1. The multimedia version of this essay requires a web browser enabled with the Shockwave plug-in and QuickTime resources. For Windows machines, a MIDI-compatible sound card is required for audio. With exception of Example 4, audio examples are MIDI files played by the author and converted to QuickTime movie format. Example 4 employs a Shockwave streaming audio sound clip of a professional ensemble. The download sites referenced in the multimedia version have links offering installation information and technical specifications for both Windows and Macintosh machines. Aspects of this study were presented at a joint session on "Computer Imaging for Music Theory and Musicology" at the National Conference of the American Musicological Society and the Society for Music Theory in Phoenix, 1997. For a study focused particularly on real-time simulations for musical analysis, see Timothy Koozin, "Graphic Approaches to Musical Analysis in a Multimedia Environment," Computers in Music Research 5 (1995): 103-117.
2. For a good introduction to the study of electronic text, see Stephen A. Bernhardt's "The Shape of Text to Come: The Texture of Print on Screens," College Composition and Communication 44/2 (May 1993): 151-175, which includes a helpful bibliography. See also "Sense and Semblance: The Implications of Virtuality" in Sven Birkerts, Readings (Saint Paul, MN: Graywolf Press, 1999), 42-58.
3. Web-based musical analyses incorporating multimedia include David Headlam's "Multimedia for Music Study on the Web: Director from Macromedia," which contains much helpful information on the use of Shockwave technology, and Ann K. McNamee's "Publishing and Pedagogy Using Multimedia on the World-Wide Web," both of which appear in Music Theory Online 3.5 (1997).
4. While developing the present study, the author was interested to note a number of messages posted to the mto-talk list addressing the topics of Schenkerian analysis and metaphor, in particular, the thoughtful postings from Nicolas Meeus (4 February 1998), Larry Solomon (19 June 1998), and Nicholas Cook (22 June 1998). For a broad assessment of research on metaphor, see Warren Shibles, Metaphor: An Annotated Bibliography and History (Whitewater, Wisconsin: Language Press, 1971).
5. Philip Wheelwright, "Semantics and Ontology" in Essays on Metaphor, Warren Shibles, ed. (Whitewater, Wisconsin: Language Press, 1972), 66-67.
8. Free Composition (Der freie Satz), translated and edited by Ernst Oster (New York: Longman, 1979), xxii. See also Nicholas Cook, "Schenker's Theory of Music as Ethics," Journal of Musicology 7 (1989): 438.
9. Important sources on the evolving rhetoric of Schenkerian analysis include William Rothstein, "The Americanization of Heinrich Schenker," In Theory Only 9/1 (1986): 5-17; William Pastille, "Heinrich Schenker, Anti-Organicist," 19th-Century Music 8/1 (1984): 29-36; Richard Littlefield and David Neumeyer, "Rewriting Schenker: Narrative-History-Ideology," Music Theory Spectrum 14/1 (1992): 38-65; Richard Cohn, "The Autonomy of Motives in Schenkerian Accounts of Tonal Music," Music Theory Spectrum 14/2 (1992): 150-170; Joseph Lubben, "Schenker the Progressive: Analytic Practice in Der Tonwille" Music Theory Spectrum 15/1 (1993): 59-75; Nicholas Cook, "Schenker's Theory of Music as Ethics"; and Felix Salzer's dialog with Joseph Straus in Unfoldings: Essays in Schenkerian Theory and Analysis. Carl Schachter, Joseph N. Straus, ed. (New York: Oxford University Press, 1999), 3-14.
10. Quoted from the Physics in Wheelwright, "Semantics and Ontology," 70.
11. Schenker, Free Composition, xxiii.
12. Schenker's important work with manuscript sources shows his great sensitivity to the visual impression of autographs, which, as he states in describing his impression of Chopin's autograph of the Op. 45 Scherzo, have the power to "speak directly to the eye and lead reliably to important insights." (From the preface to the Schenker edition of Chopin's Op. 101, as quoted in John Rothgeb, "Schenkerian theory and manuscript studies: modes of interaction" in Schenker Studies, Hedi Siegel, ed. (New York: Cambridge University Press, 1990), 5. See also William Rothstein, "Heinrich Schenker as an Interpreter of Beethoven's Piano Sonatas," 19th-Century Music 8/1 (1984): 3-27).
