This has been a fascinating thread, and I've learned a lot from it so far. But for me, the most economical statement on the question still remains this limerick:

There was a young lady from Tring,
Who said, when they asked her to sing:
"You may think it's odd,
But I cannot tell God
Save the Weasel from Pop goes the King!"

If , unlike this lady, you recognise a tune when you hear it, then you are not "tone deaf".

If you can recognise tunes, but still sing them inaccurately, or with an unpleasing tone, then good teaching and regular practice can improve your technique. (Though it may never turn you into a virtuoso.)

If, despite giving it your very best, you still hit the odd bum note, console yourself with the thought that even the best singers do this occasionally. There is a lot of snobbery in the musical world on this topic – don't let it get you down.

When an operatic diva hits a wrong note, critics say: "She's having trouble with her intonation tonight."

When a jazz singer hits a wrong note, critics say: "That was an interesting improvisation – but it didn't quite work for me."

When a rock singer hits a wrong note, critics say: "Aw, the kid's tone deaf!"

And when a folk singer hits a wrong note, critics say: "Well, I suppose folk music is meant to sound that way – isn't that why it died out?"

So, if you were written off at the age of five by your first music teacher, and ordered to open and shut your mouth in silence while the rest of the class sang - don't be discouraged. Work on your technique – be cautious about what you sing, and where – don't overtax the tolerance of your listeners – but don't give up trying. Remember, folk music belongs to the people. All the people. And that includes the many who are not gifted with brilliant voices, as well as the few who are.

Wassail!