* We are grateful to Joel Lester for his perceptive comments on an earlier version of this article, and to the anonymous readers for their suggestions. We would also like to thank Nicolas Waldvogel, conductor, for articulating a "performer�s analysis" of the orchestral introduction to the Concerto, Laurie Sampsel for her assistance in tracking down recordings and manuscripts, and Glenn Arndt, Kevin Harbison, and Daryl Burghardt, for their help with recording and converting files to suitable formats.

1. The one-movement concerto contains two cadenzas: the one presently under discussion, and a second cadenza near the work's conclusion.

2. See, for example, Schmalfeldt 1985, 27.

3. Example 2 is reprinted from Musical Form and Musical Performance by Edward T. Cone. Copyright � 1968 by W.W. Norton & Company, Inc. With permission of the publisher, W.W. Norton & Company, Inc. (Asterisks and arrow in the example added by Leong and Korevaar.)

4. De Larrocha clearly accents the notated downbeats at the asterisked points, but plays the passage relatively "straight" thereafter, allowing the mid-bar downbeats to emerge through harmonic structure and figuration changes. Nevertheless, her final tonic chords (mid-bar in the last two measures) sound uncertain of their downbeat status.

5. Example 3 is excerpted from Burkhart 1983, 99-102. Reprinted from Charles Burkhart, "Schenker's Theory of Levels and Musical Performance," in Aspects of Schenkerian Theory, edited by David Beach (New Haven: Yale University Press), by permission of Yale University Press. Copyright � 1983 by Yale University. All rights reserved. (Arrows and verbal annotation in the example added by Leong and Korevaar.)

6. Clarke 2004 provides an excellent survey of empirical methodologies, which we will not duplicate here. See also Gabrielsson 1999, especially 523-550, for an extensive overview of empirical studies. Samples of empirically-oriented studies include Johnson 1999 (relation between frequency spectra and listening experience), Clarke 1995 (semiotic interpretation of empirical analyses), Gabrielsson 1987 (comparison of empirical observations and published analyses), and Repp 1990 (comparison of empirical data to hypothesized style norms). For an example of empirical data read in historical context, see Cook 1995, which interprets Furtwängler's recorded tempi in light of the conductor's interaction with Schenker.

7. Examples of more qualitative approaches are Lester 1995, who compares expressive articulation in recorded performances with Schenkerian and durational reductions, and Barolsky 2005, who analyzes multiple recordings and explores their implications for score analysis. Bazzana 1997 provides a wide-ranging study of Glenn Gould as performer.

8. Work is beginning to be done in this area. For example, Leong and McNutt 2005 explore Babbitt's None but the Lonely Flute from the points of view of theorist and flutist; Eric Clarke and Nicholas Cook coauthor a study of Bryn Harrison's être-temps with the composer and the work's commissioning performer, Philip Thomas (Clarke et al. 2005).

9. Mead 1999 extends the concept of works as products of physical actions to the experience of listener and composer. See also Le Guin 2002 for an exploration of embodied performance in Boccherini's chamber music.

10. Writers such as Meyer 1973, 29, and Rink 1990, 323 comment on "performer's analysis." Rink, for example, states that "good performers are continually engaged in a process of 'analysis,' only ... of a kind different from that employed in published analyses. The former sort of 'analysis' is not some independent procedure applied to the act of interpretation: on the contrary, it forms an integral part of the performing process." Chaffin, Imreh, and Crawford 2002 illuminate "performer's analysis" in the course of a study of expert practice and memorization. Bazzana (1997, 87-89) provides insightful study of Glenn Gould's approach to performance. However, most literature on performance and analysis does not actually present "performer's analysis."

11. See Lester 1998 for a discussion of the gap between theorists and performers.

12. Touzelet 1990 provides a partial listing of such recordings, with a description of each performer's relation to Ravel. See also Jozaki 2000, 342-346 for a discography that includes historical recordings.

13. Clearly, the degree to which these (and any) recorded interpretations represent Ravel's desires varies greatly. For example, Ravel objected strenuously to Wittgenstein's performances of the Concerto because the pianist took flagrant liberties with the score (Touzelet 1990, 593-595). Woodley 2000 discusses performance practice in Ravel.

