The Primacy of Grammar Part 21

Chapter 6.

as well, and therefore call into question the falsifiability of claims regarding [context-free grammars] in humans compared to non-humans.'' I return to this paper.

How then do we view language as a recursive system? We develop the intuition that the number series maps onto the sequence of objects generated by the language system: discrete infinity. Then we look for an unbounded operation, and introduce heavy theory in terms of the competence-performance distinction. Not surprisingly, we begin with ''surface'' recursion that directly appeals to intuitive data such as embedding of relative clauses. The complex history of generative grammar shows that the discovery of Merge was not easy, although it looks simple once we found it.

In this light, SMH could be viewed as a plea for theory: think of Merge and the economy principles as applying to music, then find the suitable organization of musical information that would use the package to generate musical surfaces. Once that happens, demand for ''unambiguous demonstration'' will be automatically met. What are the prospects for a theoretical framework in which the actual components of CHL are viewed as implicated in music? As we will now see, the query gives rise to a new set of issues regarding the organization of the human mind that go far beyond the specific issue of music.

7 A Joint of Nature Universal Grammar (UG) specifies the initial state of the language faculty; suppose we think of UG as consisting (only) of linguistically specific items in the sense outlined. According to Chomsky (2001a), apart from parametric variations in the morphological system (and ''Saussurian arbitrariness''), human language consists of a single lexicon, as noted. We may view at least the formal features of the lexicon as specified in the initial state, perhaps much else. If CHL is not linguistically specific, as noted, then only the suggested aspects of the lexicon belong to UG: UG is ( just) a universal store of lexical features.

To expand, CHL consists of Merge and the principles of ecient computation, both viewed as purely computational principles (PCPs) in our formulation. In other words, even though Merge and the principles of ecient computation are specified in the initial state, they do not belong to UG. On this view, PCPs, which const.i.tute the generative procedure of language, satisfy two conditions at once: they are specified in the initial state without being specific to language. Hence, they may well be involved in generative procedures elsewhere, such as music. We are aiming for a generalization that there is a small cla.s.s of generative systems-the hominid set-consisting of domain-specific ''lexicon'' and CHL. The progressive austerity of the grammatical system under the biolinguistic program suggests that there could be a generalization of the suggested sort somewhere.

In his recent writings (Chomsky 2001a and after), Chomsky makes a rather dierent suggestion. According to him, the design of the language faculty consists of three factors: (i) linguistic experience, that is, primary linguistic data (PLD); (ii) UG exactly as viewed above: linguistically specific initial state; and (iii) principles of computational eciency (PCE) of least-eort and last-resort varieties: the ''third factor.''1 Since PLD is needed in any case to activate the language system, we set it aside. Before it is triggered, FL then consists of UG and PCE.

216.

Chapter 7.

Apparently, the taxonomy seems to be compatible with what I suggested.

Appearances notwithstanding, Chomsky has a very dierent conception of what falls in UG and the status of PCE. For him, UG consists of both the single lexicon and Merge. For me, UG contains just the lexical part, if anything: so my conception of UG is simpler. PCEs, on the other hand, are ''laws of nature'' for Chomsky in that they are viewed as general properties of organisms, perhaps on par with such physical principles as least-energy requirement or minimal ''wire length'' (Cherniak, Mokhtarzada, and Nodelman 2002; Cherniak 2005).2 The picture presents two problems for the conception of the hominid set: (1) Merge is specific to language, hence it cannot apply elsewhere; and (2) PCEs are general properties of organisms; they are not specifically involved in either language or music-that is, since PCEs are allegedly found across (every) cognitive system of organisms, they do not help in conceptualizing the restricted cla.s.s of human ''languagelike'' cognitive systems. At best, the hominid set is single-membered; at worst, the conception is vacuous.

I will suggest that, while (1) is an undergeneralization, (2) is an overgeneralization. In my view, the right generalization supports the conception of the hominid set. As noted, in this work I concentrate on two members of the hominid set: language and music. Hence, the focus continues to be on strong musilanguage hypothesis (SMH).

7.1.

