In a similar manner to the way that we use "sex" to differentiate male and female, I want to find the best word to differentiate major and minor.
The Wikipedia page on the subject did not use any such word in its explanation. Nor did anything in the search engine results I looked through. That doesn't sound promising, but at the same time, I would be surprised if there was truly no word for this, as music is filled with so much terminology. It seems to have a word for every teeny tiny little nuance of the subject, if there is no word to refer to whether something is major or minor, it wouldn't seem characteristic of itself.
Here is a sentence to work with:
This composition's ______________ is minor.
This person's sex is male.