We address the problem of musical variation (identification of differe
nt musical sequences as variations) and its implications for mental re
presentations of music. According to reductionist theories, listeners
judge the structural importance of musical events while forming mental
representations. These judgments may result from the production of re
duced memory representations that retain only the musical gist. In a s
tudy of improvised music performance, pianists produced variations on
melodies. Analyses of the musical events retained across variations pr
ovided support for the reductionist account of structural importance.
A neural network trained to produce reduced memory representations for
the same melodies represented structurally important events more effi
ciently than others. Agreement among the musicians' improvisations, th
e network model, and music-theoretic predictions suggest that perceive
d constancy across musical variation is a natural result of a reductio
nist mechanism for producing memory representations.