Merge and Music Is Merge involved in musical computation? The question is central for SMH because, to emphasize, Merge is the sole recursive device in language postulated in the Minimalist Program. Even if we a.s.sume music to be a recursive system in a general way, as above, SMH will not hold unless the specific recursive operation of language could be viewed as implicated in music as well. As noted, the interest is that, although Merge is certainly involved in language, its formulation-and, thus, its eects-does not seem to be linguistically specific (section 5.2.2). Since I know of no direct literature (with one exception noted below) in which the status of Merge has been studied vis-a-vis something like SMH, I will basically examine what Chomsky has to say on Merge without suggesting that he himself holds any position on musical recursion.

To recapitulate, ''unbounded Merge or some equivalent is unavoidable in a system of hierarchic discrete infinity, so we can a.s.sume that it 'comes A Joint of Nature 217.

free' '' (Chomsky 2006c). The characterization is completely general in that it does not mention any specific domain or a system. Further, Chomsky observes that Merge is an elementary operation that has the simplest possible form: Merge (a, b) {a, b}, incorporating the No Tampering Condition (NTC), which leaves a and b intact. This formulation of Merge is the simplest since, according to Chomsky, anything more complex-for example, Merge forms the ordered pair ha, bi-needs to be independently justified. As we saw (figure 6.1), musical structures are at least hierarchies of sets of progressively embedded discrete symbols: {S},{R,S},{0N,{R,S}},{R,{0N,{R,S}}},{{0N,{R,G}},{R,{0N,{R,S}}}, etc: How can Merge fail to apply to music? I can think of two possibilities in which Merge, notwithstanding its linguistically nonspecific formulation, operates only on linguistic information.

The first possibility is that there could be a domain-internal relations.h.i.+p between Merge and what it computes upon. At one place, Chomsky suggests that to be able to enter into computation a lexical item (LI) must have some property that permits it to merge with an available syntactic object: ''A property of an LI is called a 'feature,' so an LI has a feature that permits it to be merged'' (Chomsky 2006c, 139). Suppose we interpret these remarks as suggesting that Merge is sensitive only to lexical features. The suggestion looks very much like a stipulation unless it is explained why the very general characterization of Merge is satisfied only under the highly restrictive condition of lexical items of language.

In any case, even the stipulation looks suspect since the same Merge is supposed to generate the infinite system of numbers. Following Chomsky, we think of a ''language'' that has just one ''lexical item,'' called ''one.''

Now, the first application of Merge to one yields {one}, called ''two''; the second application yields {{one}}, called ''three,'' and so on: ''In eect, Merge applied in this manner yields the successor function.'' It is hard to see that Merge, so applied, is computing on lexical features of the kind available in UG. Notice that Chomsky is not saying that what applies in the domain of numbers is an ''equivalent'' of Merge; it is Merge itself, perhaps because arithmetic is routinely viewed as an ''oshoot'' of language. As far as I can see, the only reason why arithmetic is viewed as an ''oshoot'' of language is that arithmetic is recursive, which begs the current question.3 Moreover, the operation of Merge just described is restricted to a single item. This gives the most perspicuous example of recursion in which the 218

Chapter 7.

same item is fed back into the same function over and over again noniter-atively to generate new syntactic objects. Syntactic recursion in language typically does not look like arithmetic recursion at all, precisely because the human lexicon is complex. Typical examples of recursion such as The man who met the woman who . . . , or, I wonder if Susan knows that Fred a.s.sured Lois that . . . (Jackendo 2002, 3839), do not repeat the same items. So, linguistic recursion is to be understood in terms of (syntactic) types such as relative clauses. Recursion in language means that a type may be embedded in the same type indefinitely, performance factors aside. Identification of syntactic types clearly ensues from lexical features such as Gwh-. So, if Merge is sensitive only to these features, Merge cannot apply to arithmetic. It follows that if Merge is to apply to arithmetic, Merge cannot be sensitive only to linguistic information.

