Progressive spiders, inverted surrounds.

That is how a progressive spider looks, just look @ your Brahma (they get closer and smaller). I guess it has something to do with how hard it is to move certain size/closeness spider ridges at different levels... so that the force remains constant over a broader range. Thats my guess.

Inverted surround... no idea, my Dad's old 73' Sansui woofers have inverted surround on them. Not exactly sure what the advantages are either. I guess just different things for different drivers.

 

Progressive spider, you nailed it...
Just like the car spring, more coils, lower spring rate, the spider must accomplish this via the same means, becasue the progressive spiders do have less spacing between ribs near the center.

The inverted surround should have NO affect on sound, period.
Think of a subwoofer's motion, it moves in and out. As it moves out, the suspension stretches (maybe "unrolls" is a better word) in one direction, as it moves in, the suspension stretches in a different way, but either way, it works to provide a resistance against movement away from the center "at rest" position, and works to keep the cone centered.

Inherently, a surround is not supposed to affect sound quality on the forward stroke compared to the rearward stroke, although it is easy to picture that there may be some small differences due to this different type of stretch...
But inverting it won't get rid of the differences, sound quality should still net out the same.

How do you get rid of these differences, so that you have a truly symmetrical driver, forward stroke compared to rearward stroke?
I think it's fair enough to say that in reality, who cares? Difference isn't perceivable, even in high-frequency drivers.
But this has been tackled.. look at an isobaric clamshell alignment, or a side-by-side push-pull arrangement... in those setups, you have one driver moving forward, while the other driver is moving rearward... any suspension non-linearities are inherently ironed out.
But how to do it with one driver?
Maybe you have seen subwoofers with accordian surrounds? Cerwin Vega had them... in fact the Stroker had that, correct?
More popular in pro audio.. maybe the accordian surround carries an excursion penalty.

At any rate, I can imagine one benefit of the inverted surround...
Picture an Image Dynamics IDmax sub.. look at it's surround...
It is a tall surround, that is not wide, it's not a 1/2 roll surround like a 1/2 circle, it is taller than it is wide.. an interesting approach to getting more excursion capabilities from your subwoofer without carrying a big "fatass surround" reduction in cone area penalty.
However, the trade off is a surround that extends forward from your subwoofer by quite a bit.

Inverting a surround could allow for a larger surround like the IDmax surround, but without the surround sticking out from the subwoofer too far, sort of tidily packaged inside the basket in that case.
Not that i have ever seen that in production..