1. Because of the profusion of terms describing the various subcategories of contemporary dance music, I prefer to use the umbrella term "electronic dance music" when speaking of the repertoire as a whole. Dance music fans in the general public--who are highly sensitive to issues of style and genre in this repertoire--also employ this term. Other catch-all terms, such as "techno" and "electronica," are problematic in various ways: to dance music fans, "techno" frequently connotes something more specific (a particular style of electronic dance music), and "electronica" is often viewed suspiciously as a marketing term devised by the music industry. For descriptions of the various genres and subgenres of electronic dance music, see "Talking Music: Sounds from the Dance," in The New York Times Online, http://www.nytimes.com/library/music/031300dj-techno.html; links to sound files, interviews, and other features are included. Please note that "electronic dance music" will occasionally be abbreviated in this article as "EDM."

2. These particular quotations are taken, respectively, from the following articles in the Detroit Free Press describing the 2001 Detroit Electronic Music Festival: David Lyman, "Detroit Dance Fever," 28 May 2001, C6; Brian McCollum, Tim Pratt, and Tamara Warren, "Techno and Torrents in Hart Plaza," 28 May 2001, C6; and Brian McCollum, "Unbeatable," 29 May 2001, D3.

3. Similar ambiguities have been explored by the psychologist Stephen Handel, who has studied the cognition of polyrhythms such as two against three, two against five, and so on. In a series of experiments, Handel and co-researcher James Oshinsky played selected polyrhythms for listeners and asked them to tap along with what they perceived to be the beat; their results suggest that certain combinations encourage a variety of beat placements.� See Stephen Handel and James S. Oshinsky, "The Meter of Syncopated Auditory Polyrhythms," Perception and Psychophysics 30.1 (1981), 1-9.

4. Harald Krebs, Fantasy-Pieces: Metrical Dissonance in the Music of Robert Schumann (New York: Oxford University Press, 1999), 33. Krebs describes the type of polyrhythm discussed by Handel as a grouping dissonance.  This type consists of layers whose cardinalities differ (for instance, a 3-layer against a 5-layer), whereas a displacement dissonance always involves two or more layers of the same cardinality (ibid., 31).

5. Maury Yeston, The Stratification of Musical Rhythm (New Haven: Yale University Press, 1976).

6. Krebs, Fantasy-Pieces, 2, 30.

7. Krebs does refer very briefly to such a situation, noting that "where there is no metrical framework, the layer initiated earlier usually functions as the referential layer" (ibid., 261, n. 20). While this principle seems plausible, it remains hypothetical within the context of Krebs's book, as none of his examples fall into this category. Even if we do accept it, it is difficult to apply in this case, as both layers begin almost simultaneously and at a low volume. Krebs has concurred with my assertion that selective attention can change which layer functions as referential in this example (personal communication, May 2000).

8. Krebs believes that most displacement dissonances are heard as forward displacements; thus, he usually expresses them with positive numbers--for example, D4+3 rather than D4-1 (ibid., 35-36). In this example, since there is no definitive metrical layer, this distinction is not especially relevant.

9. At the same time, the increase in metrical consonance is counterbalanced by the syncopation of the new pitch pattern. Interestingly, if any other note within this pattern were taken as the downbeat, it would be considerably less syncopated; one such rearrangement is shown in Example 1c. Such a move, however, would shift the percussion parts onto weak sixteenth-note beats. It would be quite unusual for the bass drum to be syncopated in this manner; when present, it tends to function as a source of metrical stability in EDM, most likely due to its status as the lowest and most resonant element in the texture. Research in music cognition supports this claim (for instance, Handel and Oshinsky found that when the frequency between metrically dissonant elements varies, listeners tend to choose the lower frequency as stable; see "Syncopated Auditory Polyrhythms," 4), as does observation of EDM in performance (when played at a typical performance volume, the bass drum will be felt throughout the entire body).

