Tripods as turntable or component base?

3 legs making contact with the floor is the minimum needed to achieve stability. (Insects have 3 legs on the ground at any given time for that exact reason.) That doesn't make it "more stable" than more legs.

A tripod doesn't have any legs exactly opposite of its legs. Hence, you can easily push over a tripod over by taking one of its legs and pushing to a spot exactly between the other two legs. Now imagine adding 3 legs to the tripod, each one 180 degrees opposite of the existing legs. Now try that same experiment to topple the tripod by pushing with the same vector as last time, and you'll find it more difficult. Note that this new "tripod" has 6 legs rather than 3. But yet it's more stable.

So I think that your fundamental assumption of a tripod being more stable than other configurations is flawed.

Michael

I build turntables that have four feet. Three would be nice because it would be easier to level, but some designs cannot accommodate that feature. Mine is one, and it is very stable.

The reason manufacturers use three legs instead of four on a photographic tripod has nothing to do with the superior stability of three vs. four legs. Rather, three legs satisfy the minimum requirements for stability and this balances out the costs of engineering complexity, manufacturing cost, and weight penalties if you use more legs.

Reason for a tripod or 3 feet under a piece of gear: (1) Easiest to level; (2) The weight of the supported object will be evenly distributed among the 3 pods, once the object is level and if the tripod is properly implemented, (3) Fewest paths for vibrational energy to travel from the shelf or stand into the component. These are not trivial advantages, but extreme stability is not among them, as others have noted.

The people who used to market Linn specifically recommend flimsy tables

what do you expect?
something serious?