift the problem back one step: What structural conditions give rise to facial expressions? In sum, not only that Scruton fails to take into account Wittgenstein"s lifelong conviction about deep similarities in linguistic and musical understanding, he gives no clue as to how the ""internal relation"" between musical ""signs"" gives rise to a particular way of whistling them.
For Levinson (2003), in contrast, music is languagelike insofar as linguistic meaning is essentially characterized in terms of the thought expressed. In fact, he suggests that the process of musical thinking can be traced to the internal structural development of music. He calls it ""intrinsic musical thinking""; it resides ""in the mere succession from chord to chord, motive to motive, or phrase to phrase at every point in any intelligible piece of music."" Levinson ill.u.s.trates the point with an almost measure-by-measure a.n.a.lysis of the first movement of Beethoven"s Tempest Sonata (op. 31, no. 2). For example, in the first two measures, a four-note rising motif ""has about it a p.r.o.nounced air of uncertainty and wonder."" In measures 26, the initial motif is followed by a descending allegro motif which ""anxiously frets,"" ending in an adagio turn of ""ques-tioning character,"" and so on.
The richness of Levinson"s description makes it clear that he traces the ""intelligibility"" of ""intrinsic musical thinking"" essentially to the aects of the interpreter, not to the tonal and relational properties of the musical structure itself. To understand a piece of music, Levinson holds, is to learn ""how to respond to it appropriately and how to connect it to and ground it in our lives."" This not only raises all the problems about the relation between musical structure and aects all over again, it fails to give a suciently narrow interpretation of Wittgenstein"s idea that music expresses itself. In other words, Levinson places the Wittgensteinian theme of language-likeness of music in a framework that does not make durable contacts with the rest of Wittgenstein"s themes.
The theme of ""internal relations"" has been explored more directly by Yael Kaduri (2006). Instead of describing the tonal structure of music, Kaduri focuses on the general pause-silent figure (aposiopesis)-in Haydn"s instrumental music. Working through ""the immensity of Haydn"s repertoire,"" Kaduri notes that Haydn"s music ""contains so many general pauses that it seems they form an intrinsic component of his musical language."" The pauses seem to fall under definite style-specific categories, diering as styles dier: string quartets, symphonies, 208
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movements in sonata form, rondo movements, and minuets. Further, ""the pauses almost always appear in the same positions in each of the dif-ferent forms""-for example, in the rondo finale movements, the pauses are ""juxtaposed to the successive repet.i.tion of a small motif."" According to Kaduri, thus, the ""dierent ways in which Haydn employs the general pause and the logical links between them const.i.tute a "grammar" of the general pause, which provide its meaning.""
The data of (Haydn"s use of ) the general pause suggests how musical understanding can be explained in part from structural conditions alone.
To that extent, Kaduri"s adoption of the notion of ""grammar"" from Wittgenstein seems appropriate. In fact, it is another puzzle in Wittgenstein"s work that, although he gave up the notion of ""logical form""
pursued in his early work, he continued to invoke some notion of ""grammar"" in his later work on language. Without entering into exegesis, it stands to reason that he was searching for a notion that captured just the structural conditions met by symbols that furnished the underlying basis for interpreting them.
In his earlier work, Wittgenstein could have thought that the prevalent Frege-Russell notion of logical form captured those conditions. Having found that notion to be untenable, he might have searched for an alternative in the conditions of musical understanding. As Sarah Worth (1997) insightfully remarks: ""Music is often seen as being problematic because of its lack of detectable meaning, but this is precisely why Wittgenstein thinks it has an advantage. The necessarily abstract quality of music allows us to avoid being absorbed merely with the quest for referential meaning."" The phenomenon of general pause shows how the ""necessarily abstract quality"" works. As Kaduri observes, the pauses by themselves are not meaningful; they contribute to the meaning of pieces of music as it progresses by relating chunks of musical structure in formally specifi-able ways. Kaduri does not tell us how the internal significance of the chunks, that are related by the pauses, itself arises. But Levinson"s a.n.a.lysis of Beethoven"s Tempest Sonata clearly shows that such chunk-specific meaning does arise at least on a measure by measure basis, although Levinson"s idea of what that meaning is is not likely to have impressed Wittgenstein.