14. He doesn't usually use metaphors, ... but prefers antitheses, allusions, ... . (DL's translation).

15. Ravel frequently borrowed from older dance forms--menuet, pavane, forlane--as well as more contemporary ones--waltz, habanera--as evidenced by his works Menuet antique, Pavane pour une infant défunte, "Forlane," "Rigaudon," and "Menuet" movements from Le Tombeau de Couperin, Valses nobles et sentimentales, and "Habanera" from Sites auriculaires.

16. Here we assume a live performance, or at least a video reproduction of one. Some sources, such as Cone 1974, 137, consider the visual aspect of a performance to be intrinsic to it. According to Stravinsky 1936, 114, "the sight of the gestures and movements of the various parts of the body producing the music is fundamentally necessary if it is to be grasped in all its fullness." Shove and Repp 1995 argue that performers' physical motions, even when not viewed, are deduced by listeners, who then respond to the imagined motions. Mead 1999 describes a similar connection between players' physical efforts and listeners' responses as "kinesthetic empathy."

17. When I (DL) had students listen to multiple recordings of the work, several asked if it was indeed played with only one hand. Janina Fialkowska, a Canadian pianist with severe left-hand injuries, has performed this work with her right hand--a feat that raises complicated interpretive issues.

18. In the CG, the low register motion to D occurs in the orchestra.

19. Wittgenstein 1937 ends his final glissando (CG) on pitch A7 rather than D7, ignoring the parallel between OG and CG, and undermining the drive to the work's tonal center.

20. This relatively traditional use of V7-I is rare in Ravel's oeuvre, and is more characteristic of late works such as the two piano concertos. In general Ravel avoids clear statements of dominant harmonies, or resolves them in other ways. (See Teboul 1987, 67-84 for examples of Ravel's resolutions by tritones or major thirds.)

21. These terms were introduced by Cone (1968, 24) to explain the function of "integrated introductions."

22. This is a not unprecedented strategy for Ravel, particularly in evoking water as in Une barque sur l'océan and Ondine.

23. The progression recalls the harmonic motion of a traditional Classical cadenza (from cadential 6/4 to V to I). Ravel's cadenza also resembles Classical cadenzas by closing a formal section: in this case, the end of the cadenza marks the end of the concerto's introduction, while in Classical works the end of the cadenza generally signals the conclusion of a section preceding the coda or final ritornello.
Ravel was fond of defining large musical sections with pedal tones. See, for example, "Le Gibet" in Gaspard de la nuit, which features a Bb pedal throughout; also "Une Barque sur l'Océan" (Korevaar 2000, 117-119).

24. Minor seconds feature prominently in Theme 2, but occur only once between adjacent melodic pitches in Theme 1 (m.39, just preceding the change of melodic direction from up to down).

25. Generally, unlike string players or singers, pianists do not physically experience intervallic size. This one-handed work makes the physical traversal of intervals explicit.

26. Ravel's manuscript, held in the Lehman collection at the Pierpont Morgan Library, confirms Ravel's authorship of these markings. The T1 pedal markings in the published edition are later additions. We are grateful to the Pierpoint Morgan Library for supplying a microfilm of this manuscript.

27. Performers of early-twentieth-century French piano works often face such pedaling dilemnas, in which notated pedaling, clarity of harmony and voice-leading, and notated durations all compete as pedaling considerations. (See, for example, the pedal-point A's in the first movement of Debussy's Pour le piano.) The problem is due in large part to the prevalence of sustained pedal points in this repertoire; it is exacerbated on modern pianos, which have a richer tone and longer sustain than period French instruments (Winter 1990, 28-29). One solution is the use of the middle pedal, which appeared on some French pianos as early as the 1890s (Brody 1987, 181).

28. These pauses may be due in part to the physically-wide stretch of these beats.

29. Musical context and Ravel's manuscript (at the Pierpont Morgan library) confirm that E4 is the correct pitch.

30. Since Wittgenstein's (1937) top notes emerge only at the asterisk, he gives the impression (beginning at that point) of similar four-"beat" groupings.

31. Ravel provides no pedal indications here. Rather, as had become usual in French music, pedaling is implied through note values and rests.

32. See van Deusen 1999; the foregoing quote from De musica 1.4 is translated by van Deusen, 573.

33. The "measures" of four "beats" begin as hypermeasures of four 2/4 measures, contracting by m.33.3 to measures containing quarter-note beats.

