Yes, certain aspects of musical genius are intrinsic, but without a nurturing environment, a potential virtuoso cannot rise to the top
How do you get to Carnegie Hall? The psychology professors David Z. Hambrick and Elizabeth J. Meinz have a novel partial answer in the New York Times: a superior ability to memorize random information.
Not surprisingly, there was a strong positive correlation between practice habits and sight-reading performance. In fact, the total amount of practice the pianists had accumulated in their piano careers accounted for nearly half of the performance differences across participants. But working memory capacity made a statistically significant contribution as well (about seven percent, a medium-size effect). In other words, if you took two pianists with the same amount of practice, but different levels of working memory capacity, it's likely that the one higher in working memory capacity would have performed considerably better on the sight-reading task.
But do these results really refute the research of psychologists of expertise like K. Anders Ericsson and of academics like Richard Sennett and writers like Malcolm Gladwell, David Brooks, and David Shenk, who have used Ericsson's and other findings against innatists and hereditarians?
Mostly no. It is interesting that the 99.9th percentile achieve significantly more than the mere 99.1 percentile in academic degrees and publications. But whatever special gifts the very top bracket has are not necessarily the main reasons for their success. Young people who are recognized earlier get more attention and encouragement, and it's well known that a false high IQ score can become a self-fulfilling prophecy in the classroom, the famous Pygmalion Effect. (The Economist has an excellent discussion of another paradox of intelligence, the Flynn Effect.) Of course early identification as a genius can backfire too; For every John Stuart Mill there seems to be a William James Sidis.