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Reynolds used to produce a basic tubeset which consisted of 531 main tubes and presumably plain gauge (501?) stays - the green and black sticker read "made with 531 main tubes".
There was a guy in one Brit MTB magazine who claimed he could tell the difference between two bikes, one with a full 531 tubeset and the other with main tubes only. I wrote back and said if you can tell the difference in the Young's modulus between the two on a mountainbike, with a 2" tyre, uphill, in mud, then please come and work for me because you're far more sensitive than any of the test equipment I had at the time. I got a rather snotty reply back, heh.
Oh, and double butting on tubes (and single butting on fork blades) is done mostly to save weight rather than for ride quality. The thinner centre section is as thin as the tube needs to be for strength, and the ends are thicker because that's where they are brazed. Think of it as the centre thickness is how the tube should be; if tubes were glued, for example, they wouldn't need to be butted so they could be as thin as the centre section throughout their whole length. I don't think I've explained that very well, mind.
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Ha! Reminds me of this... http://www.bgcycles.com/new-page-1/
The main triangle part is true - generally x3 main tubes to get the sticker is the requirement. That said, chainstays/seatstays aren't going to make a whole lot of difference to the overall weight as they're such a small diameter it's going to have a negligible effect on overall frame weight whether they're 0.9 PG or 0.8-0.6 DB. I think this is essentially why x3 main tubes for the sticker came about - there's not a really a whole lot of sense in opting for posh stays. I'm sure some will say DB/thinner stays ride better though.