1. The discussion began with Larry Solomon's posting of May 19, 1997, and can be retrieved through the SMT discussion archive at ftp://societymusictheory.org/pub//smt-talk/.

2. Roger Scruton, "Understanding Music," Ratio 25, no. 2 (1983): 106.

3. Scruton, "Understanding Music," 107.

4. Nicholas Cook, Music, Imagination, and Culture (Oxford: Clarendon Press, 1990), 4.

5. Cook, Music, Imagination, and Culture, 4.

6. See, for instance, Cynthia Grund, "Metaphors, Counterfactuals and Music," in Essays on the Philosophy of Music, edited by Veikko Rantala, Lewis Rowell, and Eero Tarasti, Acta philosophica Fennica, vol. 43 (Helsinki: Philosophical Society of Finland, 1988), 28-53; and Daniel Charles, "Music and Antimetaphor (to Eero Tarasti)," in Musical Signification: Essays in the Semiotic Theory and Analysis of Music, edited by Eero Tarasti, Approaches to Semiotics, vol. 121 (Berlin: Mouton de Gruyter, 1995), 27-42.

7. See, for instance, Marion A. Guck, "Two Types of Metaphoric Transfer," in Metaphor: A Musical Dimension, edited by Jamie C. Kassler, reprint, 1991, Musicology, vol. 15 (Basel: Gordon and Breach, 1994), 1-12; and Robert S. Hatten, "Metaphor in Music," in Musical Signification: Essays in the Semiotic Theory and Analysis of Music, edited by Eero Tarasti, Approaches to Semiotics, vol. 121 (Berlin: Mouton de Gruyter, 1995), 373-91.

8. George Lakoff and Mark Johnson, Metaphors We Live By (Chicago: University of Chicago Press, 1980).

9. For a review of the empirical evidence supporting metaphor as a basic cognitive process see Raymond W. Gibbs, Jr., The Poetics of Mind: Figurative Thought, Language, and Understanding (Cambridge: Cambridge University Press, 1994). For discussion of the link between the study of metaphor as a cognitive process and the central concerns of cognitive linguistics see George Lakoff, "The Invariance Hypothesis: Is Abstract Reason Based on Image-Schemas?" Cognitive Linguistics 1, no. 1 (1990): 39-74.

10. The conceptual metaphor STATE OF BEING IS ORIENTATION IN VERTICAL SPACE is a variant of the STATES ARE LOCATIONS conceptual metaphor discussed by George Lakoff and Mark Turner in More Than Cool Reason: A Field Guide to Poetic Metaphor (Chicago: University of Chicago Press, 1989). On cross-domain mapping as a general phenomenon see Lakoff and Turner, More Than Cool Reason, 4; George Lakoff, "The Contemporary Theory of Metaphor," in Metaphor and Thought, 2d ed., edited by Andrew Ortony (Cambridge: Cambridge University Press, 1993), 202-51; Gibbs, The Poetics of Mind; and Gilles Fauconnier, Mappings in Thought and Language (Cambridge: Cambridge University Press, 1997). For a fine essay that anticipates a good portion of the theoretical perspective on cross-domain mapping I outline here, see Marianne Kielian- Gilbert, "Interpreting Musical Analogy: From Rhetorical Device to Perceptual Process," Music Perception 8, no. 1 (Fall 1990): 63-94.

11. The conceptual metaphor MUSIC IS A LANGUAGE structures much of our discourse about music, and often plays a part in semiotic analyses of music (inasmuch as the attribution of linguistic tropes to musical events is oftentimes dependent on this metaphor). For an intriguing analytical essay that uses the MUSIC IS A LANGUAGE metaphor as a point of departure, see Justin London, "Musical and Linguistic Speech Acts," Journal of Aesthetics and Art Criticism 54, no. 1 (Winter 1996): 49-64.

