sam2: you are correct in saying that-theoretically- one cannot listen to music all year round (shulchan aruch OC 560-3) but this minhag been ignored for many years and certainly you do not see many people follow those customs today in the middle of the year. However, in the shulachan aruch on sefira only two “minhagim” are mentioned: not to arrange weddings and not to cut one’s hair. (beards are another topic) See orach chaim 493. from what I have gathered, I did not see any acharonim discuss the laxity of listening to music all year round and THEREFORE- it must be banned during sefira. In other words, there is no specific issur or minhag concerning music during the sefira that derives from that all year round minhag.
to benigmuman: As the whole concept of aveilus during sefira only started with the geonim- it would not surprise me that the issur of cutting hair was introduced a little bit later by the rishonim. I have no way of checking that.In shulchan aruch, they are mentioned as equals.