* Catherine Nolan, Caroline Palmer, and the two anonymous
reviewers deserve my special thanks for their helpful suggestions. Dr. Nolan
provided encouragement and expert guidance throughout the project's development,
and Dr. Palmer offered thorough and unusually quick feedback on my references to
studies in music psychology.
1. See especially Jonathan Kramer, The Time of Music: New Meanings, New Temporalities, New Listening Strategies (New York: Schirmer, 1988), Ch. 4: "Meter and Rhythm," 81-122; Christopher Hasty, Meter as Rhythm (Oxford: Oxford University Press, 1997), "Preface," vii-xii.
2. Stanley Sadie, ed. The New Grove Dictionary of Music and Musicians (London: Macmillan, 1980), s.v. "Metre."
3. Stanley Sadie, ed. The New Grove Dictionary of Music and Musicians, 2nd ed. (London: Macmillan, 2001), s.v. "Metre," by Justin London.
4. See especially Mary Louise Serafine, Music as Cognition: The Development of Thought in Sound (New York: Columbia University Press, 1988), 69-74.
5. Joseph Kerman, Contemplating Music: Challenges to Musicology (Cambridge, Mass.: Harvard University Press, 1985), 60-112; Clare Detels, "Autonomist/Formalist Aesthetics, Music Theory, and the Feminist Paradigm of Soft Boundaries," Journal of Aesthetics and Art Criticism 52/1 (Winter 1994): 113-26; Kevin Korsyn, "Beyond Privileged Contexts: Intertextuality, Influence, and Dialogue," in Rethinking Music, ed. Nicholas Cook and Mark Everist, 55-72 (Oxford: Oxford University Press, 1999); Susanne Cusick, "Gender, Musicology, and Feminism," also in Rethinking Music, 471-98.
6. Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, Mass.: MIT Press, 1983). I will use the abbreviation GTTM in subsequent references to this source.
7. Empirical confirmation of claims from GTTM can be found in Irène Deliège, "Grouping Conditions in Listening to Music: An Approach to Lerdahl and Jackendoff's Grouping Preference Rules," Music Perception 4/4 (Summer 1987): 325-60; Emmanuel Bigand, "Abstraction of Two Forms of Underlying Structure in a Tonal Melody," Psychology of Music 18 (1990): 45-59; Nicola Dibben, "The Cognitive Reality of Hierarchic Structure in Tonal and Atonal Music," Music Perception 12/1 (Fall 1994): 1-25.
8. GTTM has been cited widely in the psychological literature on performance since the mid-1980s. See, e.g., Neil P. Todd, "A Model of Expressive Timing in Tonal Music," Music Perception 3/1 (Fall 1985): 33-58; Eric F. Clarke, "Generative Principles in Music Performance," in Generative Processes in Music: The Psychology of Performance, Improvisation, and Composition, ed. John A. Sloboda, 1-26 (Oxford: Clarendon, 1988); Caroline Palmer, "Mapping Musical Thought to Musical Performance," Journal of Experimental Psychology: Human Perception and Performance 15 (1989): 331-46; W. Luke Windsor and Eric F. Clarke, "Expressive Timing and Dynamics in Real and Artificial Musical Performances: Using an Algorithm as an Analytic Tool," Music Perception 15/2 (Winter 1997): 127-52.
9. See especially GTTM, Ch. 1, "Theoretical Perspective," 1-12; Lerdahl and Jackendoff, "A Reply to Peel and Slawson's Review of A Generative Theory of Tonal Music," Journal of Music Theory 29 (1985): 145-60; Lerdahl, "Composing and Listening: A Reply to Nattiez," in Perception and Cognition of Music, ed. Irène Deliège and John A. Sloboda, 421-28 (Hove, U.K.: Psychology Press, 1997).
10. GTTM, 1. Emphasis added.
11. They admit, for example, that their theory fails to consider counterpoint (GTTM, 37).
12. The term is derived from "hypermeasure," coined by Edward T. Cone in Musical Form and Musical Performance (New York: Norton, 1968), 40. I will also use the term "hyperbeat" to designate a beat that belongs to a hypermeasure.
