#angreal

In 1x08 Moiraine gives Rand a sa'angreal, rather than an angreal.

Now in the 3x01 sneak peek Verin says the 13th Depository stores the Tower's collection of ter'angreal and sa'angreal (no mention of angreal)

Masterlist

The pair of them were on the other side of the mountain and Helena seemed shocked at the damage. It was as if everyone picked up and left. No one bother to clean up the battlegrounds which were once homes. This was not Manetheren. No one was coming back, no one would claim this land, except an Aes Sedai and an Aiel who deserved it. She remembered the loss and she dared. It was theirs. Helena wondered if others would move up the mountain. Then, she doubted it with how demolished the land was. But even as she had the thought, her Power was called to her fingers and she was trying to fix it, as she did with everything. But this was accidental. She hadn't meant to so the magic was erratic, trying to piece every home this side of the mountain back together. Meeting places, forts built in the woods, workplaces. She tried to assemble it all, but the depth of the magic was too far and she did as she was so loathe to.. and gave up. She let the magic go, nothing changed. The mist faded from the air. 

decided to extend and edit my comment I made on 13depository

We know that Moiraine’s ivory bracelet angreal is “almost a sa’angreal“ and that with it she can reach the top female level.

I’d say that the bracelet is an example of what defines angreal and sa’angreal, since it is on the border between the two. Therefore, if an object would help Moiraine “jump” the whole scale then it would be a sa’angreal. It makes sense for angreal to have a “potential” of their own, since we are told they are created with a seed which lets a channeller “instil their power” in an object. So, if an angreal helps a channeler from a level +45 reach, for example +20, then this will mean that a channeller from level +30, will reach +5 with it. And a channeller from level +10 will go off the scale with 15 “units”.

It would make sense then, since a sa’angreal helps a channeller “jump” the entire scale and more, that sa’angreal were created by more than one person and were rare, even in the Age of Legends.

It doesn’t really make sense why some sa’angreal can’t be used by very weak channellers, since a very weak channeller could lead a very strong circle. The only possible explanation would be that an angreal or sa’angreal requires the channeller to draw the Power in themselves and a circle lets them use it, channelled by other people.

Then, a very weak channeller could “use” a very strong sa’angreal in a circle with someone strong enough channelling it *for* them.

So, there needs to be a second value, which shows how much a channeller can draw with a sa’angreal. I.e. a sa’angreal which gives a very strong channeller, for example 120 levels to their strength, will only give a weaker channeller, for example, 50 or 60 levels to their strength.

But it's best to approach this from the sa'angreal itself.

For angreal we could deduce that they give a channeller x to their level, no matter what their level unaided is, and for sa’angreal, that they provide a x times the sa’angreals lower limit to their level. So, for the Choedan Kal, the magnification would be for Elaida/Lelaine +x since they are at the lowest level possible to activate it, and for Nynaeve, it would be her strength level +x times the difference between her and Lelaine. I.e. the stronger you are, the more you are provided.

It would explain then why some sa’angreal have a lowest strength requirement, i.e. someone beneath the limit would be burned out, that they’d need to be able to take in the lowest limit themselves to be able to be magnified by “+x times the difference between them and the lowest limit”. In other words, the channeller is forced to take in the minimum amount required for the sa’angreal to work and then get magnified according to their strength level.

The Power has been shown to have similarities to how functions work, e.g. “reverse weaves cancel each other”, so this is one possible explanation of the provided strength that angreal sa’angreal give that I think works.

In other words, the magnification would be a function of the potential of the channeller and the Power they get will be the definite integral between the lowest level of strength needed from a person to activate it and the person's potential with respect to the amount of Power they are holding.

All we can’t figure out is how much the magnification is, the “times the difference between the channeller level and the sa’angreal minimum level” part, only that for stronger sa’angreal it would be >1, and for the weakest sa’angreal it would be 1.

It would help to think of it if it were between zero and 1. I.e the stronger you are the closer you are to the sa’angreal’s magnification potentital, but then again, that might be the case just for sa’angreal that have a buffer. For Callandor and Vora’s sa’angreal that would be a number >1 magnification, i.e. however much you want to draw, you get, having in mind the risk for the channeller.

We have the definition from the glossaries that "the Power provided by a sa'angreal compared to that provided by an angreal... ". But that is merely a comparison and something told novices or Accepted so that they realize sa'angreal are more powerful. In reality, they might differ a lot more and the Tower isn't aware of that many sa'angreal to be able to tell. Nor would they let novices in their storerooms and show them how individual objects match.

But back to the ivory bracelet, we know that "Moiraine didn't like [it]". What does this mean?