MITJANS DE COMUNICACIÓ I IDENTITAT

Correlating musical pitches with vertically or iented, two-dimensional space, for instance, leads quite naturally to an imag inary world in which pitches become things that move through space: the successive notes of a scale g radually descend and ascend; in other passages, some notes leap, while still others fall. Within this imaginary world, each traversal of space has a specific and unmistakable sound — that is, descent sounds one way, ascent another. And this is not something limited to text painting of the sort demonstrated by Palestrina, as any number of cartoon soundtracks confir m. Never mind that actual traversals of space sound nothing like those of the hyperkinetic Roadrunner or the hapless Wile E. Coyote; if the cor re-lation between the domains is properly established, elements from each will blend together to create novel relationships and elements. In the second section that fol-lows, I descr ibe the process that leads to this sor t of blending and show the role con-ceptual blending plays in text painting and program music.

an introduction to cross-domain mapping

Cross-Domain Mapping and Metaphor

The theory of cross-domain mapping is a product of a generalized approach to lin-guistic metaphor fir st taken by George Lakoff and Mark Johnson in 1980. Perhaps the most common conception of metaphor is of a literary device, a manifestation of the figural use of language to create colorful if imprecise images. Lakoff and John-son accumulated a substantial body of evidence demonstrating that metaphor was not simply a manifestation of literar y creativity but was, in fact, pervasive in every-day discourse.² As an example, consider the way up and down are used to character-ize emotions, consciousness, and health:

emotions

I’m feeling up. My spir its rose. I’m feeling down. I fell into a depression. My spir-its sank.

consciousne ss

Get up. I’m up already. He rises early in the mor ning. He fell asleep.

health

He’s at the peak of health. She’s in top shape. He came down with the flu.

Each character ization suggests not a literal representation of the spatial domain implied by the or ientation up–down but, instead, uses our knowledge of physical space to structure our understanding of emotions, consciousness, or health.

Based on evidence provided by a large number of similar examples of the

2. George Lakoff and Mark Johnson, Metaphors We Live By (Chicago: University of Chicago Press, 1980). Their work has recently been extended in Lakoff and Johnson, Philosophy in the Flesh: The Embod-ied Mind and Its Challenge to Western Thought (New York: Basic Books, 1999).

appearance of metaphor ical constr uctions in everyday discourse, Lakoff and John-son proposed that metaphor was a basic str ucture of understanding through which we conceptualize one domain (the target domain, which is typically unf amiliar or abstract) in ter ms of another (the source domain, which is most often f amiliar and concrete). Further study has provided a wealth of empirical evidence for this pro-posal and contr ibuted to the development of the field of cognitive linguistics.³

Fundamental to the theor y of metaphor that sprang from Lakoff and Johnson’s work is a distinction between conceptual metaphors and linguistic metaphor s. A conceptual metaphor is a cognitive mapping between two different domains; a lin-guistic metaphor is an expression of such a mapping through language. For instance, the conceptual metaphor state of being is orientation in vertical space maps relationships in physical space onto mental and physical states.⁴ The cross-domain mapping wrought by this conceptual metaphor then g ives rise to innumerable lin-guistic expressions. Some of these expressions are commonplace, such as “Maxwell seems a bit down today.” Others summon a r ich imagistic world, such as that of John Keats’s “Ode to a Nightingale”:

My heart aches, and a drowsy numbness pains My sense, as though of hemlock I had dr unk, Or emptied some dull opiate to the drains

One minute past, and Lethe-wards had sunk.

Here the descent to the mythical r iver gives a physical cor relate to the narcotic state of the nar rator: the act of sinking is mapped onto a melancholy emotional state.

Thus the same conceptual metaphor (state of being is orientation in vertical space) is behind both linguistic metaphor s, one commonplace (“Maxwell seems a bit down today”), the other poetic.

With respect to music, the “high” and “low” used to descr ibe pitches reflect the conceptual metaphor pitch relationships are relationships in vertical space.

This metaphor maps spatial or ientations such as up–down onto the pitch contin-uum. The mapping yields a system of metaphors replete with possibilities for describing musical pitch. We can speak in ter ms of pitch contour (meaning succes-sions of pitches, which are located at different places in pitch-space), gesture

(mean-3. For a review of the empir ical evidence suppor ting metaphor as a basic cognitive process, see Ray-mond 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 cog-nitive process and the central concer ns of cogcog-nitive linguistics, see George Lakoff, “The Invariance Hypothesis: Is Abstract Reason Based on Image-Schemas?” Cognitive Linguistics 1 (1990): 39 – 51.