Pursuing the proposed reconstruction of Wittgenstein a bit further, it is plausible to a.s.sume that, as with anyone interested in the workings of language, Wittgenstein could have been intrigued by the fact that a bunch of symbols in a.s.sociation with one another is somehow capable of conveying Language and Music 209.
meaning. A natural thought is that much of the ""meaning"" so conveyed must be ensuing from the structural conditions governing the array of symbols themselves; hence the need for some notion of grammar. In the case of music, it looks as though structural meaning is all there is to the notion of musical meaning. Once that meaning is grasped by a competent performer or listener, the music may be ""whistled"" in a particular way-the particularity being determined by the specific structural meaning a.s.signed to a selection of notes.
In the language case, this perspective is hard to maintain in view of the dominance of ""referential meaning"" in linguistic understanding. Linguistic understanding thus comes in progressively thicker layers (Mukherji 2003b). Yet, as Wittgenstein saw, insofar as a linguistic expression is essentially a structure of symbols, the notion of structured meaning must obtain for language as well at some level. Following the a.n.a.logy of musical expression and the whistling of it, a natural division thus obtains between language per se and its use. On this view, to refer, or to convey extralinguistic information by some other means, or to engage in a speech act, is to ""whistle"" the sentence in a particular way that is largely determined by the internal organization of linguistic signs.
Contrary to some popular interpretations of Wittgenstein"s later philosophy, then, the use of a sentence is not its meaning; the meaning of a sentence is in the sentence-already, prior to use, as it were. This could well be a general phenomenon for the natural symbol systems, the hominid set, at issue; it may not obtain for artificial and nonhuman systems. In my opinion, this structured meaning is what is represented at LF, the semantic output of language. In that sense, just as Wittgenstein turned to music to throw light on language, we turn to language to throw light on music. We cannot a.s.sume of course that Wittgenstein had LF in mind.
But he did have logical syntax in mind when looking for an adequate notion of grammar in his early work. And the basic reason why he gave up logical syntax is that it required a ""picture"" theory; the theory of LF does not require such ""referential meaning.""
6.2.3.
Recursion in Music Suppose then that music is a symbol system. Even then there could be reservations that music is a system of discrete infinity in the desired sense available for language. Following an influential discussion in Hauser, Chomsky, and Fitch 2002, the issue has been sharpened recently by Fitch, Hauser, and Chomsky 2005.
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Both the papers hold that, pending further research on a variety of cognitive domains in humans and nonhuman animals, only the human language system is endowed with what they call the ""narrow faculty of language"" (FLN ). FLN is to be distinguished from the ""broad faculty of language"" (FLB) which const.i.tutes what we may think of as the complex organization of the human linguistic system. The complex organization is certainly unique to humans, but all its parts may not be. Some of the parts of FLB are shared by a variety of nonhuman organisms, some others are shared with other human but non-linguistic domains. According to Hauser, Chomsky, and Fitch 2002, only FLN contains what is unique to both humans and language; hence, FLN is unique to the human linguistic system. FLN is nonempty since it contains the mechanism of recursion.
It follows that music being a dierent domain from language (I agree), FLN cannot be involved in music by definition; that is, the parts, if any, that music shares with language can only belong to FLB. Thus, music cannot contain recursion. Since the property of (hierarchic) discrete infinity arises in language essentially by virtue of the existence of a recursive mechanism, music cannot be a discrete infinity in that sense. Although neither paper rules out that FLN could turn out to be empty, currently it seems that they are inclined to place the convergences between language and music, if any, in FLB.
Hauser, Chomsky, and Fitch (2002, 1571) oer a fairly exhaustive description of the property of discrete infinity for language: (i) sentences are built up of discrete units, there are 6-word sentences and 7-word sentences, but no 6.5-word sentences; (ii) any candidate sentence can be ""trumped"" by, for example, embedding it in ""Mary thinks that . . .""; and (iii) there is no nonarbitrary upper bound to sentence length. As for music, Fitch, Hauser, and Chomsky 2005 agree that music has a phrase structure and the phrasal structure of music shows no obvious limit on embedding. Still, the authors hold that ""there are no unambiguous demonstrations of recursion in other human cognitive domains, with the only clear exceptions (mathematical formulas, computer programming) being clearly dependent upon language.""
In the absence of a lexicon-driven generative theory, it is dicult to cite precise (bottom-up) examples of musical recursion. But we might find some examples at intermediate levels of complexity. For example, Douglas Hofstadter (1979, 129130) suggests that ""we hear music recursively-in particular, that we maintain a mental stack of keys, and Language and Music 211.
that each new modulation pushes a new key onto the stack."" According to Hofstadter, the process is dramatically ill.u.s.trated in Bach"s Little Harmonic Labyrinth in which the original key in G is first nested (modulated) into the key of D; the music then ""jumps"" back again into G but at a much higher level of complexity. Kaduri (2006) suggests a very similar description for all music in the sonata form. The sonata form has two parts. In the first part, a theme is inaugurated in the key of the movement.
