We represent music as sets of points or sets of
horizontal line segments in the Euclidean plane. Via this geometric
representation we cast transposition invariant content-based music retrieval
problems as ones of matching sets of points or sets of horizontal line
segments in plane under translations.  For finding the
exact occurrences of a point set (the query pattern) of size $m$
within another point set (representing the database) of size $n$,
we give an algorithm with running time $O(mn)$, and for finding partial occurrences
another algorithm with running time $O(mn\log m)$. We also use the total length of the
overlap between the line segments of a translated query and a database (i.e., the shared
time) as a quality measure of an occurrence and present an $O(n\log n + mn\log m)$
algorithm for finding translations giving the largest possible overlap.