A second possibility is that there could be recursion elsewhere, such as music, without Merge applying. We will shortly study a specific proposal from that direction. We have already covered the problem that arithmetic poses to such proposals. Now, if music is a system of hierarchic discrete infinity and if Merge does not apply, then, the only option is that ''some equivalent'' of Merge applies: call it ''Murge.'' The human cognitive architecture then has at least two recursive devices, perhaps more. Since Merge is the simplest recursive operation, Murge is either a notational variation of Merge, or is more complex than Merge. Setting the former aside, a more complex operation, pace Chomsky, needs to be independently justified (after formulating the operation, of course).

Further, Chomsky views the emergence of Merge as a ''Great Leap Forward'' with no known evidence about how such a mechanism got inserted in the species; it is a mystery. For Chomsky, the only plausible speculation is that some critical physical event ''rewired'' the brain of an ape that had the conceptual-intentional system more or less in place. How many times did the ape's brain get rewired to incorporate Murge and other recursive devices? Finally, we can perhaps make some sense of the adaptive advantages of language to the species with Merge in place-for example, the ability to plan ahead. In contrast, as Darwin's remark pointed out, adaptive advantages of music remain a mystery (Pinker 1997; Wallin, Merker, and Brown 2000; Hauser and McDormott 2003; etc.). The addition of Murge to the architecture then (quite unnecessarily) adds to the mystery we already have with Merge.

It follows that, Merge needs to be characterized abstractly in any case independently of where it applies. Merge then yields domain-specific constructions by using specific resources available in a given domain. Chom- A Joint of Nature 219.

sky (2006a) seems to be saying something very similar: ''The conclusion that Merge falls within UG holds whether such recursive generation is unique to FL or is appropriated from other systems. If the latter, there still must be a genetic instruction to use Merge to form structured linguistic expressions satisfying the interface conditions.'' Given wide variances in the specific resources of the concerned domains (lexical features, tones, numbers), and given the plausible idea that much of these resources could have been independently available to the broad cognitive architecture from the rest of the organic world, it is a plausible a.s.sumption that each domain requires specific genetic instructions to access the otherwise general-purpose Merge. Prima facie, the a.s.sumption looks simpler than the conjecture that the architecture requires a variety of independent recursive operations.

With this general perspective in mind, I turn to what seems to be a direct rejection of the claim that musical recursion could be languagelike.

Jackendo and Lerdahl (2006; also Jackendo 2009) suggest that ''the kind of recursion appearing in pitch reductions seems to be special to music. In particular, there is no structure like it in linguistic syntax. Musical trees invoke no a.n.a.logues of parts of speech, and syntactic trees do not encode patterns of tension and relaxation.'' I have already covered the conceptual implausibility of the idea that recursion in music is ''special.''

Nonetheless, there are a variety of specific problems with the remarks just cited.

First, it looks as though the authors are making these suggestions from within the framework of the generative theory of tonal music (GTTM) proposed by them earlier (Lerdahl and Jackendo 1983) and subsequently developed in Lerdahl 2001 and Temperley 2001 among others.

As far as I can see, GTTM is at best a systematic description of how listeners pa.r.s.e a musical text. GTTM accomplishes this task by taking a musical surface and showing how a listener detects patterns of tension and release, identifies phrases in terms of, say, pauses and interludes, etc.

For example, their prolongational-reduction trees describe how a listener undergoes tension and relaxation as the music progresses; they do not describe how the concerned piece of music is generated such that listeners undergo the suggested states. Not surprisingly, the description uses traditional music-theoretic notions such as progression, inversion, and harmonic function. GTTM does not give a generative account of these traditional descriptive tools by unearthing the underlying laws that govern the generation of musical surfaces. This contrasts sharply even with the earliest proposals in generative grammar (Chomsky 1955a/ 220.

Chapter 7.

1975) that ''recovered'' traditional notions like Subject, Object, and Subject-Object asymmetry in generative terms, as we saw.

In that sense, GTTM covers some restricted aspect of perception of music in mostly music-specific terms. So the theoretical notions it invokes, such as musical recursion, is likely to be musically specific from that perspective. It makes little sense to make the general claim that musical recursion is specific to music on that basis. Consider the a.n.a.logy of the Aspects model of linguistic theory (Chomsky 1965) alluded to earlier (section 5.2). Although, in comparison to GTTM, the Aspects model was far richer and a truly generative account of all aspects of linguistic competence under usual idealizations, no significant claim about whether linguistic recursion (such as N0 ) N S) applied to anything else could be made from that model. Despite its richness, the design of the Aspects model was linguistically specific, as noted. In sum, the claim that musical recursion is specific to music is a consequence of the descriptive framework of GTTM, rather than a property of music itself.

