Scrzbill said:
While I will agree with what you say is mathematics, the two balls can be made of different components. This is what I believe is the different densities. All I know is they play different. When I started this, I was trying to find out why and how they play different. So far, not much on that except some people think the Measles is sticky to object balls. I haven't seen a red triangle ball in years.
Ah, sure, they could play differently and still have the same overall density. Bowling balls are a good example: they're mostly the same size and weight, and therefore the same overall technical density, but they have quite a number of components, all of which can be, and are, varied so that they play differently. The parts just have to "add up" to the same density.
From Aramith's web site, it seems that all of the balls are made from the same phenolic resin. The difference between their various lines (including Centennials) seems to be the "grain size" of that resin. The cheaper ones have a larger "grain size". I don't know enough about phenolic resin chemistry to know what that really means. (Spending 30 years in a chemistry department taught me a lot of things, most of which are of absolutely no use whatsoever in trying to answer rational questions like this one.)
I would expect that it means the more expensive ones polish better (analogous to sanding soft and hard wood). It seems possible that the more expensive ones might be somewhat harder, though whether that would be enough to make a difference, I don't know. I would expect them to sound a little different when they hit another ball, though I don't know if any difference would be detectable by ear.
Finally, a larger "grain size" for the cheaper ones could possibly mean that the cheaper ones are really a little less dense in the technical sense. I don't know enough to be able to say one way or the other with certainty, but it seems sort of reasonable. That would show up quickly by weighing and measuring them very carefully; if they aren't the same size and weight, then they aren't the same density. Whether there could be enough difference to be noticeable isn't clear.