People often talk about musical pitch using spatial metaphors. In English, for instance, pitches can be "high" or "low" (i.e., height-pitch association), whereas in other languages, pitches are described as "thin" or "thick" (i.e., thickness-pitch association). According to results from psychophysical studies, metaphors in language can shape people’s nonlinguistic space-pitch representations. But does language establish mappings between space and pitch in the first place, or does it only modify preexisting associations? To find out, we tested 4-month-old Dutch infants’ sensitivity to height-pitch and thickness-pitch mappings using a preferential-looking paradigm. The infants looked significantly longer at cross-modally congruent stimuli for both space-pitch mappings, which indicates that infants are sensitive to these associations before language acquisition. The early presence of space-pitch mappings means that these associations do not originate from language. Instead, language builds on preexisting mappings, changing them gradually via competitive associative learning. Space-pitch mappings that are language-specific in adults develop from mappings that may be universal in infants.