Second, the requirement that, in order for musical recursion to be like linguistic recursion, the structure of pitch reduction must look like ''ana-logues'' of parts of speech is not immediately plausible (but see below).

To my knowledge, n.o.body wants to claim that music contains a.n.a.logues of noun phrases and anaphora while language contains a.n.a.logues of octaves and dissonances. It is like asking for cardinals and surds in linguistic structure, and reflexives and pleonastic elements in arithmetic, to show that the recursive mechanisms in language and arithmetic are the same. Since music and language (and arithmetic) are no doubt distinct domains, it stands to reason that the information processed and stored thereof must be domain-specific as well. Thus, after factoring out all nonspecific aspects, it could turn out that ''tonal s.p.a.ce-the system of fixed pitches and intervals, and its hierarchy of pitches, chords, and keys and distances among them-is entirely specific to music and therefore to melodic organization'' (Jackendo and Lerdahl 2006). It does not follow that the computational principles that access and rearrange that information must also be domain-specific.

Finally, it can be shown that some of the structures proposed by GTTM can be redescribed with Merge, not surprisingly. Recall figure 5.3, in which the tree for which book the girl has read is derived with repeated application of Merge. Now, referring to the prolongational-reduction structures proposed by Lerdahl and Jackendo in GTTM, David Pesetsky (2007) claims that these structures are also ''binary branching and involve headed phrases. They are thus characterizable as A Joint of Nature 221.

Figure 7.1 Merge in music. Reproduced from Pesetsky 2007 with permission.

products of External Merge.'' To establish the point, Pesetsky redraws the diagram for prolongational-reduction structure proposed by Ray Jackendo for the opening of Mozart's piano sonata K. 331 (see figure 7.1). Skipping details, the basic idea is to treat ''I'' and ''V'' as heads of phrases, where ''I'' is the tonic chord and ''V'' the dominant chord.4 So we can think of I-phrases and V-phrases as ''parts of speech'' of musical organization after all! Those who hold the view that musical expressions are nonpropositional in character may want to rethink the issue.

a.s.suming the general validity of Pesetsky's suggestion, how do we explain the fact that a GTTM-motivated-that is, an avowedly music-specific-structure is redescribed by linguistic means? As noted, GTTM does not seem to have the form to satisfy SMH; hence, the broad properties of design that SMH seeks, in line with the design of the language faculty, are not likely to be available in GTTM. However, it goes without saying that, since GTTM does inquire into some of the aspects of the structure of musical competence, many of its specific insights are likely to find their way into a more principled SMH-guided theory, just as some of the major insights of the Aspects model, such as island constraints, are incorporated in the Minimalist Program under dierent technology. Supposing Pesetsky's proposals to form a part of the envisaged SMH-guided 222

Chapter 7.

theory of music, we saw the first example of how insights of GTTM may be incorporated within it; we will see more of this soon. In this case, as far as we know, it is plainly a fact of musical experience that musical surfaces have prolongational-reduction structures; it is a phenomenon that any theory of music must capture. Insofar as these structures are syntactically governed, Pesetsky's ingenious a.n.a.lysis shows, as Pesetsky boldly puts it, ''musical syntax is language syntax.''

Suppose then that external Merge applies to music. Does internal Merge also apply to music? To recall, (internal) Merge is not a distinct operation: it is Merge working on parts of existing SOs. So, its ''avail-ability'' is not the issue; the issue is whether it is active. After establis.h.i.+ng external Merge in music as above, Pesetsky 2007 proceeds to show that internal Merge is (also) at work in music as it maps the tonal structure shown above to the rhythmic interface. Specifically, Pesetsky suggests that internal merge dislocates/raises the tonal tree, branch by branch, to the (top) edge by constructing relevant nodes at IP and above.

