We examined the influence of incidental exposure to varied metrical patterns from different musical cultures on the perception of complex metrical structures from an unfamiliar musical culture. Adults who were familiar with Western music only (i.e., simple meters) and those who also had limited familiarity with non-Western music were tested on their perception of metrical organization in unfamiliar (Turkish) music with simple and complex meters. Adults who were familiar with Western music detected meter-violating changes in Turkish music with simple meter but not in Turkish music with complex meter. Adults with some exposure to non-Western music that was unmetered or metrically complex detected meter-violating changes in Turkish music with both simple and complex meters, but they performed better on patterns with a simple meter. The implication is that familiarity with varied metrical structures, including those with a non-isochronous tactus, enhances sensitivity to the metrical organization of unfamiliar music.