I can only give you some observations. I am not a avid carp man so you can dismiss these findings, no problem. However, I have caught a good few over the last 14 years. I keep records of everything caught including the moon phase. Using a simple scoring method of points for small, average, bigger than average for the water fished including carp and turning it into a percentage I have these results for carp.:-
new 12%
1st quarter 43%
full 21%
2nd quarter 23%
This is all day time fishing ! I do not fish at night. A better carp angler than me suggested this might mean that carp are feeding more at night and less during the day at certain times of moon phases. So, if that's right; it may suggest the 12 % for a new moon actually means they are very active at night during a new moon. And very less active during the 1st quarter given the 43% figure. I do not know, you will have to decide for yourself. However, 43% for 1st quarter day time is quite emphatic and I could easily assume that they would be feeding less at night during this moon phase.
I would never fish by the moon phase myself but, if I did; I think I would fish for them at night during the new moon and the day time during the 1st quarter. And of course, that's if the better than me carp angler's assumption was right.
Water is affected by the gravitational pull of the moon and the sun. You can see the effects of this in a large body water like the sea (tides). The tides are bigger around the new and full moons. The effect in such small bodies of water like a lake or river are minimal. I don't know if coarse fish can sense them but, who knows. The darkest moon is a new moon, this I could understand may have an effect on a fishes night time behavior.
However much my methods are unscientific and however much I am a novice-The results would have been more even if the moon had no effect whatsoever. Over time the results would even out to a degree. As that has not happened I would submit that at least it shows the moon does have an effect in some way and shouldn't be dismissed out of hand.
I am no carp expert and I don't expect to be given a lot of credence but, at least I hope you found that interesting.