Minería y ciudad: la ruptura de un viejo lazo

La ciudad de Guanajuato en la ruta de la redefinición productiva

3.1 Minería y ciudad: la ruptura de un viejo lazo

If repetition is not automatic but involves an essentially creative realization of projective poten- tial and the selection of past and future rele- vancy, one obstacle to the assimilation of meter to rhythm will be removed. Another obstacle arises from the discrepancy, in certain styles of music, between the apparent homogeneity of meter and the irregularity of larger units such as phrase and section. If the repetition of bar measures is not regarded as automatic, it can never- 174 A Theory of Meter as Process

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theless be seen to create a ﬁxed unit for the measurement of larger events. But unless phrases and sections are interpreted as measures, the measurement by bars will be very different in char- acter from the measurement that creates the bars themselves. Instead of functioning metrically or projectively, bars will measure larger units by nu- merical quantity or count. Such a count could, presumably, provide an index of relative length and lead to an analysis of proportion or an analysis of varying degrees of regularity and irregularity; but in this case, measures will be de- prived of their particularity, and the function of meter will be reduced to that of providing a nu- merical count. If bar measures are simply repli- cations of a given unit, they are all equivalent and are differentiated only by position in a given count.

Such an interpretation arises from a reifica- tion of meter. Rather than being viewed as a process, meter is identified with products conceived as spans of time. Regarded as products, bar measures can be treated as containers that in turn form the content of larger containers. In this way, bars function to segment the musical fabric into a succession of relatively small units. These unit products are then combined to form larger unit products in a hierarchy of segmenta- tions that leads from measure to subphrase to phrase to phrase group to section and finally to the unity of the entire composition. Thus, meter can be assimilated to “form” considered as a segmental hierarchy of products. However, the transition from bar measure to phrase presents a break in the composition of the hierarchy.While bar measures in many compositions are all of the same length, units above the level of bar are generally far less regular. The constancy of the bar measure can thus seem to provide a homogeneous medium for the rhythmic diversity of larger units and their nonmetrical contents. If there is activity, “motion,” or rhythm that would animate the hierarchic arrangement, it would seem to be provided not by the homogeneous metrical content but by contents that provide goals for boundary points and correspondences among units. As we saw in chapter 5, it is, above all, tonal relations that seem to make a segmental whole a rhythmic whole. Although tonal events

can also function to create metrical boundaries, they are free to transgress these boundaries and thus to diversify and enliven the underlying homogeneity and regularity provided by the re- lentless succession of measures.

Like the notion of “automatic repetition,” the notion of metrical homogeneity rests on the observation of an apparently “given” regularity. And while it might be granted that each bar measure is rhythmically (and, as I have argued, metrically) unique, the particularity and diversity of measures would seem to play no role in the creation of large-scale events. The problem here is that of connecting meter, which seems to operate only “locally” for relatively brief time spans (Lorenz’s “rationale Rhyth- mik” ), with form viewed as large-scale rhythm (the “more organic principle” Cone opposed to the metrical ). One solution — though, as I shall argue, a partial and ultimately misleading solution — is to expand the scale of meter and re- gard constituents larger than the bar as gen- uinely metrical units. It is to this solution or the analysis of “hypermeasure” that I would now like to turn.

There is considerable disagreement among musicians as to where the transition from metrical to “formal” unit (Cooper and Meyer’s “mor- phological length” ) occurs. Many musicians in- sist that a true feeling of meter rarely exceeds two-bar measures; others ﬁnd evidence of meter in larger spans, particularly in phrases as measures. A choice between these alternatives obviously depends upon what is to be meant by “meter” or “measure.” If meter simply means equal division and thus “regularity,” there is no limit to the duration of a measure, provided that we are given equal durations. If meter refers to a feeling of the distinction strong/weak, there would appear to be rather narrow durational limits to the operation of meter. However, the feeling of strong and weak is not always sharply drawn, especially in larger projections, and as metrical determinacy becomes attenuated it becomes dif- ﬁcult to clearly distinguish “metrical accent” from other types of accent. If there were, in fact, a sharp distinction in feeling, there would be no controversy.

