GUANAJUATO: UN ESTADO EXPULSOR DE POBLACIÓN
2.2 La emigración a Estados Unidos
In discussing meter as projection, I claimed that the projected duration is a potential for a repro- duction of the projective duration, but I did not claim that in projection the “contents” or the particular metrical decisions that constitute the projective duration are reproducible in the pro- jected duration. There are, however, grounds for making such a claim. In example 10.1a the con- stitution of the second bar measure is very dif- ferent from that of the first. The second may be regarded as a duple equal measure, but it will not be heard as simply duple; in fact, it may not be felt as a duple equal measure at all, but rather as a syncopated figure in which the second sound can be heard to enter too late. Here the begin- ning of the second measure projects something more than the potential for a dotted half-note duration. In example 10.1a a possible feeling of “too late” is accounted for by regarding the third beat of the first measure as projective for the fol- lowing beginning (in violation of the rule we established in the last chapter). The projection Q –Q' is not realized, and on the basis of this real potential the second sound or beat of the second measure is felt to be too late. If we also feel that the second sound is syncopated — that it begins as a weak or continuative phase of an expected second beat (and does not end with an expected beginning of a third beat) — it might be argued that we will have felt a realization of projected potential (Q') and a definite but acoustically suppressed beginning (| \) indicated in paren-
theses in example 10.1a. However, to regard the third beat as projective, we must detach it from 149
its context in the first measure and hear it simply as a beginning. Certainly, the third beat does have a beginning and can, presumably, function projectively for the following sound. But I do not believe that this interpretation can entirely account for our feeling of the second measure. And in the case of example 10.1b a similar inter- pretation will not account for the possibility of feeling that the second sound of the second measure enters too soon.
Example 10.1c presents an alternative inter- pretation of example 10.1a. Here the durational
content of the first measure provides a potential for reproduction. By “durational content” or sim- ply “content” (an unfortunate word perhaps) I will mean the particular ensemble of projective potentials and realizations that constitute the mea- sure. This potential is represented by the copy of the first measure, enclosed in braces, that appears below the second measure. This device of copy- ing the first measure may be misleading. I do not mean that the first measure is re-presented or re- called while we are attending to the second measure. I mean, rather, that there is a potential for reproduction, or, more precisely, that the range of possibilities available for the becoming of the second measure is narrowed by the defi- niteness of the now completed first measure (and thus the copying of the first measure is a very crude representation of this complex dura- tional relevance).
This potential is, in fact, inseparable from pro- jective potential. The projective potential of the first measure cannot be abstracted from the actual first measure and from everything that is involved in its becoming just this measure with just this projective potential. As I indicated earlier, the events that constitute the measure (in this case, a first, second, and third beat) can enhance or (as in the case of 5/4, for example) detract from its pro- jective potential. The projective potential or the dura-
tion of the measure is nothing apart from its constitu- tion. It is also for this reason that the term “con-
tent” is misleading. What I have been calling projective potential is not an abstract quantity or a “span of time” in which the event is contained. Nor is a measure or a duration simply a span of time reducible to the descriptions “three beats long” or “two seconds long.” I did perhaps imply the contrary in using expressions such as “a dot- ted half-note duration.” But a feeling of duration is always a feeling of particularity. Thus, even performing our poor example 10.1a again and again, the feeling of duration will not be precisely repeated. “Content” here refers to the particularity of a projective potential. Again, this particularity may be more or less relevant for the realization of projected potential, depending on our attentive- ness and interest. Indeed, to the degree such par- ticularity or complexity is not relevant, the pro- jected duration will more resemble a “span of time” (but a felt rather than a counted span). 150 A Theory of Meter as Process
EXAMPLE10.1 Inheritance of projective complexity a)
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Earlier, I said that projective reproduction is not here conceived as a reproduction of begin- ning by beginning. (As a potential for duration, beginning is not, strictly speaking, reproducible.) Instead, I argued that projective reproduction arises from a simultaneous making present and making past effected by the beginning of a new event. However, once a projection is effected — once there is a new beginning and the emer- gence of a more or less definite projected poten- tial — the second beginning can, in fact, repro- duce in its durational potential something of the realized duration of the first beginning; and if this potential is realized, the second event will have repeated (in its own particular way) the actual dura- tion of the first event. Thus, in the course of its becoming, the second event has the potential for reproducing what became of a prior beginning; and if this potential is realized, there will in effect be a reproduction of beginning by beginning.
