Here I'm going to talk about Allomancy fairly in-depth. If you don't want to know or ruin a potential surprise, don't say I didn't warn you (also there are plot points from the end of MB2 as well). Do note, however, this is merely theory. I have no more qualification to talk about this than the next person--only Brandon has the true authority. This is not fact (though I hope I'm on the right track), simply a theory.
So, we know about the Physical metals, we know about the Mental metals. We also know about the Temporal metals. Each quartet has two pushing metals, two pulling, two Internal, two External.
However, there is a fourth quartet of metals--that much should be obvious. I mean, Aluminum and Duralumin aren't classified under any of those three quartet. And, if there is a quartet, then there are two other metals that aren't named (I say this for summation purposes--many who have been looking at the Speculative topics already know this fact).
These metals influence metals and Allomancy itself. I'm going to call them the Metallic metals, even though that is an awful name--one I didn't coin, by the way.
I think it is safe to assume that Aluminum and Duralumin are the Externals of the quartet. I mean, they affect how Allomancy is burned, and burning metals has generally very External effects. So, I hereby define these metals to be:
Metal 13.
Aluminum -
Metallic External Pulling Metal. Pulls on Allomantic metals, extinguishing an Allomancers supply of metals.
Metal 14.
Duralumin -
Metallic External Pushing Metal. Pushes on Allomantic metals, flaring them so rapidly that they burn away.
So, if those are the Externals, what are the Internals? At the end of MB2, Elend ingests a strange metal. He subsequently gains the powers of a Mistborn. I--and probably others as well--are convinced that this metal is the 15th metal. It gives the user the ability of Allomancy--the powers of the Mistborn. I'm also convinced that this metal is how the Lord Ruler gave the original supporters of his rule Allomancy, and, as well, how he gives the Steel Inquisitors their Mistborn powers (now, that doesn't mean its the only thing that goes into making an Inquisitor, but definitely a part).
The effects of the metals are External in nature, but the ability to use the metals themselves are Internal. I classify the 15th and 16th metals as Internal.
There is also a very interesting pattern which evolves with the Temporal quartet. Atium sees into the future of someone else. It's pair, malatium, sees into the past of someone else. Gold sees into your past. Electrum sees into your future.
While Atium/Malatium are external, simply by the merits of each one being Pushing or Pulling, there is a symmetry. Atium, I believe, is the Temporal External Pushing metal, and Electrum is Pushing as well (because I rather think that seeing into the future is more of a Push). There is symmetry amongst a Pushing pair or a pulling pair, one that isn't as prevalent in the Internal or External metals.
So, here I get this crazy idea. Aluminum "Pulls" (once again, whether it is Pushing or Pulling is not immediately prevalent, but I'm going with this until someone tells me otherwise), taking away metals. The 15th metal doesn't exactly give you metals, but it gives you the
ability to burn metals. That seems symmetrical enough for me.
Therefore:
Metal 15.
Unknown metal #1 -
Metallic Internal Pulling Metal. Grants the ability of Allomancy to the person who ingests this metal.
Going on with the idea of symmetry, Duralumin must have some sort of similarity with the 16th metal. The 16th is one I don't think anyone has solidly defined, so here I shall attempt that!
Duralumin burns your metals away in a flare. This seems remarkably similar to how Vin describes the Well in MB2: the power had to be burned away in an instant, and then it was gone.
. That is far too coincidental to be false. It's symmetric--in that both Duralumin and the 16th metals burn things away rapidly.
Therefore.
Metal 16.
Unknown metal #1 -
Metallic Internal Pushing Metal. Burns away "the power" in an instant, power of creation.
I say "the power" because I'd like to say "The Power of Allomancy" but you can't burn an ability away. The only thing really able to burn is the power at the Well itself.
Something like that, I think, is the closest we can get to knowing what these metals do.
However, I can discern what the symbols are for these metals, if I did classify them correctly. Notice
this wallpaper that Brandon posted in the fan art thread. It shows the circle of Allomantic metals--which, by the way, further verifies that there are 16 metals.
The top left quartet--if you look at your MB2 Ars Arcanum--is Physical, top-right is Mental, and the bottom-right is Temporal. The inner ring of metals is Internal, the outer External. The bottom-left is the only quartet not in the MB2 Arcanum, so that must be our Metallic metals.
Further analyzing these symbols, we can see which ones Push and which ones Pull. Look at the dots on a symbol. It's either out or its in. The symbols which are "out" of the symbol are Pulling, and the dots which are "in" the symbol are Pushing.
So, utilizing this knowledge:
Aluminum:
Duralumin:
15th metal:
16th metal: