Folklore: Planting by phases of the moon

My father (who was born on a farm in Kentucky in 1899, and grew up there, but lived most of his adult life in the city) believed in planting by the phases of the moon.

To the best of my recollection, here is how he explained it: For most plants, you want to plant during the waxing phase of the moon (but I don't think he used that term; he probably said, "while the moon is getting bigger"). That is, from the new moon to the full moon. But the opposite is true for root crops, such as potatoes, beets, and peanuts. If you planted those during the waxing phase, you'd get lots of growth in the leaves and stalks, but very poor roots. So you planted root crops during the waning phase, from the full moon to the new moon.

I don't even know whether he bothered to follow his own advice when he planted our little garden in the city. It probably didn't matter, because, whatever he did, we often ended up with more tomatoes than we could eat.

I assume this folklore has been debunked, since I can't find anything about it at The University of Minnesota Extension Service.

It seems plausible that the light of the moon might have some effect on plants, but the effect must be minuscule compared to the sun. I haven't done the math, but I'd guess that the sun being behind a cloud for an hour has more effect than a full moon could have during a whole clear night.

What do you think? Was any such folklore passed down in your family? How seriously did people take it? Do any serious (as opposed to hobby) farmers take it seriously now?