I hope you're not implying that there is any doubt that the greatest composers were in fact geniuses, and I further hope you don't believe that high IQ, or "general intelligence", is the only representation of genius. There are probably quite a few people on these boards who have a higher conventional IQ than Beethoven did. This does not change the fact that Beethoven's creative achievements are far more impressive than those of anyone here. People with high IQs are common; immortal creative powers are not.
I agree, but I imagine that in fact the greatest composers did in fact also have superior overall intellects. There is no way to test IQ retrospectively of course, but we have Mozart, who could write operas in two different languages, Bach, who inscribed his musical dedications in any of four languages (without ever leaving Germany) and actually taught Latin as one of his duties at Leipzig, and Beethoven, who conversed with Goethe as an equal. None of these of course is a conclusive sign of anything, but these and the other greats were hardly men of oen-track minds or limited dimensions.
I have to say that we have run into a matter of semantics here. The club Mensa defines genius based precisely on certain criteria usually associated with IQ. I don't belong, but one of our esteemed posters does. Apparently there are, for instance, prisoners serving sentences in Mensa. On the other hand, if we narrow the definition to the accomplishment of someone on the level of Beethoven, Michelangelo, and Shakespeare then in a way it is equally meaningless, because there simply aren not enough of such people to need a separate word for them, unless it is demigods, tians, or something like that.
Somewhere in between these two extremes is a substantial group of people who would score well on an IQ test (if they have not actually done so) but also shown some spark of accomplishment or brilliance that most even very intelligent people never manage. That includes, as I have implied before, a lot of the second string of composers, but it also includes a lot of peope in every field that nobody but a specialist has ever heard of.