34. As notated, the first "beat" falls 1 3/64 quarter notes after the orchestral downbeat. Given the a piacere indication, however, the sixty-fourth notes could be interpreted as "durationless" grace notes.

35. This kind of "split-chord" writing is reminiscent of Bach's solo sonatas for strings. Like many passages in those sonatas (Lester 1999, 31-39), the split-chord passages mentioned here ground themselves on harmonic rather than melodic bases. This parallel seems especially appropriate given other Baroque references in the Concerto's opening cadenza (sarabande rhythm in Theme 1, French-overture characteristics of Theme 2), and the many other references to earlier periods by Ravel (especially Le Tombeau de Couperin, Menuet antique) and his French contemporaries.

36. The silence in the Perlemuter recording, and part of that in the Wittgenstein recording, sound suspiciously like botched splices.

37. See Rothstein 1989, 58�63 for a discussion of successive downbeats articulated first in the accompaniment, then in the melody. Rothstein's discussion deals with split hypermetric downbeats rather than the simple split downbeats discussed here.

38. Though the iamb originally connoted short-long, it has also acquired the meaning weak-strong, and we use the term here primarily for its weak-strong meaning. Early writers on modern rhythmic theory, including Cooper and Meyer 1960 and Cone 1968, employed Classical poetic feet with varying and controversial results. Criticisms stemmed in part from the lack of distinction between various types of accent. Here we specify that, on smaller scales, the second syllable of the iamb represents relative metrical strength, and on larger levels, a confluence of tonal and metric accent.

39. Triplets "feel" more expansive than sixteenth notes.

40. In the cadenza, the first and second themes resemble one another rhythmically, while differing from one another in intervallic vocabulary: major second, perfect fourth, and perfect fifth in the first theme, and minor second, major second, and minor third in the second theme. In the orchestral introduction, the similarities are reversed: both themes feature melodic lines in Dorian modes (E and G dorian respectively), beginning with the first three degrees of their modes (<E,F#,G> and <Bb,A,G>); Theme 1 features iambs, short-long patterns, and triple meter, while Theme 2 displays begin-accented patterns, equal durations, and motivic rather than metric organization.

41. Perlemuter's 1955 recording displays similar, though less marked, tendencies. Such a lack of distinction between different types of dotted rhythms was also reflected in much of the teaching I (DK) received from Paul Doguereau, a student of Marguerite Long, Jean Roger-Ducasse, and Ravel. For example, melodic dotted rhythms in pieces as varied as Debussy's Reflets dans l'eau and Ravel's Le Gibet might be overdotted to the point of making distinctions inaudible. Although Ravel occasionally asked for overdotting or other rhythmic performance interpretations, he was generally known for demanding adherence to "the text, only the text!", including rhythmic details. (See Perlemuter and Jourdan-Morhange 1953, 66, 24 on overdotting in "Forlane" from Tombeau de Couperin, and on playing a bird call more quickly than written in Oiseaux tristes; and Février 1939, 892 and Grey 1938, 370 on adherence to the text.)

42. Although Ravel marks the OG a piacere, he notates rhythmic values precisely, usually adding up to units of quarter or eighth notes. Since he was known for demanding rhythmic exactitude (Grey 1938, 370), we suggest practicing the opening rhythms as written, and using them as a point of departure. Several pianists change Ravel's notated rhythms measurably: Casadesus (1947) and Blancard (1953), for example, shortchange the low A0-A1's in m.33.2 by an eighth note, and linger markedly (an eighth note) on the first A1 of each sixty-fourth-note group. This rhythmic trade goes against the function of A0-A1 as pedal bass, of the peaks in the sixty-fourth-note runs as melody, and of the notes in between as harmonic filler. (Blancard further undermines the A0-A1 pedal bass by not pedaling the sixty-fourth notes.)

43. On these larger levels, the iambic stress results from a combination of tonal and metric factors.

44. Although Example 10b resembles a Schenkerian graph, it is not intended as one.

45. Breaking the line at this point emphasizes the anacrustic character of the Vivo, in parallel to the anacrustic arpeggios preceding hypermetric downbeats throughout Theme 2. The break also focuses attention on the harmonic importance of the bass G# , which eventually leads to the dominant.

End of footnotes