Is it muter to listen to music on 10 Teves. Is it b’geder what the first Biur Halacha says in Siman 551?
There is no prohibition against listening to music, but joyful music hardly suits the atmosphere of the day, and should be avoided.
In addition, we find that the Mishnah Berurah (550:6) writes that a person who can (and is a ba’al nefesh) should preferably accept the stringencies of Tisha Be’Av even for the other fasts. This appears odd: Are we supposed to avoid washing hands and wearing leather shoes on all fast days?
It is possible, however, that the intention is to act in accordance with the halachos of the nine days–meaning that it is better not to listen to music. (The context of the Mishnah Berurah does not suggest this interpretation; however, we can certainly deduce that music is not lechatchilah on fast days.)