Thanks, Don, now I'm even more confused.

The background to my original question was a combination of two things: (a) wanting to do some harmonising (on chorus songs and singing with my multi-tracked self) and (ii) noticing that the first and the fifth of the scale of X make a good drone for a song in the key of X; this made me think that I and V probably go together well, & that a good starting-point in writing harmony would be to go four steps up or three steps down (Do, Te, La, So) from any given note of the melody. Then it struck me that this would get you a harmony line that would sound a bit odd if played on its own (not that this is necessarily a bad thing). Unless you simply transposed the melody line into the key of So - but that wouldn't get you a constant interval. Hence the question.

If I understand right, you're saying that the rule (which can be broken) is "don't use parallel fifths". So if I was observing the rule, what should I use - fourths? thirds? seconds?