[32] A quite different, though not unrelated, approach to the "presence" of asymmetrical patterns is suggested by some of Stephen Handel's recent work. In a 1998 article, Handel considers how metrical structure interacts with a special type of grouping known as figural organization. When figural organization is in effect, tones are heard as discrete groups. The listener attends to the number of tones constituting each group, but not to the exact timing between the groups. This means that different rhythms can have the same figural organization. For instance, in a 16-pulse pattern, the rhythms X.X..X....X.X... and X.X....X..X.X... (where Xs stand for attacks, dots stand for unarticulated beats, and tones separated by only one beat are considered part of the same group) have an identical figural organization, which Handel defines as two tones, silence, one tone, silence, two tones, silence (or 2-1-2-). Cognitive psychologists have claimed that meter is necessary to compensate for the imprecision of figural hearing--that listeners use it to measure the differences between otherwise similar rhythms. The three experiments that form the basis of Handel's article suggest, however, that figural organization may be just as important as meter in rhythmic perception. Handel found that listeners tend to have a hard time discriminating between rhythms with the same figural structure; furthermore, the effect of meter (and of various strategies aimed at highlighting metrical organization) is particularly limited in "weakly metric" patterns (those in which the majority of attacks do not coincide with tactus-level beats). Handel's focus on the relationship between meter and "weakly metric" rhythms makes his work promising for scholars of electronic dance music, since asymmetrical patterns frequently intermingle with even rhythms in this repertory. (A classic example is 808 State's track "Cubik," in which a prominent 3+3+3+3+4 synthesizer pattern sounds against even quarter-note drumbeats.) Handel's findings, like those of Rahn, discourage us from viewing asymmetrical rhythms as embellishments of a metrical background and provide another way of accounting for their distinctive perceptual qualities.
[33] All of the grid alternatives discussed thus far emphasize rhythmic organization over metrical structure. Nonetheless, they still preserve some sort of separation between rhythm and meter. Another possibility is to reject this division altogether. This is the approach Christopher Hasty takes in his recent book Meter as Rhythm. Instead of seeing metrical accents as a series of timepoints, Hasty characterizes meter in terms of events. He claims that meter arises when the duration of an event is replicated through a process called projection. See Example 6, a reproduction of his Example 7.2. In this diagram, capital letters A and B represent two events. At first, we do not know how long A will last. When B begins, however, the duration of A becomes definite; it now has the potential to be replicated by B. This projective potential is shown by the solid arrow Q; the dotted line Q' shows the projected duration.
[34] Hasty also classifies events as beginnings, continuations, or anacruses. He then uses these concepts to discuss different types of meter, claiming that certain types involve more complex perceptions than others. Duple, or equal meter, is the simplest type because it involves the perception of a second event as a continuation of an initial event (see Example 7, part a, in which continuation is shown by the arrow Q). Triple meter involves a more prolonged sense of continuation, as shown in Example 7, part b; it is also more complex than duple because it denies a potential two-beat duration, as indicated by the crossed-out arrow Q in Example 8. Hasty describes this special type of denial asdeferral.
[35] In Hasty's system, meters consisting of irregularly spaced beats engender considerably more complicated perceptual processes. In duple and triple, all suggested projections are realized (although in the case of triple, the last projection is deferred); in an asymmetrical meter, however, some projections will never be realized. For example, in 5/4 meter with a 3+2 division, the three-beat projection suggested by the first part of the measure is denied when the second measure begins. See Example 9, in which the potential duration Q', indicated by the dotted line, is denied. A similar denial occurs in the second measure of a 2+3 pattern, as shown in Example 10 by the dotted line R'. Although Hasty claims that our perception of such patterns is complex, he notes that they should not be considered "unnatural or confused." His approach is useful for EDM because it does not simply describe irregular patterns as syncopated, but rather provides a detailed description of the processes engendering their rhythmic complexity. In this way it can provide a convincing account of the richness that one perceives in the rhythmic surface of this music.