4. By convention, conceptual metaphors are represented in capital letter s. Thus love is a journey designates a conceptual metaphor of general application, and “Love is a journey” a specific linguistic expression based on that metaphor.

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 Contemporar y Theory of Metaphor,” in Metaphor and Thought, 2nd ed., ed. Andrew Ortony (Cambridge: Cambridge University Press, 1993), 202 – 51; Gibbs, The Poetics of Mind; and Gilles Faucon-nier, Mappings in Thought and Language (Cambridge: Cambridge University Press, 1997).

c ro s s - doma i n map p i ng 67 ing successions of pitches with a specific directionality and contour), and musical space (meaning a three- or four-dimensional extension of the basic two-dimen-sional mapping).⁵ This system is g iven graphic representation in traditional musi-cal notation: notes that are the result of more rapid vibrations of the sounding medium are placed higher on the page than notes that result from less rapid vibra-tions (with the exception of sharps and flats). The two-dimensional space of the musical page thus cor relates with the spatial or ientation ascr ibed to pitch.⁶ The systematic quality that results from mapping spatial or ientations onto the pitch continuum thus leads to an entire vocabulary for descr ibing relationships among pitches that provides a r ich set of possibilities for fur thering our conceptualization of music.

As common as conceiving of pitches as “high” or “low” seems, not all cultures describe pitch relationships in purely spatial ter ms. As I noted here, Greek theor ists of antiquity used oxys (“sharp” or “pointed”) and barys (“heavy”) to character ize pitches. And traversing histor ical distance is not the only way to discover alter native conceptualizations of pitch relations. Consider three examples in which it is culture, rather than time, that creates distance:

1. Steven Feld’s research has shown that the Kaluli of Papua New Guinea describe melodic inter vals with the same ter ms they use to character ize features of waterfalls. For instance, in Kaluli sa means “waterfall,” and a mogan is a still or lightly swirling waterpool; sa-mogan is the flow of a water-fall into a level waterpool beneath it. Sa-mogan is also used to descr ibe a melodic line that descends to a repeated note, the contour of which repli-cates that of a waterfall flowing into a pool. In contrast, there are no specific names for ascending inter vals, which nonetheless do occur in Kaluli song.⁷ Behind this account of musical inter vals is the conceptual metaphor pitch relationships are waterfall characteristics, which provides the basis for a r ich set of descriptive terms that capture some aspects of melody but not other s.

2. In Bali and Java pitches are conceived not as “high” and “low” but as

“small” and “large.”⁸ Here the conceptual metaphor is pitch relation-ships are relationrelation-ships of physical size, a mapping that accurately

5. For further discussion of mappings between the spatial and pitch domains, see Arnie Walter Cox,

“The Metaphor ic Logic of Musical Motion and Space” (Ph.D. diss., University of Oregon, 1999).

6. It is worth noting that the spatial domain of the musical page is itself metaphor ical, since the way the page is or iented in physical space — that is, whether it is propped on a music stand or lying flat on a table, turned right side up or upside down — does not change what we regard as the top and bottom of the page. Two factors, each independent of the actual or ientation of the page in physical space, help establish the spatial domain of the page: the conventional or ientation of the symbols on the page (either

“rightside up” or “upside down”) and the relative distance of the symbols on the page from the reader.

Rightside up symbols that are farthest from the reader are at the “top” of the page; rightside up sym-bols that are nearest the reader are at the “bottom” of the page.

7. Steven Feld, “Flow Like a Waterfall: The Metaphors of Kaluli Musical Theor y,” Yearbook for Tra-ditional Music 13 (1981): 30 – 31.

8. Personal communication from Benjamin Br inner, 8 July 1997. See also Wim van Zanten, “The Tone Mater ial of the Kacapi in Tembang Sunda in West Java,” Ethnomusicology 30 (1986): 85.

reflects the nor ms of acoustic production: small things typically vibrate more rapidly than large things. This acoustic f act is represented through-out the numerous parts of the gamelan, the collection of instruments cen-tral to the musical practice of Bali and Java.