Directed by this (durational ) potentiality, the now of the second event specifically involves (durational ) relevancies of the now past first event. And the repetition of the first measure below the second in example 10.1c is a crude device for indicating such relevance. The realiza- tion of projective potential in a projection may be considered the relevancy of the first measure for the becoming of the second measure’s dura- tion. And since the actual duration of the first measure is the particular product of all that has transpired in the course of its becoming, its pro- jective potential is also that particular product. The durational content of the second measure may depart from a repetition of the content of the first. But to the degree we hear departure as contrast (e.g., too late, too soon) or as a repeti- tion denied, the particularity of the first measure is to this degree relevant for the second.
Contrast arises from departure, but there is no departure apart from reproduction. If there is di- vergence, it is divergence only with respect to re- production or correspondence. If the second measure comes to differ greatly from the first and does not develop projective correspondences with the first, the first measure, as measure, can lose relevance for what the second is now be- coming. Since the two measures (and, more gen- erally, the two events) are immediately succes- sive, the first will necessarily have some rele-
vance for the second, but if the divergence of projections is too great, as in example 10.1d, the metrical or projective organization of the first measure will not be corroborated and the pro- jection will be denied. In example 10.1d, al- though the second measure is “objectively” equal in duration to the first, it will not, I think, be easily heard as equal or as a realization of the first measure’s projective potential. Instead, the relevance of the first measure is expressed in a feeling of faster tempo and the contrast between unequal and equal measure. The projective func- tion of the third beat of the second measure (the dotted quarter) now excludes the projective rel- evance of the first measure.
To put the matter in more “environmental” terms, initial correspondences in a projection enhance projected potential and thus pre- dictability. It may happen that the present event ceases to corroborate predictions made on the basis of the projection, in which case we may be inclined to eschew the projection as irrelevant and turn our attention to more immediate pro- jections that offer better predictive results (as in the second bar measure of example 10.1d) or turn to the relevancy of other durational levels. But even if an immediately preceding event ceases to serve predictive aims, it must retain some relevance, if only as a contrast that sharp- ens the particularity of the newly emerging event. More generally, in the formation of a new event all the relevancies in the horizon of “now” can come into play, but the immediately preced- ing event is especially privileged. And according to the intensity of our involvement with this process, the particularity or definiteness of the previous event will be especially relevant. More- over, if (as I suggested in chapter 6) there are in the horizon of “now” manifold presents, there are also manifold pasts or immediately preceding events whose definiteness can be taken into ac- count. Or, to put this in other words, if there are several metrical or projective levels, each level’s projected duration will draw upon the definite- ness of a completed projective phase. The pro- jective “hierarchy” or the coordination of or movement within these levels will therefore pro- duce a wide range of relevancies that are (vari- ously) brought into play according to the de- mands of the newly emerging situation.
In view of this complexity, it is clear that is- sues of metrical particularity and reproduction cannot be adequately addressed in the very lim- ited contexts of the preceding examples. If we are to inquire into more complex and subtle projective relevancies, we will need to consider musical examples in which projective potentials are much more sharply and richly defined. In particular, we will need the differentiation pro- vided by tonal quality and contour. Such differ- entiation can create abundant opportunities for durational correspondence (whether in confor- mance or contrast) and can play a primary role in the distinction of end, beginning, and contin- uation (or anacrusis). Indeed, larger projections or projective complexes cannot arise in the ab- sence of tonal differentiation. In each of the sub- sequent chapters of this book, analyses of ex- cerpts from a variety of musical compositions will provide us with opportunities to explore questions of metrical particularity and reproduc- tion in more detail. And in the next section of this chapter we will begin this exploration with an analysis of excerpts from two Bach Courantes for solo cello. Our analysis of the Bach will con- tinue the argument presented here to assert that metrical type is an abstraction that, if reified and given priority over all other metrical character- istics, will result in the reduction of meter to a deterministic repetition of pulse. But before we begin this analysis I would like to return to ex- ample 10.1 to consider the role of “virtual” beats in the creation and reproduction of metrical type.
In the syncopated second bars of examples 10.1a, 10.1b, and 10.1e an actual feeling of an acoustically absent second and third beat may occur and may be more or less vivid, especially if we are performing rather than listening to a per- formance. If the tempo is slow, we may be in- clined to subdivide the second bar measure. If the tempo is faster, the projected duration of the second measure will be more highly determinate and we may simply fit a duple division into this “container” without imagining a triple subdivi- sion (in which case a feeling of syncopation will be diminished). Certainly, experienced perform- ers do not have to rely on subdivision in such situations. To perform a quintuplet, for example, it is possible to feel the projected duration more
generally as a “span of time” in which to play five notes without relating this division to a pre- vious duple or triple division. Likewise, at the other extreme, in cases where projected poten- tial is most highly conditioned by the durational determinacies of a preceding event, we should not assume that it is the pulses of an imaginary metric grid that direct the performer’s (or the listener’s) perceptions. Having developed both a capacity for comprehending relatively long pro- jections and a keen sensitivity to durational rele- vancies, an experienced performer does not have to imagine the pulses that are often indicated in metrical analyses. And I believe that this capacity and this sensitivity can be communicated in per- formance and valued as especially “rhythmic.” Of course, there are situations in which subdivi- sion becomes necessary, but only as a feeling of durational determinacy fails us or when, as be- ginners, we are learning to read from metrical notation.