Perhaps because it provides a less ambiguous

criterion for meter, regularity or equal division is often taken as the primary factor in ascer- taining the limits of meter. Cone, who links regularity and homogeneity, identiﬁes the bar as the largest metrical unit in most music of the Classical period. This limit is chosen in light of the irregularity and rhythmic diversity of the phrase:

One sometimes hears remarks about the tyranny of the four-measure phrase during this period. It is true that the four-measure phrase — or rather some sort of parallel balance — can usually be felt as a norm; but it is never, in the music of the masters, a tyrant. This is because it is for them a rhythmic, not a metric entity. Conceived metrically it would tend to become as ﬁxed and invari- able as the measure; conceived rhythmically, it is as ﬂexible as the musical surface itself.

In the Classical period, as we have seen, the measure was usually the largest metrical unit. Its steadi- ness served as a constant support for — or counter- point to — the variety of motif- and phrase- construction. When measures combined to form phrases, they did so not in any regular metrical way but as components of freely articulated rhythmic groups whose structure depended on their speciﬁc musical content. (Cone 1968, pp. 74 – 75, 79)

Since the criterion for meter here is regularity, Cone is willing to grant metrical status to phrases if they approach the regularity and homogeneity of bars:

In Romantic music, on the other hand, one can ﬁnd long stretches in which the measures combine into phrases that are themselves metrically conceived — into what I call hypermeasures. This is especially likely to occur whenever several measures in succession exhibit similarity of motivic, harmonic, and rhythmic construction. . . . It is here, and not in the preceding style, that we can justly speak of the tyranny of the four-measure phrase! (Cone 1968, p. 79)

Although meter as pure quantity may be dis- tinguished from rhythm by its regularity and homogeneity, the qualitative category of accent can be applied to virtually any constituent. Thus, it is possible to import metrical terms for the de-

scription of larger, “formal” events — for example, “large-scale anacrusis” or “structural downbeat.” In this way the qualitative or “functional” attributes of meter can be detached from men- sural or durational attributes. Lerdahl and Jack- endoff, who recognize metrical units of up to eight bars (even in music from the Classical period), make an explicit distinction between two forms of accent: “By structural accent we mean an accent caused by the melodic/harmonic points of gravity in a phrase or section — especially by the cadence, the goal of tonal motion. By metrical

accent we mean any beat that is relatively strong

in its metrical context” (1983, p. 17). Since the same term, “accent,” is applied in both cases, this separation seems to widen the gulf between meter and rhythm or form. “Structural” upbeat or downbeat and metrical upbeat or downbeat are related by analogy but are unrelated in their process of formation — the structural arising from tonal “motion” and the metrical from equal division. And this disparity can lead to nu- merous problems of reconciling tonal and metrical accent — for example, the problem of tonal “end accent” or the appearance of an accented tonal arrival in an unaccented metrical position, or, more generally, the difﬁculties of coordinat- ing the placement of “structural” tones with metrical articulations. Because of these problems it is difﬁcult to avoid concluding that meter, even if extended to the level of phrase, functions as a scaffolding for the play of rhythm.

A solution to the problem of reconciling meter with the irregularities encountered in many phrases is offered by Schenker’s concept of ex- pansion (Dehnung) or, more generally, by pos- iting an underlying regularity that is capable of retaining some sort of identity under transformations that result in “surface” irregularity. Such an approach has many antecedents (in the theo- ries of Koch and Riemann, among others) and has recently been developed systematically in the work of Carl Schachter and William Rothstein. For Schachter, repetition is again the primary cause of large measures, though repeated spans need not necessarily be immediately successive or “adjacent”:

Within long time spans . . . meter may very well recede in importance compared to tonal motion

and the tonal rhythm associated with it.Yet if the long span is a durational unit that recurs, and if it is articulated by a network of regularly recurring smaller spans, it has a metrical organization which is in principle no different from that of a bar. (Schachter 1987, p. 7)

Accent limits the extent of large measures — only if some distinction of strong and weak be- ginnings can be sensed can a measure be iden- tiﬁed. Depending on the context, Schachter identiﬁes in his examples “regular” measures consisting of two, three, four, eight, and sixteen bars. However, irregular lengths — that is, measures that are neither three nor powers of two bars long — are not nonmetrical if they can be heard as transformations of an underlying regu- lar count. The underlying form is called the pro-

totype, after Schenker’s metrisches Vorbild (Schenker

1935, pp. 192 – 193).

