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.
Tripods as turntable or component base?
Perhaps one of you who is into photography or owns a camera store can try this experiment. Since the tripod is the most stable base (ask any photographer or physicist), has anyone experimented with using them as component bases? All the best turntables and many other components now have 3 legs instead of 4 for that reason. One school of thought says heavy tables for turntables are better (less amplitude of motion for given energy input); others say not (energy storage, pickup of airborne sound energy). The people who used to market Linn specifically recommend flimsy tables (!) but they were fruitcakes. How about taking three tripods, setting up one under each foot? A cheap experiment if you have the tripods... Your colleague in science, hifigeezer