[36] As the foregoing discussion has shown, the approaches of Rahn, Handel, and Hasty each provide a distinctive contribution to our understanding of the asymmetrical patterns that occur in electronic dance music. Rahn provides a structural account of the special characteristics of these rhythms, while Handel and Hasty focus more on issues of perception. Handel suggests an alternate mode of hearing that may play a role in the cognition of such patterns; Hasty, on the other hand, applies the same perceptual principle (projection) to all meters, while also showing the unique ways it plays out in irregularly spaced meters. While there are obvious differences between these approaches, they should not be considered mutually exclusive. For instance, although Rahn and Handel, unlike Hasty, preserve a separation between rhythm and meter, their respective emphases (structural properties and figural hearing) could still be situated within Hasty's method. Likewise, Hasty's discussion of projection could be applied to asymmetrical patterns even if those patterns are not considered strictly metrical. In fact, I would ultimately conclude that such patterns are not generally metrical in electronic dance music (given that they usually occur in conjunction with regularly spaced patterns that can be heard as metrical more easily). Nonetheless, I would argue that they should not be treated as transient foreground phenomena superimposed onto an underlying regular structure. Rather, as these three methods show us, these rhythms have a distinctive presence of their own and should be considered structurally significant in their own right.
[37] Our exploration has shown a variety of ways in which rhythm and meter are used to create musical interest in electronic dance music. Displacement dissonances subvert metrical stability; inherently ambiguous patterns encourage multiple interpretations; and asymmetrical patterns counteract the regularity of persistent even rhythms. The common link between all these phenomena is an emphasis on interpretive multiplicity. In other words, electronic dance music encourages us to hear it in a variety of ways. As we have seen, this multiplicity functions on many different levels. Individual patterns are often intrinsically ambiguous. Furthermore, they frequently remain so even when used in combination: when there is no definitive metrical layer, the distinction between metrical and antimetrical layers may not be apparent. Even when all the elements of a meter are in place, reinterpretations can turn the beat around, showing the listener that the metrical structure was not quite what it seemed to be. And finally, the persistent repetition of both asymmetrical and even patterns encourages multiple perspectives on rhythmic and metrical structure, thereby undermining any sense that there is a singularstructure underlying the music.
[38] In spite of these conclusions, a number of questions remain. First, how might the instabilities and ambiguities that I have discussed be played out on a larger scale? In what ways do EDM musicians create subtlety in a work as a whole? What sorts of processes occur during the course of complete tracks, albums, and DJ sets? Second, how widespread are the phenomena considered here, and how broadly applicable are the approaches put forth to the various genres of electronic dance music? Third, since EDM is first and foremost dance music, what is the relationship of dance to these rhythmic and metrical phenomena?
[39] Each of these questions is a potentially vast topic unto itself, and further research is needed before definitive answers can be given. Instead of trying to answer these questions at this time, I will leave them for future studies of electronic dance music to address. Nonetheless, I believe that these issues, in combination with the phenomena already discussed, suggest something of the range and complexity that electronic dance music offers to listeners and scholars, both within music theory and without.
[33] All of the grid alternatives discussed thus far emphasize rhythmic organization over metrical structure. Nonetheless, they still preserve some sort of separation between rhythm and meter. Another possibility is to reject this division altogether. This is the approach Christopher Hasty takes in his recent book Meter as Rhythm. Instead of seeing metrical accents as a series of timepoints, Hasty characterizes meter in terms of events. He claims that meter arises when the duration of an event is replicated through a process called projection. See Example 6, a reproduction of his Example 7.2. In this diagram, capital letters A and B represent two events. At first, we do not know how long A will last. When B begins, however, the duration of A becomes definite; it now has the potential to be replicated by B. This projective potential is shown by the solid arrow Q; the dotted line Q' shows the projected duration.
[34] Hasty also classifies events as beginnings, continuations, or anacruses. He then uses these concepts to discuss different types of meter, claiming that certain types involve more complex perceptions than others. Duple, or equal meter, is the simplest type because it involves the perception of a second event as a continuation of an initial event (see Example 7, part a, in which continuation is shown by the arrow Q). Triple meter involves a more prolonged sense of continuation, as shown in Example 7, part b; it is also more complex than duple because it denies a potential two-beat duration, as indicated by the crossed-out arrow Q in Example 8. Hasty describes this special type of denial asdeferral.
