Halcro/Pryso
We are in agreement on the "stability" of 3 feet.
My comments on stability are in the context of draining unwanted energy using single point mechanical grounding. I also assume the tripod is correctly designed for weight distribution to give stability and deal with rotational energy around the central axis. I also assume we are not driving the TT down to the grocery store and we are not in the habit of sitting on it.
Very few surfaces that the gear is mounted on are truly level, and in that context 3 feet will naturally load predictably, whereas with 4 or more feet they will have to be adjusted precisely to provide predictable loads through each foot. This is almost impossible unless you have pressure pads under each foot. The Mana stand manufacturers' recommended set up procedure for their 4 legged stands were to adjust the 4 feet with a stethoscope and tapping technique. Imagine doing this on each shelf as well as the feet ! And if you have a wooden floor that moves, you'll need to retune them each season.
In my 30+ years of audio I have applied the Goldmund mechanical grounding principles on all my components ( and many others ) and in all circumstances converting equipment ( TT's, amps, speakers ), speaker stands etc to 3 feet, single point mechanical grounding has yielded significant improvements in clarity, focus and the removal of resonances and tonal distortions.
In the Goldmund amplifiers, the mains transformers are grounded directly by bolting the transformers to the Goldmund footer, and the transformer is attached to the chassis by lossy connectors. The electronic circuitry is directly coupled to another of the 3 feet for optimum grounding and that foot has a lossy connection to the chassis. The net outcome is that each of these sources of resonance are single point mechanically grounded, and separate from each other, even though they exist in the same chassis. The chassis is decoupled from the others and grounded through the third leg. With non Goldmund amps the "alpha" leg is best placed under the mains transformer which is usually the largest source of resonance.