However, on the one hand, much complex music does not have any p.r.o.nounced rhythmic structure, as Pesetsky notes; the aalaap is a case in point chosen specifically for that reason.5 On the other hand, as Pesetsky demonstrates, p.r.o.nunciation of linguistic items sometimes has manifest rhythmic structure: Carrots & lemons & coee & pepper (his example), or mind and body, heart and soul. Pesetsky suggests that, like music, internal Merge works in the language case also to map SOs to the rhythmic ( sound) interface. But, as discussed above (section 5.1.3), there is a deep sense in which that is not what internal Merge is (basically) for, since the sound system can be viewed as ''ancillary'' to the language system (though necessary for communication, etc.).6 The basic idea in the Minimalist Program is that internal Merge essentially creates copies for the semantic interface; in the process, it dislocates items at the sound interface. Given the existence of nonrhythmic music, it is not obvious why a similar picture can not be extended to music if musical structures are to meet conditions of ''thought.'' We speculate on this as follows.

7.2.

Faculty of Music CHL, we saw, is geared to generate complex SOs and check for uninterpretable features. For structures such as she has gone, feature checking takes place at the (base-generated) positions at which external Merge places syntactic objects; thus, as far as current understanding goes, no movement is needed. For which book the girl has read, in contrast, the A Joint of Nature 223.

SO which book needs to move to CP for checking the wh-feature; thus, a copy of which book is generated by internal Merge. The computational requirement of feature checking serves two purposes for the external systems: at the meaning interface we get the quantifier interpretation for a WP, and at the sound interface the copy is p.r.o.nounced (in English). Basically then, internal Merge is activated when copies are needed as a last resort to meet external conditions.

If internal Merge is active in music as Pesetsky suggests, then, granting that copies are generated for the rhythmic interface on suitable occasions, we would want to know if these copies are also needed for the semantic interface of music. For that to happen, at least three things are needed: (1) a computational system-CHL, under hypothesis-that generates complex musical SOs and enforces some (narrow) computational requirement on a.n.a.logy with feature checking; (2) some conception of external systems at the semantic interface, perhaps on a.n.a.logy with FLI systems of language; and (3) a need for copies generated by internal Merge to meet these external (semantic) conditions.

As noted, we have very little to go by on these topics at the current state of inquiry. In particular, the prevalent ''no semantics'' view of music leaves little room for conceptualizing the semantic interface of music. All we have for now are: (i) external Merge may be constructing base structures in music, (ii) music may have internal significance, and (iii) internal Merge may be transferring parts of base-generated structures to the rhythmic interface. Could these be put into a preliminary conception of the organization of the music faculty? I must emphasize that what follows is a very tentative sketch of how the faculty of music may look like from a minimalist perspective.

Speculating freely on the limited basis in (i)(iii) in the preceding paragraph, and borrowing from the GTTM framework whenever needed, it seems that the basic computational mechanism in music is reduction of tonal tension under the overall constraint of the designated tonal s.p.a.ce:7 a tonal s.p.a.ce is a collection of tones such as a scale, a raaga, and so on.

Once the center of the tonal s.p.a.ce, the tonic, is identified, it signals the most ''relaxed'' state; any ''motion'' away from the tonal center increases ''tension.'' The task of tonal organization is to (periodically) return to relaxed/stable states. To that end, ''an unstable pitch tends to anchor on a proximate, more stable, and immediately subsequent pitch'' (Jackendo and Lerdahl 2006, 5152), where stability is defined in terms of proximity to the tonic. It looks as though the mechanism of reduction of tension works under locality and is designed princ.i.p.ally to enforce (musical) 224

Chapter 7.

stability by eliminating instabilities, not unlike the elimination of uninterpretable features in linguistic computation.

With this mechanism in hand, we may draw what Lerdahl and Jackendo call ''prolongational-reduction'' trees showing how the listener perceives the transitions from states of relaxation to states of tension (and back) on a note by note basis, while an overall move toward relaxed states is progressively attained. In Indian music, the ''ground note'' S (Saa) is taken to be the most stable note. Drone instruments are typically tuned with this note-along with P, a fifth above S-irrespective of the raaga. In that sense, S qualifies as a ''tonic'' (Lerdahl and Jackendo 1983, 295). Thus, it has priority over the ''real'' tonic (vaadi) of a raaga, the selected tonal s.p.a.ce; as noted, the tonic for the tonal s.p.a.ce of Yaman is G and N is the dominant (samvaadi). Thus consider the first line of the aalaap for raaga Yaman (figure 6.1). We may chart the stable points of the structure as follows (the chart itself is not the prolongation-reduction tree).

