The scale generation algorithm described here is really interesting - it starts from the natural core of harmony (using rational relationships between frequencies), and gives you the option to keep the resulting natural-tempered notes, or to adapt them to the modern-day 12-tone equal temperament (12TET) and its irratonal, twelvth-root frequencies.
The question of whether 12TET is "natural" or not is an interesting one, and in my opinion, it was great for a few centuries, but at some point music will move beyond 12TET. Take a look at one of richest websites exploring this question [1], whose author has a different opinion from mine.
As for skipping the 7th harmonic -- i'd say you shouldn't do it. If you scroll down [1] until you get to the "n-tone equal temperament" graph, you'll find one of the nicest ever justifications for 12TET. However, if you added more harmonics to that graph, you'd find that the 7th does not fall anywhere close the 12TET frequencies: that's why we're not used to hearing it, and it sounds the most alien to us.