12. On the matter of the characterization of pitch by Greek music theorists of antiquity see Andrew Barker (ed.), Greek Musical Writings, Volume II: Harmonic and Acoustic Theory (Cambridge: Cambridge University Press, 1989), n. 43, p. 134. For information about the characterization of pitch in Bali and Java I am indebted to Benjamin Brinner, personal communication. Regarding the characterization of musical pitch by the Suyá, see Anthony Seeger, Why Suyá Sing: A Musical Anthropology of an Amazonian People (Cambridge: Cambridge University Press, 1987).

13. Mark Johnson, The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason (Chicago: University of Chicago Press, 1987).

14. Johnson, The Body in the Mind, 2. It should be noted that, for the most part, the image schema remains a theoretical construct. Nonetheless, two independent lines of research have leant credence to the notion: Raymond W. Gibbs Jr. and Herbert L. Colston provide a review of evidence for image schemata drawn from a wide variety of psychological studies in "The Cognitive Psychological Reality of Image Schemas and Their Transformations," Cognitive Linguistics 6, no. 4 (1995): 347-78; Gerald Edelman discusses connections between image-schema theory and research in neuroscience in The Remembered Present: A Biological Theory of Consciousness (New York: Basic Books, 1989), chapter 8.

15. It is also important to note that image schemata do not simply reduce to gestures, nor gestures to image schemata. For a discussion, see David McNeill, Hand and Mind: What Gestures Reveal About Thought (Chicago: University of Chicago Press, 1992), 263-64.

16. Mark Turner, "Aspects of the Invariance Hypothesis," Cognitive Linguistics 1, no. 2 (1990): 254; emphasis as in original. For additional writings on the Invariance Principle (which at first was called the Invariance Hypothesis) see Lakoff, "The Contemporary Theory of Metaphor"; Lakoff, "The Invariance Hypothesis"; Mark Turner, "An Image-Schematic Constraint on Metaphor," in Conceptualizations and Mental Processing in Language, edited by Richard A. Geiger and Brygida Rudzka-Ostyn, Cognitive Linguistics Research, vol. 3 (Berlin: Mouton de Gruyter, 1993), 291-306; and Mark Turner, The Literary Mind (New York: Oxford University Press, 1996), chapter 3.

A preliminary discussion of a similar sort of topographical invariance, with applications to music, can be found in Peter Gärdenfors, "Semantics, Conceptual Spaces and the Dimensions of Music," in Essays on the Philosophy of Music, edited by Veikko Rantala, Lewis Rowell, and Eero Tarasti, Acta philosophica Fennica, vol. 43 (Helsinki: Philosophical Society of Finland, 1988), 9-27.

17. A particularly interesting example of how a culture organizes their understanding of pitch relationships (and one which builds on Lakoff and Johnson's early work) is provided by Steven Feld's discussion of music theory among the Kaluli of Papua New Guinea. See Feld, "Flow Like a Waterfall: The Metaphors of Kaluli Musical Theory," Yearbook for Traditional Music 13 (1981): 22-47.

18. For additional discussion of idealized cognitive models and their relationship to cultural knowledge see Gilles Fauconnier, Mental Spaces: Aspects of Meaning Construction in Natural Language, 2d ed., with a foreword by George Lakoff and Eve Sweetser, reprint, 1985 (Cambridge: Cambridge University Press, 1994), chapter 1; George Lakoff, Women, Fire, and Dangerous Things: What Categories Reveal About the Mind (Chicago: University of Chicago Press, 1987), part I; Naomi Quinn and Dorothy Holland, "Culture and Cognition," in Cultural Models in Language and Thought, edited by Dorothy Holland and Naomi Quinn (Cambridge: Cambridge University Press, 1987), 3-40; Gibbs, The Poetics of Mind, chapter 4; and Bradd Shore, Culture in Mind: Cognition, Culture, and the Problem of Meaning (New York: Oxford University Press, 1996), chapter 13.

19. I have, however, discussed such knowledge structures elsewhere. See Lawrence Zbikowski, Large-Scale Rhythm and Systems of Grouping, Ph.D. Diss. (Yale University, 1991), chapter 4; and Lawrence Zbikowski, "Charles Seeger's Unitary Field Theory for Musicology and Recent Theories of Linguistic and Cognitive Structure," in Foundations of Modern Musicology: Understanding Charles Seeger, edited by Bell Yung and Helen Rees, forthcoming.

