Many Germanic reconstructionists in the past few years have integrated the ancient Germanic Luni-Solar calendar into their contemporary religious practice, but there is one simple fact about the ancient Germanic calendar that many get wrong - the months did not begin on new moons, but on full moons.
We can illustrate this based on a couple of sources, namely Bede's De Temporum Ratione. That the ancient Germanic months corresponded to the Lunar cycle is well-established. That the ancient Germanic people recognized two yearly seasons, winter and summer, is also well-known. We learn from Bede that among the ancient English, winter begun on a Full Moon of a month called Winterfilleth:
"Hence, they called the month in which the winter season began 'Winterfilleth,' a name made up from 'winter' and 'full Moon,' because winter began on the Full Moon of that month."
Supposing that the Germanic months begun on New Moons, this would make a season begin in the middle of a month, which would be quite odd. But let see what Bede has to say further:
"The months of Yule derive their name from the day when the Sun turns back [and begins] to increase, because one of [these months] precedes [this day] and the other follows."
We know that Bede isn't referring to the Winter Solstice in this instance, but to a generally recognized belief of the ancient cosmology that the Sun literally moves away from the Earth in winter and closer in summer, resulting in the coldness and warmth of the seasons. But what is more striking here is the fact that while it's usually claimed that Yule Moon is the Full Moon in the middle of the second Yulemonth, Bede says that the first Yulemonth precedes this point and the other follows it, he does not say that Yule takes place in the middle of the second Yulemonth. The only logical explanation here is that Yule takes place between these two months. Keeping in mind that Winter begins on a Full Moon, Midwinter, likewise, taking place three months after its beginning, must take place on a Full Moon. Therefore, this other excerpt suggests that the second Yulemonth begun on a Full Moon, thus the ancient English months begun on a Full Moon.
This logic then further explains the later English attestations of the names of the two Yulemonths - Ǣrra-ġēolamōnaþ [Ere-Yulemonth] and Æfterra-ġēolamōnaþ [After-Yulemonth]. Yule is the Full Moon between these two Yulemonths and the first month precedes Yule, while the second takes place after Yule.