13. Among the most influential sources in this genre are Erwin Stein, Form and Performance (New York: Knopf, 1962); Cone, Musical Form and Musical Performance; Janet Schmalfeldt, "On the Relation of Analysis to Performance: Beethoven's Bagatelles Op. 126, Nos. 2 and 5," Journal of Music Theory 29 (1985): 1-31; Wallace Berry, Musical Structure and Performance (New Haven: Yale University Press, 1989). See also the extensive bibliography in Cynthia Folio, "Analysis and Performance of the Flute Sonatas of J. S. Bach: A Sample Lesson Plan," Journal of Music Theory Pedagogy 5 (1991): 133-59. Some more recent contributions include Joel Lester, "Performance and Analysis: Interaction and Interpretation," in The Practice of Performance: Studies in Musical Interpretation, ed. John Rink, 197-216 (Cambridge: Cambridge University Press, 1995); Catherine Nolan, "Reflections on the Relationship of Analysis and Performance," College Music Symposium 32-34 (1993-94): 112-39; Richard S. Parks, "Structure and Performance: Metric and Phrase Ambiguities in the Three Chamber Sonatas," in Debussy in Performance, ed. James R. Briscoe, 193-224 (New Haven: Yale University Press, 1999).
14. Nicholas Cook, "Analyzing Performance, and Performing Analysis," in Rethinking Music, ed. Nicholas Cook and Mark Everist, 239-61 (Oxford: Oxford University Press, 1999).
15. J. L. Austin, How to Do Things with Words (Cambridge, Mass.: Harvard University Press, 1962), 3, 6.
16. Cook, "Analyzing Performance, and Performing Analysis," 239-47; Tim Howell, "Analysis and Performance: The Search for a Middleground," in Companion to Contemporary Musical Thought, ed. John Paynter, Tim Howell, Richard Orton, and Peter Seymour, 692-714 (London: Routledge, 1992), 709; Lawrence Rosenwald, "Theory, Text-Setting, and Performance," Journal of Musicology 11 (1993), 60-63.
17. Lester, "Performance and Analysis," 199-202.
18. Foremost in this category are Heinrich Schenker's views on performance. See, e.g., the final sentence of Schenker, "The Sarabande of Bach's Suite No. 3 for Solo Violoncello [BWV 1009]," trans. Hedi Siegel, in The Masterwork in Music: A Yearbook, Vol. 2 (1926), ed. William Drabkin, 55-58 (Cambridge: Cambridge University Press, 1996), 58: "Any other interpretation and execution will surely founder, for the immutable forces that govern this sarabande do not admit an arbitrary interpretation of any part of the composition." See also Schenker, The Art of Performance, ed. Heribert Esser, trans. Irene Schreier Scott (Oxford: Oxford University Press, 2000), 3-4, 53-57, 77-78.
19. See, e.g., Susanne Cusick, "Gender and the Cultural Work of a Classical Music Performance," repercussions 3/1 (Spring 1994), 105-7.
20. I prefer the expression "reading from the score" to both "analyzing the piece," which is vague, and "score-based analysis," which overemphasizes the visual aspect of the activity. Whether we are dealing with words or music, the word "reading" carries the connotations of aural imagery and creative participation in an often silent, private performance of sorts. In a subtle way, the word "reading" emphasizes the analyst's participation in the construction of the object of study. As Nicholas Cook once remarked, "when musicians use the notation for the purposes it is intended for--when, that is, they read it--they supply a great deal of information which is not actually in the score." Nicholas Cook, A Guide to Musical Analysis (London: Dent, 1987), 227.
21. Nicholas Cook, "Between Process and Product: Music and/as Performance," Music Theory Online 7/2 (April 2001).
22. José A. Bowen has also developed a framework for comparing different realizations of scores, but he concentrates on historical traditions and trends in performance, such as the convention of slowing down for the second theme of a work in sonata-allegro form, as well as the ontological significance of these trends, rather than the perception of structural elements. See Bowen, "The History of Remembered Innovation: Tradition and Its Role in the Relationship between Musical Works and Their Performances," Journal of Musicology 11/2 (Spring 1993): 139-73; idem, "Finding the Music in Musicology," in Rethinking Music, ed. Nicholas Cook and Mark Everist, 424-51 (Oxford: Oxford University Press, 1999).
