(siman 126:3 in kitzur sh”a)
Rabbi Avrohom Blumenkranz a”h taught that listening to music during a meal is assur, except for a seudas mitzva.
It is one of the things implemented zecher l’churban, along with a kalla not wearing jewelry during the chuppa.
There are 4 short se’ifim for more customs held in memory of the churban.
There’s more info in the shulchan aruch.