3. The Suyá of the Amazon basin do not have an extensive vocabulary for describing pitch relationships. When they are descr ibed, however, it is in terms of age: pitches are conceived not as “high” and “low” but as “young”

and “old.” The conceptual metaphor that guides this mapping is pitch relationships are age relationships, which accurately reflects the Suyá’s beliefs that the pitch of the voice becomes deeper with age.⁹

With each of these conceptions of pitch relationships it is easy to focus on what they lack rather than what they offer. That is, it is natural (if not quite excusable) to reckon difference in somewhat chauvinistic ter ms: that the Kaluli do not have terms to describe ascending inter vals, where we do; that the way pitch relationships are charac-terized in Bali and Java does not transfer into g raphic representations with the same ease as do “high” and “low.” It has to be remembered, however, that mapping “high”

and “low” onto music has its own limitations: “high” and “low” cannot reflect the sub-tle play of flowing water, nor do they provide much of an explanation for how acoustic features cor relate with pitch relationships. Such differences show that each mapping between domains makes some conceptualizations possible, while it disables others.

Image Schema Theor y

The variety of conceptual metaphor s used to character ize pitch relations leads to the question of the ultimate g rounding of the process of cross-domain mapping.

Even if we grant that we understand a target domain (such as pitch relationships) in ter ms of a source domain (such as or ientation in vertical space), how is it that we understand the source domain in the fir st place? Mark Johnson answered this ques-tion by proposing that meaning was grounded in repeated patter ns of bodily expe-rience.¹⁰ These patter ns give rise to what Johnson called image schemata, which pro-vide the basis for the concepts and relationships essential to metaphor. An image schema is a dynamic cognitive construct that functions somewhat like the abstract structure of an image and thereby connects together a vast range of different expe-riences that manifest this same recurring structure.¹¹ Image schemata are by no means exclusively visual — the idea of an image is simply a way of captur ing the organization infer red from patter ns in behavior and concept for mation.

As one example of an image schema, consider the verticality schema, which might be summar ized by a diagram of the sort given in figure 2.1.We grasp this struc-ture repeatedly in thousands of perceptions and activities that we exper ience every day. Typical of these are the exper iences of perceiving a tree, our felt sense of stand-ing upr ight, the activity of climbstand-ing stair s, formstand-ing a mental image of a flagpole, and

9. Anthony Seeger, Why Suyá Sing: A Musical Anthropology of an Amazonian People (Cambridge:

Cambridge University Press, 1987), 100 – 02.

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

11. Johnson, The Body in the Mind, 2.

c ro s s - doma i n map p i ng 69

figure 2.1 Diagram of the ve rticality schema

watching the level of water r ise in the bathtub. The verticality schema is the abstract structure of the verticality experiences, images, and perceptions. Our concept of verticality is based on this schema, and this concept is in tur n invoked by the various conceptual metaphors that use vertical space as a source domain through which to structure such target domains as emotions, consciousness, health, and musical pitch.

By definition, image schemata are preconceptual: they are not concepts, but they provide the fundamental str ucture upon which concepts are based. In consequence, it is important to emphasize that any diagram used to illustrate an image schema is intended to represent the key structural features and inter nal relations of the schema; it is not meant to summon a r ich image or mental picture that we some-how have “in mind” and use actively to structure our thought. More directly, what-ever actually occupies our thoughts is not, by definition, an image schema. We can conceive of image schemata, just as we can conceive of any of a number of non-conceptual or prenon-conceptual cognitive processes. We can also note general patter ns in the way concepts are structured, which can be attr ibuted to image schemata.

However, there are, by definition, no “image-schema concepts.”

The relationship between the verticality schema and our character ization of musical pitch with reference to the spatial or ientation up–down is fairly immediate:

when we make low sounds, our chest resonates; when we make high sounds, our chest no longer resonates in the same way, and the source of the sound seems located nearer our head. The “up” and “down” of musical pitch thus cor relate with the spatial “up” and “down”— the vertical or ientation — of our bodies. The verti-cality schema offers a straightforward way to explain why we character ize musi-cal pitch in ter ms of high and low even when the actual spatial or ientation of the means through which we produce pitches either does not reinforce the character-ization or r uns directly counter to it.

At present, the image schema remains largely a theoretical constr uct.Work across a variety of fields, however, has made strong arguments for the impor tance of such a construct, including that by Leonard Talmy in linguistics, Gerald Edelman in neu-roscience, David McNeill in psychology, and Raymond W. Gibbs Jr. and Herbert L.