23. For insights on these types of ambiguities and associated ontological problems, see the following: Leo Treitler, "History and the Ontology of the Work," Journal of Aesthetics and Art Criticism 15/3 (Summer 1993): 483-97; Bowen, "History of Remembered Innovation"; Nicholas Cook, "At the Borders of Musical Identity: Schenker, Corelli, and the Graces," Music Analysis 18/2 (July 1999): 179-233.
24. I will address the latter issue in some detail in a paper entitled �Rethinking Schenker�s Musical Ontology through Gadamer�s Critique of Aesthetic Consciousness,� scheduled for presentation at "The Intellectual Frontiers of Music," University of Aberdeen, June 25, 2002.
25. On the connection of ontology and performance, see Treitler, "History and the Ontology of the Work"; Bowen, "The History of Remembered Innovation"; and Cook, "At the Borders of Musical Identity." See also Peter Johnson, "Play School," The Musical Times (June 1995): 275-77, and the ensuing, rather heated scholarly exchange between Jonathan Dunsby and Peter Johnson, The Musical Times (January 1997): 12-17, (August 1997): 4-11, (October 1997): 2, (January 1998): 2. Much has also been written on this subject by Anglo-American philosophers specializing in aesthetics. See especially Peter Kivy, Authenticities: Philosophical Reflections on Musical Performance (Ithaca: Cornell University Press, 1995); Lydia Goehr, "Conflicting Ideals of Performance Perfection in an Imperfect Practice," in The Quest for Voice: On Music, Politics, and the Limits of Philosophy, 132-73 (Berkeley: University of California Press, 1998).
26. Early research on Gestalt phenomena, including the work of Christian von Ehrenfels and Alexius Meinong, was largely speculative. The Berlin school (consisting of Max Wertheimer, Kurt Koffka, and Wolfgang Köhler, all of whom were students of Carl Stumpf) is generally regarded to have initiated Gestalt psychology as a scientific movement, but nevertheless shared the earlier scholars' interest in aesthetics. Gestalt psychology is second only to transformational linguistics in its influence on GTTM.
27. Mitchell G. Ash, Gestalt Psychology in German Culture, 1890-1967: Holism and the Quest for Objectivity (Cambridge: Cambridge University Press, 1995), 1.
28. Max Wertheimer, "Untersuchungen zur Lehre von der Gestalt, I," Psychologische Forschung 1 (1922): 47-58, condensed and translated as "The General Theoretical Situation," in A Source Book of Gestalt Psychology, ed. and trans. Willis D. Ellis, 12-16 (New York: Humanities Press, 1967).
29. Kurt Koffka, Principles of Gestalt Psychology (London: Routledge and Kegan Paul, 1935), 110, 171. See also Wertheimer, "Untersuchungen zur Lehre von der Gestalt, II," Psychologische Forschung 4 (1923): 301-50.
30. GTTM, 304.
31. P. Kruse and M. Stadler, eds., Ambiguity in Mind and Nature: Multistable Cognitive Phenomena (Berlin: Springer Verlag, 1995): (a) 58, (f) 9, (g) 8. (d-e): Koffka, Principles of Gestalt Psychology, 195.
32. See L. H. Shaffer, "Timing in Solo and Duet Piano Performances," Quarterly Journal of Experimental Psychology 36A (1984): 577-95; Alf Gabrielsson, "The Performance of Music," in The Psychology of Music, 2nd ed., ed. Diana Deutsch, 501-602 (San Diego: Academic Press, 1999).
33. An index of acronyms is included as Appendix 4.
34. Lerdahl and Jackendoff were among the first theorists to describe beats not as sounding events, but instead as points in time inferred from the acoustic signal. See GTTM, 18; Kramer, The Time of Music, 82, 97.
