Ok so it took a bit of bravery mixed with a dash of foolhardiness. 2 broken magnets and some shrapnel that I will have to remove from my dry wall at one time or another. Luckily I wear safety glasses when running experiments. The shrapnel part is heavily exaggerated btw but why not add a little drama for the readers entertainment
But finally I think I understand the suggestion of stacking side by side (horizontal in an axial configuration). I'd like to make sure I do.
Now at first I thought one meant keeping the poles aligned. That would be a complete nuclear accident waiting to happen as the magnets would strongly repel and I do not have to explain here how difficult it would be to contain that.
Now the other way, and the way one probably meant to advice me on, is to side by side them while opposite. So they attract.
Hahha. Now this does not mean things can not get out of hand as my dry wall can confess if one were to ask it privately

Anyway story telling mode aside.
What will happen to the coils, I think, is that the flux will have a quick field reversal every 3.75 degrees of magnet movement.
So a quick up down with a short period where it flows over to the next cycle.
I have not taken out my oscilloscope yet but the frequency of field reversal seems to be involved.
Although I am going to introduce a formula I would still like things to stay at a beginner level.
I have been trying for the last hours to find my misplaced bookmark on a simplified version of lenz's law (I think)
E= b * v * I
I think it was as it was too long ago ;(
I can only advice one to not organise their documenting like I do. You will struggle to find things back when you need them most.
Anyway I did not find a frequency component in that formula. So now I am puzzled as I thought it was the frequency of field reversal that was important. But this formula seems to imply that it is the v(velocity) that is a part of the equation.
You see? It is easy for some of us to get a little lost in the fast woods.
But I like exploring them anyways

ahhh I think I remember now someone already mention it to me.
The velosity dictates the frequency. so it all boils down to the same thiing in the end.