Which one is the Twelfth Night?

So when is Twelfth Night? My mother has always insisted that it is on 6th January. My eldest brother has always had his decorations down by 5th.

My mother has then acused him of not being able to count.......

If you count twelve days from 25th December, it is indeed 6th January. However, if the first day of Christmas is 25th December which most of us would assume it is, then to me it looks like this:

On the first day (25th December:)
of Christmas,
my true love sent to me
A partridge in a pear tree.

On the second day (26th December:)of Christmas,
my true love sent to me
Two turtle doves,
And a partridge in a pear tree.

On the third day (27th December:)of Christmas,
my true love sent to me
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the fourth day (28th December:)of Christmas,
my true love sent to me
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the fifth day (29th December:)of Christmas,
my true love sent to me
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the sixth day (30th December:)of Christmas,
my true love sent to me
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the seventh day (31st December:)of Christmas,
my true love sent to me
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the eighth day (1st January:)of Christmas,
my true love sent to me
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the ninth day (2nd January:)of Christmas,
my true love sent to me
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the tenth day (3rd January:)of Christmas,
my true love sent to me
Ten lords a-leaping,
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the eleventh day (4th January:)of Christmas,
my true love sent to me
Eleven pipers piping,
Ten lords a-leaping,
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

On the twelfth day (5th January:)of Christmas,
my true love sent to me
Twelve drummers drumming,
Eleven pipers piping,
Ten lords a-leaping,
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree!

Which makes it 5th January.......

And, on looking up the lyrics for the song, (because I am ashamed to admit that my ageing memory failed me), it talked about the twelfth night being the eve of Epiphany, rather than Epiphany itself. Or, is it that the calendar was changed, during all the Gregorian stuff and as such there didn't used to be a 31st December?

Or is it that you should indeed do as my mother always has done and count up from the 25th. This means though that 25th is not a day of Christmas, which seems a bit daft to me.

In the meantime:

Do I take my decorations down on the 5th for good measure?

Do I wait for the 6th when I will have help because the family is home?

Or indeed, is it bad luck to take them down on 5th, if 6th is officially twelfth night?

Now we really could do with some of the good luck variety this year. So do comment please, and let me know.....

UPDATE.........

I have done some searching around on the net and found that the song may have originated not in England, but in France and that according to the Snopes Website
January 6th is indeed the twelfth day of Christmas.....

In some church traditions, January 5th is considered the eleventh Day of Christmas, while the evening of January 5th is still counted as the Twelfth Night, the beginning of the Twelfth day of Christmas the following day.

What's more, for the seriously brief period of time that The French Revolutionary Calendar was used, in France, December did in fact have 30 days.

So if these three websites are correct, and if the song was orginally of French origin around about the end of the 18th Century (from whichever calendar you feel like using)then that makes the twelfth night 6th January after all.

But with our calendar, it's still 5th isn't it? Oh I don't know! What do you think?