In examples 10.1b and 10.1e I have not indi- cated quarter-note subdivisions, and although I did copy the three quarter notes of the first mea- sure beneath the second in example 10.1c, I do not mean to imply that these three beats are re- peated; in fact, they are not. It may, however, be objected that there is one very good reason for postulating a succession of three beats — or, rather, pulses — in every bar. How else could we account for the first measure of example 10.1b or 10.1e, for instance, being felt as a triple un- equal measure? To feel inequality we do not need to feel three beats; we need only feel a de- ferral of projective potential, as is indicated in examples 10.2a and 10.2b.
Without a deferral of projected potential, however, there will be nothing to distinguish what I have called “mediated inequality” from “pure” inequality. (Conversely, in example 10.2c without a third beat there will be deferral of projected potential but no fully explicit deferral of projective potential.) Certainly there is a clear distinction in feeling. Examples 10.2d and 10.2e can also be heard to present a deferral of projec- tive potential, but they clearly sound more un- equal than examples 10.2a and 10.2b (unless, of course, through the vagaries of mensural deter- minacy we can hear in example 10.2d and ex- ample 10.2e rallentandi). The first duration in 152 A Theory of Meter as Process
example 10.2d is not, as in example 10.2a, ex- actly “twice as long” as the second. It might be said that simplicity of proportion results in a greater feeling of “equality.” But unless we as- sume that there are specific feelings of numerical proportion—“twice/half as long” or “two-thirds/ one-third as long” (or, in the case of the eighth note in example 10.2b, a feeling of “a quarter as long as the half-note duration” or “a third as long as the dotted quarter” ) — it seems we must grant some sort of perceptual reality to the acoustically suppressed “second pulse.”
Let us assume that we hear something resem- bling example 10.2a without having heard a pre- ceding measure of 3/4 or without a prior deci- sion to hear this as a measure of 3/4. In this case, we will first hear a measure of 3/4 only with the beginning of a second measure (*). To say that the second sound of the first measure is now heard as, in some sense, a “third” beat would seem to imply that we have retrospectively divided the first half note. I think that this could be taken as an adequate account, provided that the notion of “retrospective division” is clarified.
The first measure is now past for the second measure. The second measure, or what is becom-
ing a second measure, is present and is being constituted, in part, by the “presence” of the first measure as projected potential. Thus, it is this definite potential that is “retrospective.” And the “division” is therefore a potential division. Now that there is the possibility of reproducing the particular projective potential of the first mea- sure, there is a great variety of metrical arrange- ments that could conform in one way or an- other to this potential. If there is an actual sec- ond beat articulated in the second measure, it will be a division of the half note as reproduced for the second measure and a confirmation of the relevancy of the first measure as a mediated unequal measure. What was “given” to the sec- ond measure by way of potentiality includes a potential for subdivision, and what is “taken” by the second measure by way of realization is an actual division. If there is no actual second beat in the second measure, the potential for division is nonetheless real, and the first measure will be, “retrospectively,” no less a mediated unequal measure. (And, of course, in the becoming of the two-bar measure decisions pertaining to “type” are in flux until the end of this larger present.) Although I have used unequal measure as an ex-
Metrical Particularity 153 EXAMPLE10.2 “Retrospective” emergence of metrical type a) W W
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ample since it is more problematic, a similar analysis applies to equal measure in situations where what we might regard as beats are sup- pressed (as in syncopations, dotted figures, and ties).
Having acknowledged a real potential for divi- sion, I will not argue that the practice of includ- ing indications of all “virtual” beats in a metrical analysis is entirely inadequate as a representation of metrical organization. But I do argue that this practice oversimplifies the issue of meter in two ways: first, by implying a reduction of meter to a coordination of more or less autonomous (and es- sentially atemporal ) pulse “strata,” and, second, by eliminating a distinction between “virtual beats” that are clearly felt and those that are not. Among those that are felt there is a great range in the vividness of feeling, and this variation contributes to the rhythmic/metrical particularity of musical experience. Both of these reasons have, I think, far-reaching implications for our study of meter and rhythm.