13. Schenker, Free Composition, xxiii, n. 1.
14. I am grateful to Timothy Jackson for help on this point. In his study, "Heinrich Schenker as Composition Teacher: the Schenker-Oppel Exchange" forthcoming in Music Analysis, he cites references to the creation of "Bilder" (pictures) in Schenker's so-called "Lesson Books" for 1929-31. The term also appears in later writings. For example, in Der Freie Satz Schenker writes, "Die von mir Urlinie-Tafeln benannten Bilder zeigen die vorletzte Stimmf�hrungsschicht, auf sie folgt der Vordergrund." Neue musickalische Theorien und Phantasien, Vol. III, Der Freie Satz, second ed., edited and revised by Oswald Jonas (Universal Edition, 1956), 58. Ernst Oster's translation in Free Composition appears on p. 26.
15. Christopher Collins, Reading the Written Image: Verbal Play, Interpretation, and the Roots of Iconophobia (Pennsylvania State University Press, 1991), 1. In contrast, see Felix Salzer's comments on the "self-sufficient and self-explaining" aspect of Schenker's approach in Heinrich Schenker, Five Graphic Analyses (Dover, 1969), 16-17.
16. See Amarnath Gupta, Simone Santini, and Ramesh Jain, "In Search of Information in Visual Media," Communications of the ACM 40/12 (1997): 35-62. The volume is devoted to visual information retrieval and includes several bibliographies.
17. See Schenker's comments on technology and culture in Free Composition, xxiii-xxiv, 6, and 160.
18. Allen Forte and Steven Gilbert. Introduction to Schenkerian Analysis (W. W. Norton, 1982), 20.
19. Wallace Berry, Musical Structure and Performance (Yale University Press, 1989), 29-30. Schenker's sketches of the entire theme appear in Free Composition, Fig. 42, 2 and Fig 138, 3. Many writers have discussed this passage, including Lerdahl and Jackendoff, William Benjamin, Allen Forte, Joel Lester, and Jonathan Kramer. For a summary, see Kramer, The Time of Music (Schirmer Books, 1988), 444-45, n. 74. The piece is also discussed in H. Lee Riggins and Gregory Proctor, "A Schenker Pedagogy," Journal of Music Theory Pedagogy 3/1 (1989): 13-21.
20. David Beach. "Schenker's Theories: A Pedagogical View" in Aspects of Schenkerian Theory (Yale Univ. Press, 1983), p. 7.
22. Peter Westergaard sets Schenker's three levels for the first waltz in Brahms' Op. 31 in "Geometries of Sound in Time," read as the keynote address of the 1994 Annual Meeting of the Society for Music Theory in Tallahassee, Florida, printed in Music Theory Spectrum 18/1 (1996): 20-21. See Felix-Eberhard von Cube's three-dimensional renderings in The Book of the Musical Artwork: An Interpretation of the Musical Theories of Heinrich Schenker. Trans. and ed., David Neumeyer, George R. Boyd, and Scott Harris (Lewiston, NY: Edwin Mellen Press, 1988), 226 and 275.
23. Friedrich Nietzsche. "On Truth and Falsity in their Extramoral Sense" in Essays on Metaphor, Warren Shibles, ed. (Whitewater, Wisconsin: The Language Press, 1972), p. 5, reprinted from The Complete Works of Friedrich Nietzsche, Vol. 2, trans. by M. A. Mugge (New York: Russell and Russel, 1964).
24. Nicholas Cook. Music, Imagination, and Culture (Oxford: Clarendon Press, 1990), p. 4.
25. Lawrence M. Zbikowski. "Metaphor and Music Theory: Reflections from Cognitive Science" Music Theory Online 4/1 (1998), part 2.2.