1. David Epstein, Shaping Time: Music, the Brain, and Performance (New York: Schirmer Books, 1995). See Part Four, "Flexible Tempo."

2. See David Rowland, "Chopin's tempo rubato in context," in Chopin Studies 2, ed. John Rink and Jim Samson, 199-213 (Cambridge: Cambridge University Press, 1994).

3. Carl Czerny, Von dem Vortrage, vol. 3 of Vollständige theoretisch-practische Pianoforte-Schule, op. 500. Vienna, 1839; 2nd ed., 1846; facsimile of 2nd ed., Wiesbaden: Breitkopf & Härtel, 1991.

4. Mathis Lussy, Musical Expression: Accents, Nuances, and Tempo in Vocal and Instrumental Music, trans. M. E. von Glehn (London: Novello and Ewer, 1892). Lussy's prescriptions for the performance of excerpts by Mozart are, in general, the least convincing in the book.

5. Riemann, Musikalische Dynamik und Agogik. Lehrbuch der musikalischen Phrasirung auf Grund einer Revision der Lehre von der musikalischen Metrik und Rhythmik. Hamburg: Rahter, 1884.

6. Schenker's The Art of Performance, ed. Heribert Esser, trans. Irene Schreier Scott (New York: Oxford University Press, 2000), is a compilation of previously unpublished material by Schenker, most of it written in the early 1910s.

7. Lerdahl and Jackendoff define an afterbeat as a weak beat that groups with the preceding strong beat, not with the following strong beat. See A Generative Theory of Tonal Music (Cambridge, Mass.: The MIT Press, 1983), 28.

8. See Riemann 1884, 29-30, 98, and 174-76.

9. An excellent source on Italian prosody and its relation to operatic music is Robert Moreen, "Integration of Text Forms and Musical Forms in Verdi's Early Operas" (Ph.D. dissertation, Princeton University, 1975).

10. I have presented a similar versification of a Chopin melody in "Ambiguity in the Themes of Chopin's First, Second, and Fourth Ballades" (Intégral 8 [1995]: 1-50). The melody there is the main theme of the First Ballade, op. 23.

11. The relation to settenario is imperfect because only Chopin's primary accent corresponds to the poetic meter; his secondary accent does not. In settenario, the secondary accent normally falls on the fourth syllable.

12. For an illuminating example, see Reinhard Strohm, "Merkmale italienischer Versvertonung in Mozarts Klavierkonzerten," Analecta musicologica 18 (1978): 219-36.

13. In his book Musikalische Rhythmik und Metrik (Magdeburg, 1917), Theodor Wiehmayer disputes the idea that an appoggiatura or suspension must group with its resolution. Some of his examples (�50) are convincing; see especially those from Bach's F-minor Prelude (WTC, Book 1), his motet "Jesu, meine Freude," and Liszt's Sposalizio.

14. In his personal copy of the score to this Prelude (Oster Collection, New York Public Library for the Performing Arts), Ernst Oster also shows a 10-9 appoggiatura in m. 7.

15. Chopin's autograph, which has been published in facsimile, lacks a sharp sign before F4 in m. 19, thus forming another minor ninth with the bass. Some editions, including Ewald Zimmermann's for Henle, follow the autograph here. Most other editions read the note as F#4. I assume that the note should be F#4 partly because of the accent mark over A4 in m. 21. If m. 21 were merely a sequential transposition of m. 19, it is hard to see what purpose the accent would serve.

16. The idea that the F4 at the end of m. 9 is a passing tone originates, so far as I know, with Ernst Oster, who noted the ascending third in his score of the Prelude (see note 14).

17. Lussy describes the performance of ascending phrases (not only sequences) in terms of physical effort; see Lussy 1892, 165-66.

18. Frank Samarotto, "A Theory of Temporal Plasticity in Tonal Music: An Extension of the Schenkerian Approach to Rhythm with Special Reference to Beethoven's Late Music" (Ph.D. dissertation, City University of New York, 1999).

19. Lerdahl, Tonal Pitch Space (New York: Oxford University Press, 2001).

20. This principle might not hold when the first of two spaces contains very few notes per octave, and the succeeding space is heard to fill in elements of a normative space. An example would be the motion from fifth-space to triad-space to diatonic space at the beginning of Beethoven's Ninth Symphony (cited by Lerdahl on p. 53).

21. Quoted in Jean-Jacques Eigeldinger, Chopin, pianist and teacher, as seen by his pupils, trans. Naomi Shohet (Cambridge: Cambridge University Press, 1986), 272.

22. This principle is consonant with Lerdahl and Jackendoff's Grouping Preference Rule 2a, which addresses proximity of attack points (Lerdahl and Jackendoff, 45).

23. The situation in mm. 42-43 differs in that the bass note does not change (it is enharmonically respelled), and the left hand leaps an octave across the bar line. These factors tend to encourage the treatment of the eighth notes in m. 42 as an upbeat, whereas the dissonant interval traversed by the left hand between mm. 18 and 19--a major seventh spelled as a diminished octave--tends to encourage separation.

24. Robert Philip, Early recordings and musical style: changing tastes in instrumental performance, 1900-1950 (Cambridge: Cambridge University Press, 1992).

25. In my decision to �rush� the two pedal points I again find myself in agreement with Lussy, who advises accelerando for long-held notes in the melody.

26. Compare the Nocturne in E-flat Major, op. 9, no. 2, where the 12/8 measure corresponds to the four-bar hypermeasure in Prelude No. 21.

27. The use of "phrase" as a verb meaning "to shape a phrase" (in German, phrasiren) may be traced to Riemann 1884; I am not aware of this usage earlier. I criticized this use of "phrase" in Phrase Rhythm in Tonal Music (New York: Schirmer Books, 1989), 11-12.

28. See Rowland op. cit. on the type of rubato in which the melody is shaped independently of the bass. A vestige of late-eighteenth-century practice, it was described by Mozart in a famous letter to his father (quoted in Rowland, 202). This type of rubato requires a clear textural distinction between the rhythms of melody and accompaniment, a distinction that does not exist in Prelude No. 17 but does exist in Nos. 13 and 21.   

29. That two simultaneous but conflicting grouping structures may coexist at the same level violates Lerdahl and Jackendoff's Grouping Well-Formedness Rule 4 (Lerdahl and Jackendoff, 38). I would maintain, however, that conflicting low-level groupings are a part of everyday musical experience, especially in late-Baroque and Romantic music.

30. I am indebted to my colleague Joseph Straus, theorist and cellist extraordinaire, for information on cello technique.

31. Victor Zuckerkandl, The Sense of Music (Princeton: Princeton University Press, 1959), 122.

32. There are comparable passages in Prelude No. 13. In m. 6, for example, the leaps of sevenths, C#3-D#2 and F#3-G#2, suggest a temporary change to beginning-accented groups.

33. See the present author's "Chopin and the B-major complex: a study in the psychology of composition," Ostinato rigore 15 (2000): 149-72.

End of footnotes