10. Here I employ a distinction between conservative and radical listeners first suggested by Andrew Imbrie. (See Andrew Imbrie, "'Extra' Measures and Metrical Ambiguity in Beethoven," in Beethoven Studies, ed. Alan Tyson [New York: Norton, 1973], 45-66.) When presented with conflicting cues, conservative listeners tend to hold onto previously established metrical interpretations for as long as possible, whereas radicals move on to new interpretations more readily. In Example 2b, a conservative hearing is supported by the lack of a strong downbeat orientation in the drumbeat pattern and by the fact that the articulations of this pattern occur on weak beats of the previously established meter; a radical hearing is supported by the previously mentioned tendency of low drumbeats to function as metrically stable in EDM (in contrast to cymbals, which usually function as backbeats) and by the fact that the drum pattern begins one eighth note before the synth and cymbal patterns (if the drum were the backbeat, its pattern would more logically begin on the "and" of beat one).

11. Dave Headlam, "Blues Transformations in the Music of Cream," in Understanding Rock: Essays in Musical Analysis, ed. John Covach and Graeme M. Boone (New York: Oxford University Press, 1997), 73-79. Headlam does not use the term "displacement dissonance"; this application of Krebs's terminology is my own.

12. See John Covach, "Progressive Rock, 'Close to the Edge,' and the Boundaries of Style," in Understanding Rock, 11-14. It should be noted, however, that Covach's examples differ from those previously cited, in that (in Krebsian terms) they would be considered grouping rather than displacement dissonances. (As before, the application of Krebs's terminology is my own rather than the author's, though Covach does use the term "metric dissonance.") While displacement dissonances are quite common in electronic dance music, grouping dissonances are relatively rare.

13. For instance, see Cynthia Folio, "An Analysis of Polyrhythm in Selected Improvised Jazz Solos," in Concert Music, Rock, and Jazz since 1945: Essays and Analytical Studies, ed. Elizabeth West Marvin and Richard Hermann (Rochester, N.Y.: University of Rochester Press, 1995), 103-34. Folio finds examples of both grouping and displacement dissonances (which she refers to as type A and type B dissonances, following an earlier usage of Krebs), as well as a third type (type C) involving out-of-phase tempos.

14. Cf. Covach, "Progressive Rock," 14.

15. For the most part, however, Folio's examples present a succession of distinct, short-lived dissonances, a feature that distinguishes them from Covach's examples (in which considerable time intervals separate appearances of related dissonances) and from EDM (in which a single dissonance often repeats continuously for a long period of time).

16. There are a few notable exceptions to this trend: certain styles of house music feature vocals quite prominently; drum-n-bass/jungle DJs sometimes perform in conjunction with rappers (MCs); and "crossover" artists such as Moby are also more likely to utilize vocals. Nevertheless, the above statement holds true for the majority of electronic dance music; it is quite common to hear several hours worth of music at an EDM performance without encountering a single vocal. Furthermore, the exceptions to this phenomenon tend to push toward or be classified as other genres; for instance, certain performers are classified as crossover acts because their vocally driven songs are seen as moving toward the style and structure of radio-friendly pop.

17. DJs also play an important role in certain other genres, such as rap and turntablism. Rap in particular shares many aspects of EDM's layered approach to musical construction, and layering has been emphasized in analytical approaches to rap as well. For instance, see Tricia Rose, Black Noise: Rap Music and Black Culture in Contemporary America (Hanover, N.H.: Wesleyan University Press, 1994); Robert Walser, "Rhythm, Rhyme, and Rhetoric in the Music of Public Enemy," Ethnomusicology 39.2 (1995), 193-217; and Adam Krims, Rap Music and the Poetics of Identity (Cambridge: Cambridge University Press, 2000). Nonetheless, the absence of vocals, in combination with the more central role of the DJ, creates significant textural differences between EDM and rap.
        It should also be noted that live performances (generally called "live p.a.'s") are becoming increasingly common in electronic dance music, especially in its more experimental genres. These performances are usually quite different from those seen in other types of popular music, though. The artists do not play any sort of standard instrument; instead, they manipulate studio technology and software in a real-time environment. (An extreme example occurred at the 2001 Detroit Electronic Music Festival, when artist Nobukazu Takemura and another musician performed solely on laptop computers.) Another difference is that many EDM artists create new works when performing rather than attempting to recreate their recorded works.