As an example of a relatively simple expansion, I quote in example 11.4 Schachter’s ana- lytic representation of the Trio from Mozart’s

Haffner Symphony, K. 385. (A score is provided

in example 12.1.) Here bars 16 – 20 are interpreted as an extension of the fourth bar of a four-bar metrical unit beginning in bar 13 (see levels e and d). The prototype for this transformation is the four-bar unit, bars 9 – 12, which presents a similar middle-ground structure (prolongation of scale degree 2 by the upper auxil- iary CS). Schachter also recognizes a large measure of eight bars formed by the ﬁrst part of the Trio — a complete phrase, bars 1 – 8. And, thus, the twelve bars of the second section (bars 9 – 20) are also regarded as an expanded eight- bar phrase measure based on the prototype of the ﬁrst section. The entire twenty-bar (or expanded sixteen-bar) formation is not in this case regarded as a metrical unit because it is not repeated:

. . . might we infer a metrical relation of strong- weak between the downbeats of bars 1 and 9? The answer must be no. Time spans of twenty bars (the sum of the ﬁrst two phrases) or of sixteen (the ﬁrst phrase plus the eight bars that underlie the second) do not function as durational elements in this piece; there are no recurrent sixteen- or twenty- bar spans. (Schachter 1987, pp. 7 – 8)

Schachter does acknowledge an “accented” ﬁrst phrase, but in the absence of recurrence this accent cannot function as a metrical accent:

Of course a special emphasis accrues to the downbeat of bar 1, partly because it is the ﬁrst downbeat and partly because it carries the opening tonic. In this sense, therefore, the downbeat of bar 1 may in- deed be “stronger” than that of bar 9. But its pri- ority is not metrical; it results from what Lerdahl and Jackendoff call a “structural accent.” (Schachter 1987, p. 8)

Incidentally, treating the second eight-bar phrase as unaccented in relation to the ﬁrst might imply that the second phrase is “continuation” in relation to the ﬁrst and that the (accented) reprise in bar 21 is a second beginning. Although this interpretation would seem to accord with the Schenkerian notion of interruption, Schachter does not pursue such a parallelism.

In the case of the Trio, the four-bar prototype (bars 9 – 12) and the eight-bar prototype (bars 1 – 8) are “literal”— they occur before the transformations as explicit models to which the expansions can be compared. However, the presence of a literal prototype is not necessary for there to be a transformation. Later events and more “ab- stract” middleground structures can also provide models. And, following Rothstein (1981), Schach- ter notes that the difference between literal and nonliteral prototype is not as great as it might appear since the prototype, even if literal, is not, in fact, present in itself for the transformed replica:

If the expansion has no actual model in an earlier passage, its underlying metrical structure exists “only at some higher level that is not literally ex- pressed [Rothstein 1981, p. 170].” A literal prototype, of course, announces its metrical structure more directly, but in the expanded variant, the meter of the prototype no longer occurs in the immediate foreground. It, too, withdraws to a higher level, though the listener’s memory of the earlier passage helps him draw the necessary infer- ences. (Schachter 1987, p. 44)

Although Schachter does not bring up the ques- tion, it might be argued that certain metrical prototypes (for example, the four-bar phrase) are 177 A Theory of Meter as Process

178

EXAMPLE11.4 Carl Schachter, “Rhythm and Linear Analysis: Durational Reduction,” Music Forum, vol. 5, edited by Felix Salzer, example 8. Copyright © 1980 by Columbia University Press. Reprinted with permission of the publisher.

given as stylistic norms “prior” to the composition (as residues of past experiences). In any case, the opening of meter to the apparent irregularities and heterogeneity of the musical “surface” through the prolongation (by expansion) of a “hypermetric beat” suggests a novel construal of metrical hierarchy:

