Sorry, but I agree with Teri and Magda here. Wearing anachronistic clothing would be an issue, but singing an old folk melody certainly wouldn't. There are many tunes that have been recorded solely through being sung by people into the twentieth century, having had no other record in printed music or otherwise. If they aren't singing them, how do you propose they were kept alive?
Comparing the clothes is a red herring, too. Fine, wearing a ruff would be an anachronism, but would wearing a buttons on the clothes be an anachronism? Of course not. Fashion may change, but that doesn't mean everything becomes unfashionable. Look at the preponderance of Mozart for mobile phone ringtones - are these anachronistic?
Greensleeves is an amazingly persistant song - it has been sung in one form or another for centuries and will continue to be so. just as Shakespeare is still performed (would a character going to a play be anachronistic just because people go to cinema more often?). 'On Ilkely Moor' is still sung all over the Ridings, despite 'more recent' songs having been written.
Finally, Music Hall was seen as entertainment for the lower classes - and singing the tunes may have annoyed the employers somewhat. Country houses were amazingly good at being anachronistic when compared to wider society at the time.
Oh, and as for the last time I heard it sung casually - a girl at the end of my road was singing it last week as she played in the garden, and it's played by virtually every ice-cream van, making it one of the best known melodies in the country. It also became a standard ballad of the West, apparently - [
www.cs.rice.edu]
PSD
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This is the work of an Italian narco-anarchic collective. Don't bother insulting them, they can't read English anyway.