18. This contrasts with the example given by Headlam, in which a meter is definitively established before the introduction of an antimetrical layer. Covach also argues for a clear distinction between metrical and antimetrical layers in the first presentation of the dissonance he discusses (Covach, "Progressive Rock," 11 and 13).

19. Steve Reich, "Non-Western Music and the Western Composer," Analyse musicale 11 (1988), 49.

20. Cf. Simha Arom, "Time Structure in Music of Central Africa: Periodicity, Meter, Rhythm, and Polyrhythmics," Leonardo 22 (1989), 91.

21. Christopher Hasty, Meter as Rhythm (New York: Oxford University Press, 1998), 3.

22. Cf. Gretchen Horlacher, "Multiple Meters and Metrical Processes in the Music of Steve Reich," Intégral (forthcoming), 2, where this point is made with respect to minimalist (as opposed to more generally "minimal") music.

23. In EDM, measures usually consist of either eight eighth-note or sixteen sixteenth-note pulses; measure lengths of eight, nine, twelve, or sixteen pulses are common in African music. In both repertoires, however, the number of attacks articulating an asymmetrical pattern is usually an odd number, such as 3, 5, or 7.� See Jay Rahn, "Asymmetrical Ostinatos in Sub-Saharan Music: Time, Pitch, and Cycles Reconsidered," In Theory Only 9.7 (1987), 27-28, for a listing of some of the patterns that commonly occur in African music.

24. In turning to this body of scholarship, I am not attempting to suggest a relationship of influence between West African percussion music and electronic dance music. Rather, I consider this literature because it addresses a musical characteristic shared by the two repertories. While I personally believe that EDM probably has been influenced by African music, either directly (e.g., through musicians' experiences with African music) or indirectly (e.g., through African-American musical traditions), to consider this possibility in detail would take us well beyond the scope of this paper.

25. Robert Kaufman, "African Rhythm: A Reassessment," Ethnomusicology 24 (1980), 394. Other scholars who argue for the existence of irregularly spaced beats in African music include Ruth Stone and Rose Brandel. See Ruth M. Stone, "In Search of Time in African Music," Music Theory Spectrum 7 (1985), 139-48; and Rose Brandel, The Music of Central Africa (The Hague: Martinus Nijhoff, 1961).

26. For instance, see Richard Waterman, "African Influence on the Music of the Americas," in Acculturation in the Americas (Proceedings of the 19th International Congress of Americanists), ed. Sol Tax (Chicago: University of Chicago Press, 1952), 207-18; J. H. Kwabena Nketia, The Music of Africa, (New York: W. W. Norton, 1974); and David Locke, "Principles of Offbeat Timing and Cross-Rhythm in Southern Eve Dance Drumming," Ethnomusicology 26.2 (1982), 217-46.

27. Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, Mass.: MIT Press, 1983), 69. Lerdahl and Jackendoff do posit these rules as idiom-specific, however, and acknowledge (97) that "certain other metrical idioms have more complex rules in place of MWFR4, permitting structured alternation of different-length metrical units." (MWFR4, or Metrical Well-Formedness Rule 4, is the second of the rules given above.) Nonetheless, they address these idioms only briefly, and this exception is rarely mentioned in applications of their work.

