Twelve Days of Christmas - one or twelve pear trees?

I was discussing the Twelve Days of Christmas song with my son as a maths exercise. We worked out how many items are received, but I then wondered if pear trees are a singular or plural item.

On day one the line is

My true love gave to me, a partridge in a pear tree

and on every day after it changes to

and a partridge in a pear tree.

As they use the indefinite article, does this mean the recipient also gets twelve pear trees, or could it be the same tree from day one?

I would say 12 partridges and 12 pear trees are sent in total.

Looking at just one day:

On the ninth day of Christmas

my true love sent to me:

9 Ladies Dancing

8 Maids a Milking

7 Swans a Swimming

6 Geese a Laying

5 Golden Rings

4 Calling Birds

3 French Hens

2 Turtle Doves

and a Partridge in a Pear Tree

So those are the gifts of just the ninth day. It doesn't say or suggest: on the ninth day my true love sent me just X, in addition to Y-Z from the previous days.

Fun question. From the language alone, the most obvious conclusion is that the speaker (singer) receives all the items, each day, so that by the end they have 12 partridges in 12 trees, 22 turtle doves, 30 french hens, etc.

From a pragmatic point of view, the most sensible interpretation is that they get each gift only once, as if the lyrics said *"By the end of the Nth day of Christmas, my true love had sent to me..."*.

Perhaps we can assume that this is an example of poetic license, and was what the writer intended. My version, above, certainly doesn't scan as well.