There is no explicit issur of listening to Music during Sefira (there is however an issur of listening to music the whole year!) However people are makil to listen the whole year, however not during sefira since the poskim learn out that since one shouldn’t dance during sefira one also shouldn’t listen to music. However what about music that would not lead to dancing (for example classical music, instrument music, etc what people listen to for relaxation or even pleasure.)
One can be lenient in listening to classical music (not suitable for joyful dancing) for purposes of relaxation and pleasure.
Please see our article of last year, here, for more details and sources.