35. GTTM, 28. The annotations indicating metric and hypermetric levels are mine.
36. Noam Chomsky, Syntactic Structures (The Hague: Mouton, 1957).
37. See GTTM, 9.
38. Ibid., 21-2.
39. For a review of this controversy, see Sadie, ed., The New Grove, 2nd ed., s.v. "Rhythm: Current Rhythm Research," by Justin London.
40. GTTM, 24, annotated with beat labels in the form "measure.beat".
41. These two readings are informed by Andrew Imbrie, "'Extra' Measures and Metrical Ambiguity in Beethoven," in Beethoven Studies, ed. Alan Tyson (New York: Norton, 1973), 45-66. Imbrie uses the terms "conservative" and "radical," respectively, for these types of hypermetric shifts.
42. GTTM, 25.
43. The depth and regularity of hypermeter are controversial issues. Jonathan Kramer, for example, argues that irregularities involving the addition or deletion of weak beats need not cause hypermeter to be attenuated. See Kramer, The Time of Music, 98-102.
44. George Hartmann proposed that "eidotropy" is a better translation of the word "Prägnanz," as it was used by the Gestalt theorists, than "precision." Eidotropy is the tendency of an image or representation to become typical or conventional. See Hartmann, Gestalt Psychology: A Survey of Facts and Principles (New York: The Ronald Press, 1935), 48.
45. GTTM, 70.
46. Transformation plays a much larger role in generative linguistics than in GTTM. The distinction is touched upon in GTTM, 62.
47. See especially GTTM, 60-61.
48. Leonard Bernstein, The Unanswered Question: Six Talks at Harvard (Cambridge, Mass.: Harvard University Press, 1976), 95-97.
49. Leonard Bernstein, adaptation of Mozart, Symphony No. 40 in G Minor, K. 550, first movement, mm. 1-24, in Leonard Bernstein at Harvard: The Norton Lectures, vol. 2: "Musical Syntax," side 3 (issued New York: CBS Masterworks BL 33019, 1974), LP vinyl recording.
50. See Caroline Palmer and Carol L. Krumhansl, "Mental Representations for Musical Meter," Journal of Experimental Psychology: Human Perception and Performance 16/4 (November 1990): 729-41. Further support for the notion that metrical memory is distinct from pitch memory may be found in the following sources: D. J. Povel and P. Essens, "Perception of Temporal Patterns," Music Perception 2 (1985): 411-40; C. Palmer and C. Q. Pfordresher, "From My Head to Your Ear: The Faces of Meter in Performance and Perception," in Proceedings of the Sixth International Conference on Music Perception and Cognition, ed. C. Woods, et al., 1-9 (Keele, U.K.: Keele University, 2000).
51. Jonathan Kramer uses the terms "extension" and "contraction" for these processes. Kramer, The Time of Music, 102-3.
52. See, e.g., Lerdahl and Jackendoff, "Reply to Peel and Slawson," 158-9: "The issue in any case is not one of value but of how listeners organize musical surfaces." See also Lerdahl, "Cognitive Constraints on Compositional Systems," in Generative Processes in Music, ed. Sloboda, 231-59.
53. More recently, a consensus has emerged that formalism can be divorced from idealism by considering the latter to be nothing more than a useful fiction. This postmodern ideology has sometimes been referred to as "provisional autonomy." For a passionate defense of it, see Leo Treitler, "The Historiography of Music: Issues of Past and Present," in Rethinking Music, ed. Nicholas Cook and Mark Everist, 356-77 (Oxford: Oxford University Press, 1999), 358.
54. I do not mean to imply that Gestalt psychology is free of ideological baggage, but merely that it successfully evades the influence of neo-Platonic idealism and the aesthetic tradition associated with it. Indeed, the view that perceptual experience can be explained independently of socio-historical factors is itself the product of a specifically modernist socio-historical milieu. See Mitchell G. Ash, "The Academic Environment and the Establishment of Experimental Psychology," in Gestalt Psychology in German Culture, 1890-1967: Holism and the Quest for Objectivity, 17-27 (Cambridge: Cambridge University Press, 1995).