20. Heinrich Schenker, Der freie Satz, 2d ed., edited by Oswald Jonas, Neue musikalische Theorien und Phantasien, vol. 3 (Vienna: Universal Edition, 1956); English translation from Heinrich Schenker, Free Composition (Der Freie Satz), edited and translated by Ernst Oster, New musical theories and fantasies, vol. 3 (New York: Schirmer Books, 1979). I have used the 1956 edition of Der freie Satz on account of its general availability. I have used Oster's 1979 translation for similar reasons, and also because it invokes a debate about translation that may be profitably viewed through the lens of cross-domain mapping. For one viewpoint on this debate see Robert Snarrenberg, "Competing Myths: The American Abandonment of Schenker's Organicism," in Theory, Analysis and Meaning in Music, edited by Anthony Pople (Cambridge: Cambridge University Press, 1994), 29-56. My thanks to Janna Saslaw for bringing the different uses of Spannung in Der freie Satz to my attention.

For a brief discussion of a similar contrast between meanings of Spannung in the first volume of Das Meisterwerk in der Musik see Robert Snarrenberg, Schenker's Interpretive Practice, Cambridge Studies in Music Theory and Analysis, vol. 11 (Cambridge: Cambridge University Press, 1997), 93-94.

21. Janna K. Saslaw, "Forces, Containers, and Paths: The Role of Body-Derived Image Schemas in the Conceptualization of Music," Journal of Music Theory 40, no. 2 (Fall 1996): 217-43.

22. Janna K. Saslaw, "Life Forces: Conceptual Structures in Schenker's Free Composition and Schoenberg's The Musical Idea" (Under review).

23. Lawrence Zbikowski, "Conceptual Models and Cross-Domain Mapping: New Perspectives on Theories of Music and Hierarchy," Journal of Music Theory 41, no. 2 (1997).

24. Most of us find descent--especially scalar descent--well represented by the thought of walking down a staircase, but I think it could be argued that walking down a hillside works as well. The reason is that it isn't so much the neat, two-dimensional image of stairs that is operative but the regular transfer of weight from one leg to another. Indirect evidence is provided by a striking anecdote related by John Hockenberry, from a time when he was a reporter for National Public Radio. In order to get to a group of Kurdish refugees on a remote edge of Iraqi Kurdistan during the aftermath of the Gulf War, Hockenberry, a paraplegic since 1976, had to temporarily abandon his wheelchair and get a ride on a donkey. He comments on the effect of becoming reacquainted with a non-wheeled mode of transportation through the rhythm of the donkey's gait: "It was walking, that feeling of groping and climbing and floating on stilts that I had not felt for fifteen years. I had long ago grown to love my own wheels and their special physical grace, and so this clumsy leg walk was not something I missed until the sensation came rushing back through my body from the shoulders of a donkey." John Hockenberry, Moving Violations: War Zones, Wheelchairs, and Declarations of Independence (New York: Hyperion, 1995), 2-3.

25. Ray Jackendoff, Consciousness and the Computational Mind (Cambridge, Mass.: MIT Press, 1987), 238.

26. Zoltán Kövecses, Emotion concepts (New York: Springer-Verlag, 1990).

27. Gibbs, The Poetics of Mind, chapter 7.

28. For work on conceptual blending and conceptual integration see Mark Turner and Gilles Fauconnier, "Conceptual Integration and Formal Expression," Metaphor and Symbolic Activity 10, no. 3 (1995): 183-204; Gilles Fauconnier and Mark Turner, "Conceptual Integration Networks," Cognitive Science (1996); Fauconnier, Mappings in Thought and Language, chapter 6; and Turner, The Literary Mind, chapters 5 and 6.

29. Lawrence Zbikowski, "Conceptual Blending and Song," unpublished paper (1997). Conceptual blending can also be used to account for relationships between instrumental works, text, and images, such as those outlined in Kielian-Gilbert's analysis of Erik Satie's "Le Water-chute" in "Interpreting Musical Analogy," 90-91.

End of Footnotes