(122).

[S, 0N-R-S, 0N-R-G-R-0N-R-S, S-0N-0D-0N-0D-0P, 0M-0D-0N-R-0D-0 N, R-G-R, S].

g d g d t d g g d d d d t g g ground note, d dominant, t tonic Roughly then, the motion from the first note S to 0N increases tension which is further increased in the motion from 0N to R, followed by a motion of relaxation to S. Thus, the overall motion over the first two phrases is toward relaxation. Taking into account dierences in duration of notes and the distribution of relative stability with respect to the ground note, the tonic and the dominant respectively, these motions can be suitably represented in a tree diagram, as noted (Lerdahl and Jackendo 1983, chapter 8). This rather narrow computational mechanism generates the immensely complex melodic structures of music.

Prolongational-reduction trees describe what motion an experienced listener of a musical style perceives; it does not explain why the music has the structure to trigger the specific motion for the listener, as noted.8 It stands to reason that, other things being equal, just the mechanism of tension and relaxation enforcing least eort considerations suggests that a music (preferably) stays at the tonic (and its neighbourhood) to sustain the most relaxed state. In fact, much music does precisely that: sections of rap, chants, choruses, lullabies, cheers, and so on. So, why does music rise and fall prominently at all?

A Joint of Nature 225.

Specifically, we would want to know why the line above is heard as a line of Yaman, but not, say, as the raagas Kedaar or Bhupali, which also belong to the same Kalyan scale (thaata), sharing essentially the same tonal s.p.a.ce. We saw (figure 6.1) that the structures of raaga Yaman are so generated that the characteristic features of the raaga are sustained over growing complexity. It looks as though the computational system works ''blindly'' to increase stability; the characteristic features of the raaga, which is an organization of a certain tonal s.p.a.ce, constrains the working of the computational system. Suppose we capture the phenomenon by making a principled distinction between the computational system per se and the ''external'' conditions that constrain its operations. The resulting musical surface then is to be viewed as an optimal solution to these interface conditions.

As an aside, I note that Lerdahl and Jackendo frequently appeal to tonal s.p.a.ces to describe musical motion-for example, Jackendo and Lerdahl (2006, 35) suggest that the melody in the Beatle's song Norwegian Wood so moves as to satisfy the E major triad, BGaEB. In their framework, it is unclear to me where this information about the triad is located and how it is accessed. In general, most theories of music cognition appeal to the notion of an ''experienced listener'' without unpacking it. They simply tell us what experienced listeners do without telling us what it is about experienced listeners-how the relevant material is organized in their mind-such that they are able to do it.

The perspective just sketched oers some conception of the relevant external systems, that are internalized by an experienced listener, such that interface conditions are enforced in music. As a certain set of notes are selected from the (largely) universal musical lexicon, certain interpretive conditions-scales, modes, ascent/descent structures, characteristic motifs, delineated musical forms, and so on-are enforced on the selection.9 I am calling these ''interpretive'' conditions since, in some sense, these are available in advance to create a s.p.a.ce of expectations about how the melody is going to be organized; these conditions are already in store before the onset of music, so to speak. When these conditions dier, the melodic organization ensuing from the same selection of tones diers as well. Indian music has many sets of raagas-such as Yaman, Bhupali and Kedaar, as noted-in which members of a given set share exactly the same set of tones; in Western music, a sonata in G Major is a very dierent form of music than a symphony in the same key.

