Can you listen to music on the fast of the tenth of tevet?
Nitei Gavriel - Chanuka - 60:6 says that one should not listen to music on a fast day.
(sources: Rokeiach, Kitzur Shulchan Aruch 121:1)
In the Shulchan Aruch it does not say that music is prohibited on the 10th of Tevet, however 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. (source)
That one should not listen to live music on Tisha B'Av is codified by many later authorities and it is assumed to be absent from the SA because there’s a general prohibition of Listening to Music (ibid)