55. In his influential publications in the 1930s, music psychologist Carl E. Seashore conceived performance expression as departures from a mechanically regular norm. See Seashore, Psychology of Music (New York: McGraw-Hill, 1938), 29-30. This approach was later taken up at Uppsala by Ingmar Bengtsson and his colleagues, who coined the term SYVAR. See Ingmar Bengtsson and Alf Gabrielsson, "Analysis and Synthesis of Musical Rhythm," in Studies of Music Performance, ed. Johann Sundberg, 27-59 (Stockholm: Royal Swedish Academy of Music, 1983).
56. In this paper, I am adhering to Lerdahl and Jackendoff's policy of theorizing aspects of comprehensibility rather than aesthetics. See GTTM, 7-8, as well as paragraph 5.3, below.
57. I do not mean to suggest that performances are entirely unambiguous in meaning, or that performers never introduce additional ambiguities by their ironic handling of structures that seem unequivocal on the basis of the score. Intriguing as such phenomena may be, I will instead focus on situations in which performing nuances seem to eliminate, or at least mitigate, some of the ambiguities found in scores.
58. Lerdahl, "Atonal Prolongational Structure," Contemporary Music Review 4 (1989), 73. See also GTTM, 108-9, for a preliminary discussion of the need to distinguish between structural importance and surface salience.
59. GTTM, 17-18.
60. GTTM, 78.
61. GTTM, 347-8.
62. GTTM, 70.
63. See John A. Sloboda, "The Communication of Musical Metre in Piano Performance," Quarterly Journal of Experimental Psychology 35A (1983): 377-96; idem, "Expressive Skill in Two Pianists: Metrical Communication in Real and Simulated Performances," Canadian Journal of Psychology 39/2 (1985): 273-93; Eric Clarke, "Structure and Expression in Rhythmic Performance," in Musical Structure and Cognition, ed. P. Howell, I. Cross, and R. West (London: Academic Press, 1985), 209-37; Clarke, "Generative Principles."
64. Sloboda found six types of cues that accounted for 82% of the statistically significant differences in performers' treatment of alternate metrical renderings of a melody. These are summarized in Sloboda, "Expressive Skill in Two Pianists," 290-91. Sloboda used a metronome in his experiment, which might account for the relatively insignificant appearance of AMs in his study. Clarke did not use a metronome, and perhaps consequently, his study reveals more convincing results pertaining to AMs. See especially Clarke, "Generative Principles," 11-14. It would seem that a further implication of Sloboda's and Clarke's studies is that Lerdahl and Jackendoff's omission of time signatures and barlines from their analyses of MS is an unnecessary precaution. If the performer uses PM cues that lie within the listener's scope of experience, then the performance essentially makes the time signatures and barlines audible. The only type of performance that corresponds to their unmeasured notation would be a computer-generated mechanically regular performance.
65. Listeners vary greatly in their ability to decipher performers' metrical cues, including DMs and AMs, but these differences appear to be proportionate to the extent of listeners' musical experience. See Sloboda, "The Communication of Musical Metre," 393.
66. Compare nos. 3 and 5 under the "General Discussion" in Sloboda, "Expressive Skill in Two Pianists," 290. Also compare nos. 2 and 3 under the discussion of expressive timing in Clarke, "Generative Principles," 19.
67. GTTM, 348. See also  Appendix 1.
68. A. R. Halpern and C. I. Darwin, "Duration Discrimination in a Series of Rhythmic Events," Perception and Psychophysics 31/1 (1982): 86-89; E. Zwicker and H. Fastl, "Just-Noticeable Sound Changes," in Psychoacoustics: Facts and Models, 2nd ed., 175-201 (Berlin: Springer-Verlag, 1999), 175-6.
69. See J. Vos and R. A. Rasch, "The Perceptual Onset of Musical Tones," Perception and Psychophysics 29 (1981): 323-35; Bruno H. Repp, "Patterns of Note Onset Asynchronies in Expressive Piano Performance," Journal of the Acoustical Society of America 100/6 (December 1996): 3917; Scott D. Lipscomb and Donald Hodges, "Hearing and Music Perception," in Handbook of Music Psychology, ed. Donald Hodges, 83-132 (San Antonio, Tex.: IMR Press, 1996), 113.