28. See David Temperley, "Meter and Grouping in African Music: A View from Music Theory," Ethnomusicology 44.1 (2000), 65-96, and "Syncopation in Rock: A Perceptual Perspective," Popular Music 18.1 (1999), 19-40. Although there are similarities between the GTTM approach and some of the views of meter expressed by ethnomusicologists, I would disagree with Temperley's assertion that "there is almost unanimous agreement" among ethnomusicologists that African music has meter as defined by Lerdahl and Jackendoff (Temperley, "Meter and Grouping in African Music," 68; see also 76). In fact, scholars present very diverse opinions on meter and rhythm in this music; even those who seem to share the same general view often differ markedly on various points. Furthermore, due to an unfortunate lack of intellectual exchange between music theory and ethnomusicology--a situation that has only begun to change quite recently--it is difficult to make claims that relate ethnomusicological views of meter to specific music-theoretical ones with any certainty.
        In his 1999 paper, Temperley argues that syncopations in rock can be understood as displacements from specific positions in a metrical grid. While this is helpful in showing how Lerdahl and Jackendoff's model might be extended to highly syncopated repertoires, it will not be discussed at length here, as it is not especially applicable to situations like the one presented above for several reasons: first, it is based on textual accentuation, which is rarely a factor in EDM; second, in all of the examples considered by Temperley, the accompanying instruments clearly convey an evenly spaced metrical structure; and third, none of Temperley's examples contain regularly recurring asymmetrical patterns like the ones shown in Example 4e.

29. Kaufmann, "African Rhythm," 394; Stone, "In Search of Time," 140.

30. Temperley notes a similar problem with respect to Lerdahl and Jackendoff's theory. In their approach, patterns that dissonate with the meter are simply described as syncopated; the ways in which syncopation functions remain relatively untheorized. Temperley, "Syncopation in Rock," 25-26.

31. Ibid.

32. Rahn, "Asymmetrical Ostinatos," 25.

33. Arthur M. Jones, Studies in African Music, (London: Oxford University Press, 1959), 20-21.

34. This general observation may be less applicable to subgenres that feature vocals or instrumental solos. In such cases, the voice or solo instrument may function as a rhythmic and textural "figure" against an accompanimental metrical "ground," and Temperley's rock-based model of syncopation may be more applicable.

35. Headlam, "Blues Transformations," 87. Headlam ultimately concludes that either approach may be relevant for different songs and even within the same song.

36. Rahn, "Asymmetrical Ostinatos," 25-26.

37. See Rahn, "Asymmetrical Ostinatos," and "Turning the Analysis Around: African-Derived Rhythms and Europe-Derived Music Theory," Black Music Research Journal 16.1 (1996), 71-89. Another important article adopting a similar approach is Jeff Pressing, "Cognitive Isomorphisms between Pitch and Rhythm in World Musics: West Africa, the Balkans and Western Tonality," Studies in Music 17 (1983), 38-61.

38. John Clough and Jack Douthett, "Maximally Even Sets," Journal of Music Theory 35.1 (1991), 93-173.

39. In this paragraph I use Rahn's term "diatonic rhythms" in place of "asymmetrical patterns"; describing the rhythm provided as an example (2+1+2+1+2) as "asymmetrical" is problematic, since its durations form a palindrome. In both "Compression" and "Pearls Girl," however, this pattern is treated as a variant of 3+3+2, which clearly divides the measure asymmetrically. In fact, all of the diatonic rhythms I have observed in EDM are either literally asymmetrical or are grouped asymmetrically. Rahn himself includes 2+1+2+1+2 in a list of "asymmetrical ostinatos" in his 1987 paper (see pp. 27-28), though he replaces this term with "diatonic rhythms" in his 1996 article. Since my paper as a whole is not about the "diatonic" aspects of these rhythms, I will continue to use the term "asymmetrical patterns" throughout the article.

40. Rahn, "Turning the Analysis Around," 79-80.

41. Stephen Handel, "The Interplay between Metric and Figural Rhythmic Organization," Journal of Experimental Psychology: Human Perception and Performance 24.5 (1998), 1546-61.

