According to these suttas the observance is to be held on the 8th, 14th, & 15th days of the lunar fortnight.
Per my understanding of the Buddhist Calendar, the quarter moon phases always fall on the 8th day. The full moon phase always falls on a 15th day, & the new moon phase falls on either the 14th (in which case the fortnight ends a day early & the lunar month becomes 1 day shorter) or 15th day, alternating between the two from month to month.
By my understanding the classical observation of the Uposatha falls just on the new moon, quarter moon, & full moon days.
But according to these suttas where it says "fourteenth and fifteenth days", along with the 8th, it seems to me that the day prior to the full moon should also be observed since it is the 14th day, & on whichever case the new moon day falls on a 15th then the day prior to it, the 14th, should also be observed. None of these suttas say anything like "the fourteenth or the fifteenth days" or anything indicating that the 14th should only be observed when it is the day of the new moon, or that it should be excluded in the case of the fortnight leading up to the full moon.
The suttas also say that on the 8th day the ministers of the 4 Great Kings observe the world to see if humans are living righteously, on the 14th day their sons observe the world, & on the 15th day they themselves do it, & then report it back to the Tāvatiṃsa Devas. This is described in AN 3.37 which I mentioned above. So again this seems to suggest that the 14th day is to be observed even when it does not correspond to one of the lunar phases.
So is the classical method of observance only 4 times a month wrong? Am I missing something?
Now, to make things even more complicated, after saying to observe on the 8th/14th/15th day the suttas go on to say "...and during special fortnights", or in another translation, "...as well as on the fortnights of special displays". In an Āgama Sūtra, SA2 46, it says "...as well as on the during the fortnight when the spirits walk". It seems the relevant pāli word is pāṭihāriyapakkha. Can anyone tell me what all of this refers to?
I found this in the Vinaya.
As far as I can tell this confirms the fact that there's 3 Uposatha days in a fortnight (except when there is no 15th day), inclusive of the 14th day. So for example the day of the full moon & the day prior to it are both observance days.Now at that time monks, thinking: “The recital of the Pātimokkha on an Observance day is allowed by the Lord,” recited the Pātimokkha three times during the half-month—on the fourteenth, on the fifteenth and on the eighth (days) of the half-month. They told this matter to the Lord. He said:
“ Monks, the Pātimokkha should not be recited three times in the half-month. Whoever should (so) recite it, there is an offence of wrong-doing. I allow you, monks, to recite the Pātimokkha once in the half-month: either on this fourteenth or on the fifteenth (day).”