In dealing with these black and white tartans, the difference between "ancient" and "modern" colors gets a bit fuzzy, and really most mills wouldn't even bother weaving two versions of these tartans.

Remember than an "ancient" tartan is just the "modern" woven with lighter shades. However, when this is done, it is typical that any black or white stripes will still be rendered in black and white. And anything blue, green, red, etc., will be lightened in hue.

However, what then do you do when you ONLY have black and white in the tartan?

I have seen some mills weave "ancient" versions of these tartans by using instead of black a very, very dark charcoal grey, or instead of a pure white using more of an ecru or cream color. It is hard to tell from your photo if that was the case here, but it does seem like the black used in the "ancient" version might be a hair lighter than in your swatch.