[35] In Hasty's system, meters consisting of irregularly spaced beats engender considerably more complicated perceptual processes. In duple and triple, all suggested projections are realized (although in the case of triple, the last projection is deferred); in an asymmetrical meter, however, some projections will never be realized. For example, in 5/4 meter with a 3+2 division, the three-beat projection suggested by the first part of the measure is denied when the second measure begins. See Example 9, in which the potential duration Q', indicated by the dotted line, is denied. A similar denial occurs in the second measure of a 2+3 pattern, as shown in Example 10 by the dotted line R'. Although Hasty claims that our perception of such patterns is complex, he notes that they should not be considered "unnatural or confused." His approach is useful for EDM because it does not simply describe irregular patterns as syncopated, but rather provides a detailed description of the processes engendering their rhythmic complexity. In this way it can provide a convincing account of the richness that one perceives in the rhythmic surface of this music.
[36] As the foregoing discussion has shown, the approaches of Rahn, Handel, and Hasty each provide a distinctive contribution to our understanding of the asymmetrical patterns that occur in electronic dance music. Rahn provides a structural account of the special characteristics of these rhythms, while Handel and Hasty focus more on issues of perception. Handel suggests an alternate mode of hearing that may play a role in the cognition of such patterns; Hasty, on the other hand, applies the same perceptual principle (projection) to all meters, while also showing the unique ways it plays out in irregularly spaced meters. While there are obvious differences between these approaches, they should not be considered mutually exclusive. For instance, although Rahn and Handel, unlike Hasty, preserve a separation between rhythm and meter, their respective emphases (structural properties and figural hearing) could still be situated within Hasty's method. Likewise, Hasty's discussion of projection could be applied to asymmetrical patterns even if those patterns are not considered strictly metrical. In fact, I would ultimately conclude that such patterns are not generally metrical in electronic dance music (given that they usually occur in conjunction with regularly spaced patterns that can be heard as metrical more easily). Nonetheless, I would argue that they should not be treated as transient foreground phenomena superimposed onto an underlying regular structure. Rather, as these three methods show us, these rhythms have a distinctive presence of their own and should be considered structurally significant in their own right.
[37] Our exploration has shown a variety of ways in which rhythm and meter are used to create musical interest in electronic dance music. Displacement dissonances subvert metrical stability; inherently ambiguous patterns encourage multiple interpretations; and asymmetrical patterns counteract the regularity of persistent even rhythms. The common link between all these phenomena is an emphasis on interpretive multiplicity. In other words, electronic dance music encourages us to hear it in a variety of ways. As we have seen, this multiplicity functions on many different levels. Individual patterns are often intrinsically ambiguous. Furthermore, they frequently remain so even when used in combination: when there is no definitive metrical layer, the distinction between metrical and antimetrical layers may not be apparent. Even when all the elements of a meter are in place, reinterpretations can turn the beat around, showing the listener that the metrical structure was not quite what it seemed to be. And finally, the persistent repetition of both asymmetrical and even patterns encourages multiple perspectives on rhythmic and metrical structure, thereby undermining any sense that there is a singularstructure underlying the music.
[38] In spite of these conclusions, a number of questions remain. First, how might the instabilities and ambiguities that I have discussed be played out on a larger scale? In what ways do EDM musicians create subtlety in a work as a whole? What sorts of processes occur during the course of complete tracks, albums, and DJ sets? Second, how widespread are the phenomena considered here, and how broadly applicable are the approaches put forth to the various genres of electronic dance music? Third, since EDM is first and foremost dance music, what is the relationship of dance to these rhythmic and metrical phenomena?
[39] Each of these questions is a potentially vast topic unto itself, and further research is needed before definitive answers can be given. Instead of trying to answer these questions at this time, I will leave them for future studies of electronic dance music to address. Nonetheless, I believe that these issues, in combination with the phenomena already discussed, suggest something of the range and complexity that electronic dance music offers to listeners and scholars, both within music theory and without.
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