A nigh-universal feature of Greek funerals was the wailing of women, as they beat their breasts and tore at their hair. This was originally the province of women of the household of the deceased, but they were eventually joined by professional mourners.
Modern scholars tend to dismiss wailing as "a show of excessive grief", as if it were a kind of conspicuous consumption of mourning, and not genuine. This, to my mind, is offensive, myopic nonsense. Just because our society expects us to be more restrained in our grief, and are embarrassed when people contravene that, doesn't mean that when other cultures do demonstrate great sorrow, that they're somehow faking it. Wailing, and its Irish cousin keening, has been a part of funeral tradition in a number of cultures, and there's no reason to believe it's anything other than genuine from family and friends. Hired mourners were there to show extra honor to the Dead, to say that their death affects the whole community, but just because hired mourners grieved on command doesn't necessarily mean that they did not grieve truly. Just as some people now feel that any death diminishes us all and should be mourned, some people then would have mourned any death. True grief is hard (though not impossible) to fake.
I'm sure I'll write at greater length about this on Rewriting Death, and especially about the parallels with keening, which I've been studying a little, and listening to examples of. The most moving is this example of actual funeral keening:
The very few others I've found on YouTube have been songs or improvisations, not recordings from actual funerals. I'm still looking for more. If you happen to know of any online, please let me know at firstname.lastname@example.org.
I did some trancework around wailing and its possible purpose as a way to speed the soul onward, and was told, "The purpose of wailing is to give voice to your grief." I'm holding tight to that.