R’ Moshe wrote some teshuvos in the Igros Moshe regarding music during sefirah. I’m not sure exactly where, though – check OC 1:166. R’ Moshe also holds that recorded music has the same status as live music.
R’ Scheinberg holds that music which won’t lead to dancing is ok, so slow music isn’t an issue.
R’ Willig (from YU) holds that since we are lenient during the year on listening to music, we can be lenient during sefirah as well, we just need to make sure we don’t dance at all.