- The practice to refrain from listening to music during the period - not discussing the prohibition the rest of the year, which is clearly not followed by most - is a (comparatively) recent trend.
I see no one else has pointed this out, so I will.
Leket Yosher (pg 97) writes that his teacher (the Terumas Hadeshen) would even say "Eliyahu" on Motzaei Shabbos, except when Lag B'omer was on Sunday, in which case he would say "Eliyahu".
This is an explicit source from a Rishon not to sing vocally during Sefirah.
And if instrumental music itself is a problem why is recorded a cappella ok?
There are indeed those who hold that it's not ok, but there are also those who say it's fine. While he doesn't explain the why, Tzitz Eliezer (15:33) writes that recordings have the same status as the original, meaning if the recording is of vocal, then the recording is considered vocal, and if the recording is of instruments, then the recording is also considered an instrument.
By contrast, Shevet HaLevi (8:127) writes that recordings of any type (even of vocal singing) have the status of instrumental music, and are thus prohibited (yearlong, as he holds like Shulchan Aruch, that all such music is prohibited yearlong).