70. English Chamber Orchestra conducted by Benjamin Britten (recorded Snape, U.K., May 1968; issued London: Decca 430 494-2, 1991), compact disc recording; Academy of St. Martin-in-the-Fields conducted by Neville Marriner (recorded London [ca. 1970]; issued [n.p.]: Philips 6500 162, ; reissued Netherlands: Philips 422 610-2, ), compact disc recording; Columbia Symphony Orchestra conducted by Bruno Walter (issued New York: Columbia MS 6869, ), LP vinyl recording; Vienna Philharmonic Orchestra conducted by Leonard Bernstein (recorded 1984; issued Hamburg: Deutsche Grammophon 413 776-2, 1984), compact disc recording. I will refer to these recordings as Mozart/Britten, Mozart/Marriner, Mozart/Walter, and Mozart/Bernstein.
71. Note that both this rule and the rule for metrical completion given in paragraph 4.8 apply specifically to duple-meter contexts. Further transformational rules could readily be constructed to account for similar phenomena in the context of a prevailing triple meter. According to Lerdahl and Jackendoff's MWFR3, duple and triple meter are the only allowable well-formed metrical structures in Western tonal music.
72. See also paragraph 2.7, above. Like the authors of GTTM, I will refrain from speculating on the temporality of the cognitive process of metrical transformation. For a preliminary exploration of real-time cognitive processing of music, informed by research on listeners' parsing of language, see Ray Jackendoff, "Musical Parsing and Musical Affect," Music Perception 9/2 (Winter 1991): 199-230.
73. See Appendix 2 for an explanation of the terms I use in reference to the quantitative performance analyses.
74. According to the amplitude statistics, IOI 10.1 is louder than 11.1, although the difference (0.24 dB) lies below the threshold of discrimination. This discrepancy can be attributed to the fact that amplitude stats fail to differentiate between the contributions of the melody and accompaniment. In this case, the lower strings seem to be playing m. 10 more intensely than m. 11, probably because of local harmonic tension and resolution. I would argue that the salient DM in the melody is more relevant to a discussion of Walter's MS interpretation. The accent at 13.1 also seems to be confounded by this effect.
75. See also MPR 2 (GTTM, 347), included in my Appendix 1.
76. Actually, 11.1 is a full 2.6 dB quieter than 10.1, but this reflects only the net intensity, not the melodic accent. Sloboda and Clarke don't propose timbre-related PMs, no doubt largely because their subjects were pianists and the piano timbre cannot normally be controlled independently of dynamic level. Sloboda and Clarke also describe substitutions such as these. They identify some SYVARs in different parameters of performance that project the same aspect of a metrical interpretation. See especially Clarke, "Generative Principles," 14; Sloboda, "The Communication of Musical Metre," 394; and Sloboda, "Expressive Skill in Two Pianists," 292.
77. GTTM, 25.
79. Again, the intensity data here can be a bit misleading. In all voices combined, 5.1 is louder than 3.1 by a margin of 0.8 dB, but this measure does not capture melodic accents.
80. GTTM, 347. See also Appendix 1.
81. Also note that this interpretation conflicts with the score-based interpretation offered by Lerdahl and Jackendoff (my Example 14), in which 20.1 and presumably 14.1 are considered weak beats. While my interpretation of Britten's recording is based mainly on phenomenal accents, Lerdahl and Jackendoff's interpretation of the score is based on the effect of the structural accents articulated by the arrival of dominant and tonic harmonies at mm. 16 and 20, respectively. Because of the relative obscurity of this hypermetrical level after m. 10, I would speculate that the choice between these two possible MSE interpretations for this recording of the piece will depend on whether the listener happens to be attending more closely to harmonic cues or to PMs. As explained in the passage from GTTM quoted above (paragraph 3.2), both phenomenal and structural accents can serve as cues for the construction of metrical accents. See also GTTM, 30-35.
