We investigate the idea that the languages of the world have developed coherent sound systems in which having one sound increases or decreases the chances of having certain other sounds, depending on shared properties of those sounds. We investigate the geometries of sound systems that are defined by the inherent properties of sounds. We document three typological tendencies in sound system geometries: economy, a tendency for the differences between sounds in a system to be definable on a relatively small number of independent dimensions; local symmetry, a tendency for sound systems to have relatively large numbers of pairs of sounds that differ only on one dimension; and global symmetry, a tendency for sound systems to be relatively balanced. The finding of economy corroborates previous results; the two symmetry properties have not been previously documented. We also investigate the relation between the typology of inventory geometries and the typology of individual sounds, showing that the frequency distribution with which individual sounds occur across languages works in favor of both local and global symmetry.
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