The dominant theory of what people can learn implicitly is that they learn chunks of adjacent elements in sequences. A type of musical grammar that goes beyond specifying allowable chunks is provided by serialist or 12-tone music. The rules constitute operations over variables and could not be appreciated as such by a system that can only chunk elements together. A series of studies investigated the extent to which people could implicitly (or explicitly) learn the structures of serialist music. We found that people who had no background in atonal music did not learn the structures, but highly selected participants with an interest in atonal music could implicitly learn to detect melodies instantiating the structures. The results have implications for both theorists of implicit learning and composers who may wish to know which structures they put into a piece of music can be appreciated.