Colston in psycholinguistics.¹² Recently, Lawrence Barsalou and his associates have

12. Leonard Talmy, Concept Structuring Systems (vol. 1 of Toward a Cognitive Semantics) (Cambr idge, Mass.: MIT Press, 2000), 409 – 70; Gerald M. Edelman, The Remembered Present: A Biological Theory of Con-sciousness (New York: Basic Books, 1989), chap. 8; David McNeill, Hand and Mind: What Gestures Reveal about Thought (Chicago: University of Chicago Press, 1992); Raymond W. Gibbs, Jr., and Herbert L. Col-ston, “The Cognitive Psychological Reality of Image Schemas and Their Transformations,” Cognitive Linguistics 6 (1995): 347 – 78.

developed a comprehensive theory of mental representation based on perceptual symbols (which are analogical structures similar to image schemata) and have begun to provide empir ical work to support the theor y.¹³ Antonio Damasio, working from a neurophysiological perspective, has made compelling arguments for the impor-tance of the body to consciousness and thought.¹⁴ Although research on image schemata and similar str uctures is still preliminary, it is also highly promising and offers some of the best prospects for solving some of the problems of the relation-ship between mind and body that have dogged cognitive research throughout this centur y.

The Invariance Pr inciple

The theory of image schemata provides a way to explain how conceptual meta-phors are grounded. It does not, by itself, explain why some conceptual metaphor s seem intuitively better than other s. For instance, the conceptual metaphor pitches are fruit could provide the grounding for such expressions as “You must play the first note more like an apple, the second more like a banana.” Although such map-pings are possible, they are certainly not common. Pitches and fr uits just do not seem to be a good match.

To account for why some metaphor ical mappings are more effective than oth-ers, George Lakoff and Mark Turner proposed that such mappings are not about the imposition of the structure of the source domain on the target domain, but are instead about the establishment of correspondences between the two domains.

These cor respondences are not haphazard, but instead preserve the image-schematic structure latent in each domain. Lakoff and Turner for malized this perspective with the Invariance Pr inciple, which Turner states as follows: “In metaphor ic mapping, for those components of the source and target domains deter mined to be involved in the mapping, preserve the image-schematic str ucture of the target, and import as much image-schematic str ucture from the source as is consistent with that preser-vation.”¹⁵ According to the Invariance Pr inciple, mapping the spatial or ientation

13. Lawrence W. Barsalou,Wenchi Yeh, Barbara J. Luka, Karen L. Olseth, Kelly S. Mix, and Ling-Ling Wu, “Concepts and Meaning,” in Chicago Linguistics Society 29: Papers from the Parasession on the Corre-spondence of Conceptual, Semantic, and Grammatical Representations, ed. Kathar ine Beals, Gina Cooke, David Kathman, Sotaro Kita, Karl-Er ik McCullough, and David Testen (Chicago: University of Chicago, Chicago Linguistics Society, 1993), 23 – 61; Lawrence W. Barsalou, Karen Olseth Solomon, and Ling-Ling Wu, “Perceptual Simulation in Conceptual Tasks,” in Cultural, Psychological, and Typological Issues in Cog-nitive Linguistics: Selected Papers of the Bi-Annual ICLA Meeting in Albuquerque, July 1995, ed. Masako K.

Hiraga, Chris Sinha, and Sher man Wilcox (Amsterdam: John Benjamins, 1999), 209 – 28; Lawrence W.

Barsalou, “Perceptual Symbol Systems,” Behavioral and Brain Sciences 22 (1999): 577 – 609.

14. Antonio R. Damasio, The Feeling of What Happens: Body and Emotion in the Making of Conscious-ness (New York: Harcourt Brace, 1999), chaps. 5 and 6.

15. Mark Turner, “Aspects of the Invariance Hypothesis,” Cognitive Linguistics 1 (1990): 254. For additional wr itings on the Invariance Pr inciple (which at fir st was called the Invariance Hypothesis), see Lakoff, “The Invariance Hypothesis”; Mark Turner, “An Image-Schematic Constraint on Metaphor,” in Conceptualizations and Mental Processing in Language, ed. Richard A. Geiger and Brygida Rudzka-Ostyn,

15. Mark Turner, “Aspects of the Invariance Hypothesis,” Cognitive Linguistics 1 (1990): 254. For additional wr itings on the Invariance Pr inciple (which at fir st was called the Invariance Hypothesis), see Lakoff, “The Invariance Hypothesis”; Mark Turner, “An Image-Schematic Constraint on Metaphor,” in Conceptualizations and Mental Processing in Language, ed. Richard A. Geiger and Brygida Rudzka-Ostyn,