> dyad

Correct, though you'll much more commonly hear about triads, as in major and minor triads, and you'll hear "power chord" more often than "dyad," even though it's one specific dyad.

> if you hear a pitch against a second pitch that's double/quadruple/etc. the frequency of the first, your ear marks this interval as special.

Some of that is that the higher octaves reinforce existing overtones, so the higher note is already there in a sense.