At traditional Jewish funerals, songs are not sung. As far as I know, there is no prohibition against singing songs at funerals; it’s just that, in fact, singing is seldom done.

(There is the occasional funeral at which a soul-moving melody can be heard, but this is the rare exception, rather than the norm.)

Why? Although I have not seen this explanation applied to this particular question, I think it fits:

Song is a powerful device. It has the power to exalt a person to the highest realms, by awaking the divine spark embedded within him. But music also can be used to hurl a person to the lowest depths, by directing our emotions to unworthy places. Music can be used to help us train our sights on our G‑d-given goals in life; but it can serve, too, as a narcotic that dulls our heart from confronting a painful life experience, and prevents us from uncovering the G‑dly message it contains.

Our feelings, too, at a funeral are very private. And because of the magnetic pull of a song, the emotions of everyone attending are commandeered by the song. We are forced to leave our own thoughts, our own feelings, and feel the underlying emotions conveyed by the song. As a result, we are prevented from experiencing the funeral in a manner that is most suitable for ourselves.

So if a song is to be sung at a funeral, it is best a melody chosen by each individual, and sung to an audience of one.

Best wishes for a good and sweet year!

Rabbi Eliezer Danzinger for