It is important to note that these interpretive systems are cognitive systems in that their organization is only weakly determined, if at all, by the 226

Chapter 7.

physical properties of sound. Lerdahl and Jackendo (1983, 11.5) forcefully argue that all attempts to determine the scale systems across the world from, say, the overtone series, turn out to be unsuccessful. It is even more so for the Indian raaga system-not really a scale-system-which directly ill.u.s.trates Helmholtz's idea that ''the princ.i.p.al of tonal relations.h.i.+p'' must be regarded ''to some extent as a freely selected principle of style'' (cited in Lerdahl and Jackendo 1983, 293; see also Vijaykrishnan 2007, 2.2.5). Needless to say, the more consciously constructed musical forms such as sonata, concerto, dhrupad, gazal, and so on, are even more specific to musical traditions. In this sense, I am proposing that the interpretive conditions const.i.tute the ''thought'' systems of music.

I am not suggesting that these are irreducibly ''cultural'' constructs of some sort where a ''system of dierences'' rule. The suggestion is rather that any investigation into the universal basis of these systems ought to search for cognitive categories rather than acoustic ones. For example, an explanation of how ''inexperienced listeners [are] able to adapt quite rapidly to dierent musical systems'' (Krumhansl et al. 2000, 14) is not likely to follow from acoustic properties alone. If this picture is roughly valid, then, in some sense, music creates and enforces its own external conditions: music expresses itself. Also ''parameters'' of music are likely to be located here rather than in the ''lexicon'' since the musical lexicon-individual tones, not tonal s.p.a.ces-appears to be by and large universal.

One advantage of this ''in-house'' organization of interpretive conditions is that it keeps the significance of music inside music, so to speak; it seems to guarantee that music has only internal significance. In that sense, the external conditions that a particular musical computation must meet is enforced by the faculty of music (FM) itself. I am obviously suggesting a parallel between these FM-driven interpretive conditions (FMI ) and what I earlier called FLI systems-interpretive systems driven by FL itself (section 5.1.3.2). If the parallel holds, then, both lend direct internal significance to structures transferred by the computational system. For music, the basic point is that these interpretive systems impose conditions on the selected tones that progressions with these tones must meet. Apart from these, musical progression may also meet more general requirements of thought systems that are adapted to music, as suggested earlier (section 5.2.2). These could include musical a.n.a.logues of such ''pragmatic'' linguistic phenomena as topicalization, focus, new informa- A Joint of Nature 227.

tion, and the like-perhaps, things such as highlight and continuity as well.

Notwithstanding these crucial parallels, even these earliest reflections on the organization of the music faculty seem to lead to a markedly dif-ferent conception of the music faculty when compared with the language faculty. We noted that the musical lexicon is largely universal unlike the lexicon of language which has parametric properties. Further, no intelligible notion of numeration of lexical items seems to apply in the music case. In the language case, a numeration signals a ''one-time'' selection of lexical items; in the music case, a ''selection'' is stored in the interpretive systems, such as a raaga or a scale, from which the selected items are repeatedly drawn ''online.''10 At many places, Chomsky explains why CHL computes only on a selection from the lexicon once and for all. If CHL is allowed to go back to the lexicon, the entire lexicon needs to be ''carried along'' for each computation. It is like carrying a refinery, not just a tank, in a moving car (Chomsky 2002). Since the musical lexicon is very small, it might as well be carried along.

With respect to the interpretive systems, structural significance perhaps terminates with the FMI systems in the music case; in the language case, semantic interpretation apparently extends beyond FLI systems to interface with cla.s.sical C-I systems, suggesting a major dierence in the organization of language and music. In this sense, the picture sketched above ''saves the appearance,'' namely, the wide phenomenal divergence between music and language. However, the computational system remains the same with very similar internal operations. In a way, then, the sameness of the computational system, required by SMH, forces a very dierent conceptualization of FM (almost) everywhere else: a pleasing result, if true.

With the thought systems of music in place, we might want to know if the conditions imposed by these systems are sometimes met by internal Merge. Internal Merge, we know, essentially generates copies of structures already generated by external Merge. Thus, we are asking if conditions of optimal computation are sometimes met when copies are made available by internal Merge as a last resort. The need for copies in music seems all pervasive since ''most background level of reduction for every piece is a statement of the tonic; hence the tonic is in some sense implicit in every moment of the piece'' (Lerdahl and Jackendo 1983, 295, emphasis added). If a generative theory of music is to make explicit what is implicit in the understanding of music, such as the ''presence'' of the tonic 228