Calendars can be very complicated. To my eyes at least.
How about the lunisolar year?
'A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year, then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year, then the calendar will predict the constellation near which the full moon may occur. Usually there is an additional requirement that the year have a whole number of months, in which case most years have 12 months but every second or third year has 13.'
This page on wiki also gives links to a variety of ancient calendars.
'The Hebrew, Buddhist, Hindu, Kurdish, Bengali, and Tibetan calendars, as well as the traditional Chinese, Japanese, Vietnamese, Mongolian and Korean calendars, plus the ancient Hellenic, Coligny, and Babylonian calendars are all lunisolar. Also some of the ancient pre-Islamic calendars in South Arabia followed a lunisolar system. The Chinese, Coligny and Hebrew lunisolar calendars track more or less the tropical year whereas the Buddhist and Hindu lunisolar calendars track the sidereal year. Therefore, the first three give an idea of the seasons whereas the last two give an idea of the position among the constellations of the full moon. The Tibetan calendar was influenced by both the Chinese and Hindu calendars. The Germanic peoples also used a lunisolar calendar before their conversion to Christianity.'https://en.wikipedia.org/wiki/Lunisolar_calendar
The metonic cycle combines lunar and solar years in a nineteen year period.
'For astronomy and calendar studies, the Metonic cycle or Enneadecaeteris (from Ancient Greek: ἐννεακαιδεκαετηρίς, "nineteen years") is a period of very close to 19 years that is remarkable for being nearly a common multiple of the solar year and the synodic (lunar) month. The Greek astronomer Meton of Athens (fifth century BC) observed that a period of 19 years is almost exactly equal to 235 synodic months and, rounded to full days, counts 6,940 days. The difference between the two periods (of 19 years and 235 synodic months) is only a few hours, depending on the definition of the year.'https://en.wikipedia.org/wiki/Metonic_cycle
Closer to home and perhaps the druids is the Norwegian Runic calendar.https://en.wikipedia.org/wiki/Runic_calendar
'The runic inscriptions of the Franks Casket (7th century) seem to constitute a lunisolar calendar. While the number of runes can be seen as a 10 year solar calendar (10 for eternal), their runic value stands for the lunar counterpart. Both calendars seem to be “synchronized” by a Latin fragment which is inserted into the Anglo-Saxon text. It consists of 20 letters (12 uncials, 2 half uncials, 6 runes), thus creating a sequence of ordinary years of 12 months and embolismic years of 13 months. If we figure the value of this text by the position of the characters according to the fuþorc we count 238. A Metonic cycle of 19 years counts 235 lunations; in this particular case the rune master needed 3 more lunations to take his protégé from death in Midwinter to life – here a pagan resurrection into Valhalla – at Easter.'https://en.wikipedia.org/wiki/Runic_calendar
This site goes into more detail of the Primstav and shows how Christianity added saints to the various times of the year. It may be that these 'saints' are saints of convenience and represent a much older naming system.http://www.digitalkunst.com/NewFiles/primstav.html
'The symbols tell an interesting story. Pagan symbols remained, not only because they were so much a part of the ancient culture but also the church had retained some of the pagan celebrations and had given them religious significance. Other symbols reflected stories told of the apostles, saints, and martyrs. Still others were tied to the daily work of the bonde - farming, fishing and struggling to exist. The meaning of some of the symbols on this stick are unclear and your own interpretation of them may be clearer than those given here.'