Actually, there is a correlation! They did a study on this.
The article talks about music and personality, and it suggests that people who like complex music (opera, jazz, etc.) are likely to be more intelligent than people who like simple music (country, sound track, etc.). Here is the excerpt:
Music preferences also appear to be influenced by cognitive ability. The relationship between cognitive ability and music preferences is consistent with the idea that people prefer music that provides optimal levels of stimulation. Berlyne (1971, 1974) hypothesized that individuals prefer aesthetic stimuli that produce moderate amounts of stimulation to objects that produce too much or too little stimulation. Previous research on aesthetic preferences in literature and visual arts has supported this notion, and this suggests that individual differences in cognitive complexity moderate preferences for particular aesthetic stimuli. Whereas cognitively complex individuals tend to prefer complex aesthetic stim- uli, less cognitively complex individuals tend to prefer simple aesthetic stimuli (Barron, 1955; Frances, 1976; Kammann, 1966). The relationship between intelligence and preference for complex music supports this previous work and suggests that the optimal level of stimulation for highly intelligent individuals is produced by complex music whereas the optimal level of stimulation for less intelligent individuals is produced by comparatively simpler music.
http://homepage.psy.utexas.edu/homepage/faculty/gosling/reprints/JPSP03musicdimensions.pdf
You don't have to read the article, it's kinda long. I just wanted to point out the important part.
