That is the Black Watch tartan. The blue looks to me to be blue, not purple (though some mills' blues look more purple than others). That's a minor variation between weavers and not a major matter for concern.

As to the black lines being "2 threads thick" this is a matter of proportion, not a specific number.

This is definitely the Black Watch tartan -- it just may have some minor differences from other versions of the Black Watch tartan you may have seen before.

M