What I meant by that millisecond order of magnitude was that the clocks on the phones would need to be highly synchronized, with each other, to high precision,

What I meant by that millisecond order of magnitude was that the clocks on the phones would need to be highly synchronized, with each other, to high precision, which would require pre-planning and special efforts. In 10ms sound can travel about 3 meters, which is on the order of magnitude of a room, and represents the range of time offsets we're talking about. This has nothing to do with the actual frequencies of the sound itself, or the rate of PCM-type sampling you need to record quality sound. That's a different issue, and doesn't have to do with synchronization of different devices. Regarding the math: A circular array is better than a grid (or random placement) because there's only one single math formula that's used to compare any mic to any other mic. With a grid array the number of unique formulas involved goes up as the square of the size of the array. And the mics at the 'center' of a grid are basically worthless, and offer no added value.