Conceptual Models and Cross-Domain Mapping: New Perspectives on Theories of Music and Hierarchy

structure of the VERTICALITY experiences, images, and perceptions. Our concept of verticality is based on this schema, and this concept is in turn the basis for the spatial orientation of up and down so crucial to conceptual models such as HEIGHT. The theory of image schemata is also fundamental to current explanations of what makes cross-domain mapping possible. As George Lakoff and Mark Turner have suggested in their writings on the Invariance Principle, 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 (Lakoff 1990, 1993; Turner 1990, 1993). These correspondences are not haphazard, but instead preserve the image-schematic structure latent in each domain. For instance, mapping the simple spatial relationship up-down onto the domain of emotions relies on our repeated experiences with what we ourselves feel and what we observe in others: buoyancy (up) when exhilarated (she walked with a spring in her step; I was floating on air); deflation (down) when depressed (he walked as though he carried the weight of the world on his shoulders). Mapping up-down onto the domain of emotions preserves the image-schematic structure of the physical states we associate with emotions, and imports the spatial orientation of the underlying VERTICALITY schema in order to provide a coherent account of these states. We also map up-down onto the domain of musical pitch: we typically speak of high notes and low notes. We needn't look far to find a correspondence of up-down in our experience of musical pitch: when we make low sounds, our chest resonates; when we make high sounds,