82. Note that this MSE comes very close to the one mentioned by Lerdahl and Jackendoff. Marriner's first hyperbeat occurs a measure later than the one shown in Example 14, however, and a transformation at level H1 makes the MSE a two-beat rather than a three-beat hypermeasure at level H2.
83. GTTM, 63.
84. Palmer, "Mapping Musical Thought," refers to the principles summarized in Clarke, "Generative Principles," but neither adopts nor refutes Clarke's idea of considering GTTM an "input" to the generation of a performance. Note also that Palmer does not explore the pianists' hypermetric interpretation, so the relationship between her findings and my study is rather tangential. Nevertheless, Palmer clearly demonstrates a situation where the performer's conscious intentions have a marked effect on the perception of an ambiguous structure.
85. See Noam Chomsky, Aspects of the Theory of Syntax (Cambridge, Mass.: MIT Press, 1965), 4.
86. I should also mention that, although Lerdahl and Jackendoff attempt to transpose the "competence/performance" dichotomy directly to music and to address only competence in their theory, it should by now be clear that a sharp distinction between the terms of this dichotomy is somewhat unconvinving in the case of music (or, for that matter, any performing art). For example, musical competence includes, in addition to the factors addressed in GTTM, an understanding of performers' SYVARs, and conversely musical performance often involves the clarification of ambiguous musical structures. A full exploration of this problem, which goes much further than nomenclature, would, no doubt, require a separate article.
87. GTTM, 10; Lerdahl and Jackendoff, "Reply to Peel and Slawson," 147.
88. See especially Palmer, "Mapping Musical Thought"; William E. Frederickson and Christopher M. Johnson, "The Effect of Performer Use of Rubato on Listener Perception of Tension in Mozart," Psychomusicology 15 (1996): 78-86. Lerdahl's more recent work on pitch space, which is closely related to Prolongational Reduction, is widely discussed in Music Perception 13/3 (Spring 1996), a special issue on musical tension that includes much fodder for further performance-related research.
89. This appendix includes all the rules pertaining to MS in the Rules Index of GTTM. See GTTM, 347-48. Also included are the new preference rules and transformational rules that I am proposing, with paragraph references.
90. Lerdahl and Jackendoff claim that all their MS rules except MWFR3 and MWFR4 apply to all musical traditions. Note that I have made no such claims with regard to the performance-related rules, all of which I consider to be specific to the Western art-music tradition.
91. For example, José A. Bowen, "A Computer-Aided Study of Conducting," Computing in Musicology 9 (1993-94): 93-103.
92. For example, Peter Johnson, "Performance and the Listening Experience: Bach's 'Erbarme Dich,'" in Theory Into Practice: Composition, Performance, and the Listening Experience, ed. Nicholas Cook, Peter Johnson, and Hans Zender, 68-84 (Leuven, Belgium: Leuven University Press, 1999).
93. For example, Christopher M. Johnson, "The Performance of Mozart: A Study of Rhythmic Timing by Skilled Musicians," Psychomusicology 15 (1996), 90.
94. My methodology for analyzing expressive timing is based that of Bruno H. Repp. See his "A Microcosm of Musical Expression: I. Quantitative Analysis of Pianists' Timing in the Initial Measures of Chopin's Etude in E Major," Journal of the Acoustical Society of America 104/2, part 1 (August 1998), 1087.
95. Lipscomb and Hodges, "Hearing and Music Perception," 114.
96. Bruno H. Repp, "A Microcosm of Musical Expression: II. Quantitative Analysis of Pianists' Dynamics in the Initial Measures of Chopin's Etude in E Major," Journal of the Acoustical Society of America 105/3 (March 1999), 1974.
97. Caroline Palmer and Judith C. Brown, "Investigation in the Amplitude of Sounded Piano Tones," Journal of the Acoustical Society of America 90/1 (1991): 60-66.
98. My methodology is similar to Bruno Repp's, though perhaps less sophisticated. See Repp, "Microcosm of Musical Expression: II," 1973-74.
End of footnotes