By connecting the idea of expansion to his theory of levels, Schenker made it a far more powerful an- alytic tool than the old and familiar notion of “phrase extension,” which it obviously resembles and from which it almost certainly derives. The superiority of Schenker’s approach lies ﬁrst of all in his taking into account the levels of tonal structure and diminutional content that are associated with the prototype and the expansion; it is never simply a matter of counting extra bars. In addition Schenker brings a new perspective to the study of purely metric phenomena. An expansion — especially a large-scale one — can establish its own metric structure. As Rothstein acutely observes, “in such cases we must distinguish two levels of hypermeter: a higher level, which is the level of the metric prototype; and a lower level, the level of the hypermeasures within the expansion. . . . Ac- cordingly, we may speak of hypermeasures of higher or lower structural order [Rothstein 1981, p. 172].” (Schachter 1987, pp. 44 – 45)

Thus, the expanded fourth measure shown in level e of example 11.4 is, as it were, “composed out,” forming a subsidiary four-bar metrical unit (or what is potentially a four-bar unit — the fourth bar being shown in parentheses).

Rothstein (1989) pursues this idea and de- velops a distinction between “surface hypermeter” and “underlying hypermeter.” However, he also acknowledges that in very large expansions it may become difﬁcult to retain a feeling of the underlying measure:

Expansions of any length tend to fall into their own hypermetric patterns, resulting in a conﬂict between the surface hypermeter within the expan- sion and the underlying hypermeter of the basic phrase. Often it is possible for the listener to per- ceive both hypermeters simultaneously; at other times the underlying hypermeter may be pushed so far into the background that it virtually disap- pears. (Rothstein 1989, p. 97)

That the underlying hypermeter might become relatively obscure does not result so much from the length of the extension as from complica- tions that arise in the structure of the extended phrase. To give some idea of factors that are in- volved in the formation of such a metrical hierarchy and factors that contribute to ambiguity, I would like to refer to Rothstein’s analysis of a passage at the end of the exposition of the ﬁrst movement of Mozart’s Piano Concerto in C Major, K. 467 (bars 171 – 194). In example 11.5 I have represented Rothstein’s analysis in sche- matic form. The prototype for the expansion in bars 180 – 194 is the preceding eight-bar phrase (bars 171 – 178), a hypermeasure composed of two four-bar hypermeasures. Bars 180 – 185 re- peat bars 171 – 176 in many respects. And the cadence in bars 177 – 178 is clearly reiterated in bars 192 – 194. The “added” bars (186 – 191) delay the cadence of the second phrase and are read by Rothstein as an extension of the sixth “bar-beat.” Of the two subsidiary or foreground hypermeasures (bars 184 – 187 and bars 188 – 191), the sec- ond is regarded as a parenthetical insertion. It con- tributes to the metrical expansion, but it is subsidiary to the ﬁrst foreground hypermeasure in the sense that bar 187 could have proceeded directly to bar 192 (as a resolution of the CS di- minished seventh):

The metrically weak m.187 leads to the metrically strong m.192, as well as to the surface downbeat of m.188. The parenthetical passage, once perceived as such, recedes in the listener’s mind to make way for the larger connection. Comparison with the preceding basic phrase facilitates this metrical hearing. (Rothstein 1989, p. 98)

Rothstein acknowledges two factors that in this case weaken a “feeling of long-range metrical continuation.” One reason is that the surface hypermeter overlaps the underlying hypermeter in bars 184 and 185; that is, bars 184 and 185 are simultaneously the ﬁfth and sixth measures of the underlying hypermeter and the ﬁrst and second measures of the surface hypermeter. The other reason is that bar 185, the sixth bar of the “basic phrase,” could not be directly followed in the solo part by the seventh bar, bar 192.

Although he is less explicit in his treatment of problems of meter than is Schachter, Rothstein more explicitly links large-scale meter to the phrase as an essentially rhythmic phenomenon. And while Rothstein makes a sharp distinction

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