42. Ibid., 1546-47.

43. Handel first demonstrated this point in "The Differentiation of Rhythmic Structure," Perception and Psychophysics 52 (1992), 492-507.

44. Although Handel presents a wide variety of weakly metric rhythms, he does not focus specifically on the figural properties of asymmetrical patterns. This is certainly a promising topic for future research, however. He does in fact single out the rhythm found in "Cubik", 3+3+3+3+4 (or X..X..X..X..X...), for special comment, noting that it differs from the other rhythms in his study in that it is comprised entirely of single-tone figures (its figural organization is 1-1-1-1-1-; Handel, "Metric and Figural Rhythms," 1559). This attribute suggests an interesting relationship to the maximal evenness discussed by Rahn.

45. Hasty, Meter as Rhythm, 84-86.

46. Ibid., 131, 133-34.

47. Ibid., 146.

48. Another work that should be mentioned in this regard is Gretchen Horlacher's article "Bartok's 'Change of Time': Coming Unfixed," Music Theory Online 7.1 (2001). Horlacher claims that the processive approach suggested by Hasty is "especially relevant for music that is vitally 'irregular,' for it values such irregularities as capable of shaping the essential nature of time within the context of a given piece" (paragraph 4.1).

49. While figural hearing might seem incompatible with Hasty's emphasis on the projection of specific durations, I would argue that it could still be posited as an additional mode complementary to projective hearing. Furthermore, Handel's characterization of meter as "emergent" ("Metric and Figural Rhythms," 1560) also resonates with Hasty's approach. Hasty does in fact discuss research by Handel (see Meter as Rhythm, 124-25 and 173), though the passages cited do not address figural organization in particular.

50. In other words, situations in which they occupy every layer of the texture without opposition for the course of an entire track (as in "Compression") are somewhat exceptional. It is not uncommon, however, for them to dominate entire sections of a track (as in Walt J's track "Reborn," as remixed by Juan Atkins on WaxTrax! MasterMix Volume 1); even more common are situations in which they compete for prominence with symmetrical patterns, as in "Cubik."

51. Though (as I will argue in the concluding paragraph) further research is necessary to answer these questions fully, I would like to comment briefly on the issues raised in this sentence. As discussed above (paragraphs 10-15), the phenomena addressed in this paper are not limited to EDM, though their manifestations within it are part of a distinctive constellation of features. Regarding the various genres of EDM itself, I believe that the research presented here can be applied to a broad cross-spectrum of the music, though as I have noted elsewhere, certain features may be more applicable to some genres than others. In selecting the musical examples presented here, I have chosen works from relatively well-known artists with the intent of making the paper more accessible. The artists represented incorporate a variety of genres into their work. The Chemical Brothers are most commonly classified as "big beat," a term referring to dance music that incorporates some of the song structures and sonic elements of rock and hip-hop (though I believe this aspect of their work has been overemphasized). Everything But the Girl have a long history that has only recently (ca. 1995) begun to include EDM elements; since then, however, they have collaborated with many prominent dance musicians and have successfully incorporated a variety of EDM styles into their work. Underworld (who recently disbanded) are difficult to place within a particular genre, as their individualistic sound shows the influence of techno, deep house, breakbeat, and dub; however, their music has often been characterized broadly as techno (for instance, see Dom Phillips, "Underworld," in The Rough Guide to Techno [London: The Rough Guides, 2000]). In spite of the commercial success of these artists and the fact that some of their work includes elements of other popular music genres, I have avoided work that might be considered "crossover" (such as The Chemical Brothers' collaborations with Oasis and other pop musicians), and I believe that the music included here represents trends central to EDM.

52. Many of these questions will in fact be addressed in my doctoral dissertation, "A Study of Rhythm and Meter in Electronic Dance Music, with a Consideration of the Enactment of These Features in Dance" (Indiana University, in progress).

End of footnotes