My daughter has been playing piano for five years now, and she is definitely gifted in mathematics... but she isn't one of those people that I would say have a linked ability with the two. Well, maybe she is, actually. She definitely has a good ear and always has, starting playing in quite a focused way on any keyboard she could find at about 12-16 months old, etc.
She hates to practice (in either area) which is distinctly limiting in terms of her performance. But her "sight-reading" skills are phenomenally good, and that is something that, IMO, is a natural gift that one either has or doesn't. When she's "on" she can learn things in either area with pretty amazing speed... but as I said, 'drill/practice' is another matter.
In our extended families, we have four professional musicians. Only one of those people also exhibited mathematical gifts, though all of them are multi-instrumentalists, good theoreticians, etc. Only one of them (and not the same one) exhibited another realm of gifted ability, so far as I can tell. The other two are "merely" musically gifted, if that makes sense. Anecdote is of limited use, granted.
I suspect that the link isn't entirely causative. That is, I think it is possible to have one without the other, but the coincidence rate is high. Perhaps that is because there is a single underlying area of cognitive giftedness that contributes to prodigy in BOTH-- but is not sufficient for either. (If that makes sense.) That is if A + B + C, then musically gifted, and if A + C + D, then mathematically gifted... meaning that if a person has A + B + C + D, then that person has BOTH profiles.
If the person is 'missing' only B, then they might be tone deaf but mathematically brilliant, or something. If they only have A and B, then they might appear to be 'good' but not exceptional at either area. I'm guessing that the commonalities between the two areas (A and C in my example) are probably not unusual, which accounts for the observation that it seems to be statistically true that many individuals are gifted in BOTH areas. For the visual among us, this is the same as saying that this is a Venn diagram with a HUGE area of overlap in the middle.
Both abilities are extremely complex, cognitively. Assuming that only four factors contribute is likely a vast oversimplification.
Does it make sense to group musically gifted children with mathematically gifted ones? Well, probably not much more than it makes sense to group verbally gifted children with artistically gifted ones. Sure, there is more overlap within the two groups than with other manifestations of giftedness, but there are probably going to be plenty of examples of children that have high potential in one area but not the other.
