Just Intonation Afterthoughts

Though it is probably clear to all of us what Just Intonation means, I thought the following was a very concise definition:

Just Intonation: system of tuning in which the distances between pitches are based on the natural harmonic series instead of the octave being equally divided

Now, can anyone explain to me the meaning of terms like 5th's, 3rd's, 7th's, etc? I know we said in class that 3's are 5's and 5's are 3's to remember that two particular ratios were called a perfect 5th and a perfect 3rd (at least I think we said it was 3 and 5), but that really doesn't mean anything to me. What is a 5th and whats a 3rd?

In the Just Intonation article 5th's, 3rd's, 7th's, and a myriad of even stranger terms were equated to all sorts of unusual ratios. Now I couldn't see any obvious correlation between the factors of these ratios and the 5th, 3rd, 7th, etc being used to describe it. Therefore when he started speaking in terms of these constructs I really couldn't follow along - I'm sure he was making a very interesting point but I don't have a clue what he was trying to say.

Any help out there?

Unusual Scale Similarity

Reading the piece of Just Intonation I made my way to the authors mp3 recording where he claimed to use a 16 pitch octave. When listening to it, I immediately recalled the Marilyn Manson track from Resident Evil. I have no idea if Marilyn Manson used a similar scale or if its just the way I'm hearing it, but to me the two tracks seem to have some striking similarities:

Author's Track:

http://www.kylegann.com/FracturedParadise.mp3

Marilyn Manson Track:

http://www.youtube.com/watch?v=EBGvtkVVas0

Also since we will be talking about the effects of certain audio choices on the listener, I find that the unusual pitch in the Manson track is really what makes that song feel a bit terrifying...when I watched the movie for the first time that song really up'ed the anxiety level, but somehow in an exciting way.

Just Intonation vs. Equal Tuning

Ok, I am just weighing in on the mathematics/logic of the scale/tuning. I read up on the "Just intonation" and I thought it made sense until I read down partway through #2 and realized we were not talking about the scale I was thinking we were talking about (now I know the one I am thinking about is the Equal Tuning scale). I think I need to discuss these concepts more in class if I am going to understand them...