Then, ""a transitional section"" leads to a second theme in a dierent key.
The second part then modulates from one to another while developing the theme of the first part. This part ends with the ""retransition"" section that leads back to the tonic.
However, these descriptions of musical recursion, if valid, seem to lean on specific aspects of Western tonal cla.s.sical music such as modulation and harmonic changes. Hence, they do not directly generalize to other forms of music (Jackendo and Lerdahl 2006). I will now give an example of endless embedding of musical phrases from Indian cla.s.sical music, which does not have the cited features of Western tonal music. In general, the Indian raaga system crucially depends on the experienced listener"s ability to periodically recover versions of the same chalan (progressions typical to specific raagas) and bandish (melodic themes specially designed to highlight the tonal structure of a raaga) through ever-growing phrasal complexity and at varying pitch levels.
The basic recurring feature of the tonal structure of a raaga is best ill.u.s.trated in a ""noise-free"" way in the first part of Indian cla.s.sical music known as aalaap (melodic prelude); the part is central for both Hindustani (North Indian) and Carnatic (South Indian) music. This part systematically introduces the basic tonal structure of a raaga. The part is noise-free because it is free of any definite beat (taala). Hence, except for a drone marking the tonic and the fourth or the fifth above the tonic, no other accompaniment is used.16 For the same reason, it stays away from any specific melodic theme (bandish) since melodic themes are composed around specific beats (taalas). In this sense, the aalaap part represents what may be viewed as pure tonal music, and nothing else. A study of the initial phases of this part, thus, presents something of a test case for the recursion issue that may be linked directly to the tonal form of music itself.
I have sketched the first few lines of a typical ( beginner"s) aalaap of the common raaga Yaman of North Indian cla.s.sical music (figure 6.1); the raaga is widely used in compositions of popular-including film- 212.
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Figure 6.1 Structure of a raga music. I have chosen this raaga since it belongs to the Kalyan scale (thaata) which includes all seven notes with one sharp note (marked by ) and no flat notes, reminiscent of the common G-Major scale in the Western system.17 These properties make it by far the simplest of the scales.
The basic notes are given in the middle octave; lower and higher octaves are marked by " before and after a note respectively.18 Looking at the organization of the raaga, it is obvious that the system satisfies each property of discrete infinity mentioned by Hauser, Chomsky, and Fitch 2002 for the language case. The structures are built out of a small set of discrete units: S, R, G, M, P, D, N. Items selected from this set are combined and repeatedly embedded in more complex structures to sustain the character of the raaga as follows (boldfaced sequences show embedding): Language and Music 213.
S.
R-S.
0N-R-S.
R-0N-R-S.
0N-R-G-R-0N-R-S.
0N-R-G-M-P-M-G-R-0N-R-G-R-0N-R-S, etc.
I have listed just five relatively simple lines of aalaap for expository purposes. Barring human fatigue, there is no principled limit to these embeddings. The example suggests that, if anything, the phrasal complexity of music resembles language far more than arithmetic.19 There are other interests in this example to which I return in the next chapter.20 Skeptics are not easy to please. So, let us ask: What counts as ""unambiguous demonstrations of recursion"" in cognitive domains? For example, what is the unambiguous demonstration of recursion in the language case? As noted, the only ""demonstration"" we have is that we can keep embedding, say, relative clauses at will, but we can never demonstrate empirically the presence of discrete infinity in any domain. Daniel Everett 2005 has proposed that the piraha language does not have recursion because speakers of piraha do not comment on anything except ""immediate experience."" Chomsky oered the following counterexample (in English): the apple that I am now looking at is rotten (cited in Nevins, Pesetsky, and Rodrigues 2007). What else could Chomsky do to show that piraha, like any human language, allows endless embeddings? For arithmetic, once we have the successor function, we do have reductio proofs that the concept of the largest number is incoherent. But that is theory, not an (empirical) demonstration; anecdotally speaking, young children find it dicult to comprehend that the number system has no limit.
There is no such proof in the language case. While reporting their work on possible recursive mechanisms in songbirds, Gentner et al. 2006 observe: ""In practice, however, the stimulus sets used to test such claims must be finite."" This leads to ""theoretical diculties in proving the use of context-free rather than finite-state grammars."" As they proceed to note, these diculties ""extend to studies of grammatical competence in humans 214