The study was described in Tom DeMarco's excellent book "Peopleware." I think it was said to be done at Cornell University.
IIRC, the gist was that they gave a programming problem to a bunch of students, involving reading a list of input numbers, doing some math on them, then outputting the transformed list. They divided into "listen to music" and "silent". The two groups turned out to have the same average time to complete the project and the same rate of bugs. But the series of computations was carefully designed so that the output was identical to the input (but not obviously so by the instructions). The punch line was that of the minority of students who discovered this insight, most of them were in the "silent" group.
A number of years ago I tried to track it down and was unable to find a real published citation. Perhaps it never was published in a real journal? Even if it was, it was a small sample size of a limited demographic (CS undergrads at one university) and deserves a more rigorous follow-up, because the implications if it's a real effect are staggering.