1. The bracketed melodic and durational pattern shown in Example 1 repeats four more times, a fact that will be central as the analysis continues.
2. The terms radical and conservative come from Andrew Imbrie's "'Extra' Measures and Metrical Ambiguity in Beethoven," in Alan Tyson, ed., Beethoven Studies (New York: Norton, 1973), 45-66. Imbrie suggests that in the face of metrical irregularity, conservative listeners prefer to maintain an established periodic counting as long as possible, whereas radical listeners prefer immediately to adjust to a new counting.
3. According to Benjamin Suchoff's Guide to the "Mikrokosmos" (New York: Da Capo Press, 1983), Bart�k remarked that the changes of time in #126 were similar to those found in Romanian folk music (p. 109). Janos Breuer identifies the changing rhythms in this piece as representative of the Romanian kolinda (carol); see "Kolinda Rhythm in the Music of Bart�k," Studia Musicologica Academiae Scientiarum Hungaricae 17 (1975): 39-58.
4. In its emphasis on moment-to-moment decision-making, this analysis draws upon meter as described by Christopher Hasty in Meter as Rhythm (New York: Oxford University Press, 1997). Hasty describes meter as arising processively, that is, by comparing one's expectations for beginnings (and therefore accents) with how they actually occur. Any misrepresentations of his terminology and symbols are of course my own. I also recognize that the reading given below may not correspond with the reader's preferred one. The point is not to choose a single reading, but rather to focus on the notion that readings emerge rather than come to us fully formed. Any reading (not just the one given above) takes time to come about.
5. Although Hasty does not describe processive meter as an act of counting, I will frequently use this verb in my descriptions to draw attention to our active, in-time engagement with meter. In other words, I do not intend "counting" to represent an independently imposed or periodic schema. Victor Zuckerkandl describes counting analogously (as a process); see for example Sound and Symbol Music and the External World, trans. Willard Trask (New York: Pantheon Books, 1956), 167-68.
6. Directly above the first measure of Example 1 is a vertical slash followed by a diagonal one. This is Hasty's way of indicating that the very beginning event (the first two quarter notes) becomes an anacrusis, and therefore (eventually) does not create additional projections.
7. Hasty describes possible "early" entries of beginning events in his Example 7.3 (Meter as Rhythm, 87). The various cases shown there are distinguished by how early a third event arrives. My description of G's early arrival is most similar to Example 7.3d, where the third event comes so early that the potential of the previous beginning comes into question. This will be discussed below.
8. Maury Yeston first described metrically defined strata as consonant or dissonant with one another in The Stratification of Musical Rhythm (New Haven: Yale University Press, 1975). The model has been considerably amplified by Harald Krebs in "Some Extensions of the Concepts of Metrical Consonance and Dissonance," Journal of Music Theory 31.1 (Spring 1987): 99-120, and more recently in Fantasy Pieces: Metrical Dissonance in the Music of Robert Schumann (New York: Oxford University Press, 1999).
9. The metrical grid developed by Fred Lerdahl and Ray Jackendoff is perhaps the clearest representation of fixed meter. Lerdahl and Jackendoff define meter as strictly periodic at the levels of tactus and measure, permitting metrical reinterpretation (their term is metrical deletion) only at hypermetrical levels and in conjunction with grouping elision. See A Generative Theory of Tonal Music (Cambridge, Mass.: MIT Press, 1983), especially pp. 99-104.
10. Yeston, Stratification, first formalized hemiolas above the level of the notated measure. Cohn has developed more sophisticated models. See especially his "Metric and Hypermetric Dissonance in the Menuetto of Mozart's Symphony in G Minor, K. 550," Int�gral 6 (1992): 1-33.
11. Breuer, "Kolinda Rhythm in the Music of Bart�k," discusses the practice of rebarring difficult passages periodically as a performance aid, citing Bart�k's suggestion to the conductor Hugo Balzer in 1930 that the changing time signatures at rehearsals 47 to 49 in the first movement of the First Piano Concerto might be rebarred entirely in 2/4. In his Example 10 Breuer aligns the original notation with a 2/4 rebarring, and concludes that in addition to being unmusical, the periodic version actually makes the orchestral parts harder to read.
12. This reading is similar to readings of Stravinsky's metrical irregularity by Pieter van den Toorn. See, for example, his discussion of background periodicity in chapter 3 of Stravinsky and "The Rite of Spring" (Berkeley: University of California Press, 1987).
13. See my analyses of portions of Renard and Les Noces in "Metric Irregularity in Les Noces: The Problem of Periodicity," Journal of Music Theory 39.2 (1995): 285-309.
14. In the latter part of my 1995 article, I suggest that when irregularities are repeated, they may become contextually regular. That we may experience repeated irregularities differently at different points of the piece is an idea central to this paper.
15. Full consonance, a term from Cohn's "Metric and Hypermetric Dissonance" is the partitioning of a span where each level is exclusively subdivided by either two or three, terminology that echoes the metrical well-formedness rules of Lerdahl and Jackendoff and highlights the typical metrical ease with which such passages are associated. By distinguishing the "normal situation" of full consonance, Cohn is able to describe situations outside the norm, such as ongoing competing partitions of two and three at a single level.
16. One's perception of quarter-eighth has been heavily colored already in this piece by the repetitions of bar 3, where a double neighbor figure around G is also anacrusic.
17. Hasty argues that a span of 5 cannot give rise to strong projections precisely because neither 2 nor 3 is exclusively fundamental to its identity; he describes the quality of 5 as "limping." Instead he focuses on the larger groupings within 5; he would label the 5 here as "duple unequal." See his discussion in Meter as Rhythm, pp. 142-45.
18. Alternatively, some counters might come to count by 10s as early as bar 20 (i.e., beginning hypermeasures a bar earlier than shown in Example 4, in what Lerdahl and Jackendoff would call an "out-of-phase" manner). This reading considers bar 21 as a continuation of bar 20 based on the precedent of bars 4 and 5. An expectation for continuation after bar 20 has been shaped by appending to bar 4's cadential arrival an anacrusic gesture (the two stepwise, ascending quarters that begin each phrase); this joining is reinforced in each succeeding phrase. We might hear a similar continuation take place at bar 21, for its E and F mimic the anacrusis from earlier in the piece. The larger point remains unaffected, however: in either reading, counting in part two becomes smoother sailing: both 5s and 10s continue easily and without significant interruption until near the end of the piece.
19. Hasty, Meter as Rhythm, describes a hiatus as "a break between the realization of projected potential and a new beginning" (p. 88); in other words, a hiatus takes place when projection is temporarily interrupted.
20. The animations in Examples 2, 4, and 6 were designed by Indiana University music theory doctoral student Brent Yorgason. I wish to thank him for his efforts.
End of footnotes