For the benefit of balance when playing Apocalypse games I've worked on the theory that for auspices and such like each of the phases should be roughly the same size. To this end to get the five auspices roughly equal time you need to have five or six days per phase.
The way I've always done that is as follows assumin Day 0 is the new moon:
- Days -2 to 2 (5 days)
- Days 3-5 - waxing crescent (3 days)
- Days 6-8 - waxing Half moon (3 days)
- Days 9-11 - waxing gibbous (3 days)
- Days 12-16 - Full moon (5 days)
- Days 17-19 - Waning gibbous (3 days)
- Days 20-22 - waning half moon (3 days)
- Days 23-25 - waning crescent (3 days)
- Days 26-30 (day 30 is day 2 of the new cycle) - New moon (again) (5 days)
As you can see this gives 5 days for the new and full moon and 6 days total for the intermediate three (in groups of three days wwaxing and three days waning). Lunar cycles are funny things so these might be a bit fuzzy but this I think is a good rule of thumb.
To the best of my knowledge I don't recall ever having seen this clearly defined in any literature, hence the need to make it up ourselves.
As a final note the reason I've attempted to make each of the phases roughyl the same length is because if birth time is random then if half moon was only two days (once each way) then only about 7% (2/28) of werewolves would come under that auspice compared to the crescent which if correspondingly larger might be 10/28 = 35% of werewolves, five times as many proportionally. I've always assumed the auspices are balanced, hence this plan.