All my friends who craft use this when trying to craft those Scorp Harness +1's and other high priced HQ's and seems to work pretty well. And it works for cooking too, and all crafts.
Just enter in what crystal you are using, how much skill you have, and how much skill the synth is capped at and it will tell you the next best possible time to synth it for a HQ to occur. The more negative the number of "difficulty" the more chance you have of HQing the recipe. And from playing around with this you can see what day/moon phase is best for your craft to create HQ's.
Now if you are concerned with what moon phases don't determine HQing, but govern better success and less fails, I have no idea.