Of necessity, ritual is performed in time, and not just incidentally – there are definite rules for when they are and when they are not enacted. Such rules were never accepted or imposed universally on Mediterranean polytheists (nor on all Greeks, etc.), but almost by necessity, a practitioner must settle into observing some of them.
The calendar which has now been imposed on all of humanity to some extent, the Gregorian, is a slightly modified form of the Julian calendar, developed at the direction of Julius Caesar and officially adopted at Rome in 45 BCE. It is meant to be as true to the solar cycle as possible, and uses leap days to compensate for the discrepancy between the conventional year and the true solar year (365 days 5 hours 48 minutes 46 seconds). Since the Julian reform changed much more than the Gregorian did, and was nevertheless adopted without exceptions by the Roman priesthoods, there is no doubt in my mind that the Gregorian calendar is equally valid for ritual purposes. On the other hand, since the Julian calendar is still maintained by Orthodox Christian churches, it is not difficult to observed this instead if one wishes.
Similarly, it is easiest to observe ancient Egyptian festivals by following the Alexandrian or Coptic calendar maintained by the Coptic Orthodox Church (and also used by non-Christian Egyptians for some purposes). Following a decree of the Roman emperor Augusts in 25 BCE, this calendar has been synchronized with the Julian calendar (which itself was inspired by the Egyptian model), meaning one year of the one corresponds to one year of the other, although the system of months still functions differently. Of course, there is no reason not to observe different computations if one prefers, although it was also accepted by the indigenous priests (after an earlier reform attempt under the Ptolemaic dynasty had failed). A very similar calendar, albeit without leap years, is used by the Mandaean community.
Another ancient calendar which has remained in use to this day is the Babylonian, which was once broadly used across Southwest Asia, although its modern descendants strongly diverge from each other. On the one hand, the calendar used in Iraq and the Levant, as well as by Syriac Christians elsewhere, has been assimilated to the Gregorian calendar (and previously to the Julian), preserving only the Babylonian names:
January : Kānūn II (hebr. Ṭēbēth)
February : Šubāṭ
March : ˀĀdhār
April : Nīsān
May : ˀAyyār
June : Ḥazīrān (hebr. Sīwān)
July : Tammūz
August : ˀĀb
September : ˀAylūl
October : Tišrīn I
November : Tišrīn II (hebr. Marḥešwān, akk. Samnu)
December : Kānūn I (hebr. Kislēw)
Quite faithful to the pre-Julian Babylonian count, on the other hand, is the Hebrew calendar, which still uses lunar months, based on the observation of the moon, whereas all the above-mentioned calendars have made months into purely conventional subdivisions of the solar year. Consequently, it also uses intercalation, the insertion of additional months at certain intervals to compensate for the discrepancy between lunar and solar cycles.
Of the Greek calendars, the most commonly used was the Macedonian, which used the lunisolar computation of the Babylonian calendar, but the month names traditional in Macedonia; as such, it is essentially equivalent to the modern Hebrew calendar. It was developed in the wake of Alexander’s conquests, and became so widespread that it was often simply designated as ‘Greek’ or ‘Hellenic’ – in distinction to the Attic or Athenian calendar, which had great cultural importance for understanding classical literature, but was not observed outside of Athens. Other local or regional calendars were more rarely remarked upon and are less well understood, although some (such as the Delphic) are better attested than others.
There were two versions of the Macedonian calendars that synchronized it with the Julian calendar. The closer equivalence is given by the so-called Syro-Macedonian (as opposed to the ‘Asian’) calendar, where Greek months correspond exactly to Roman ones.
January : Audonaîos
February : Perítios
March : Dýstros
April : Xanthikós
May : Artemísios
June : Daísios
July : Pánemos
August : Lôos
September : Gorpiaîos
October : Hyperberetaîos
November : Dîos
December : Apellaîos
From Marinus’ Life of Proclus it emerges that, by the 5th century CE, the Attic calendar was also synchronized with the Roman solar calendar:
January : Gamēliōn
February : Anthestēriōn
March : Elaphēboliōn
April : Mounychiōn
May : Thargēliōn
June : Skirophoriōn
July : Hekatombaiōn
August : Metageitniōn
September : Boēdromiōn
October : Pyanepsiōn
November : Maimaktēriōn
December : Poseideōn
(All stressed on the last syllable.)
In short, it is fairly easy to transfer ancient festivals (at least those with known dates in well-understood calendars) to purely solar Gregorian or Julian dates, either using the equivalences listed above or through the Hemerology of the Months.
However, there are some observances which are strictly tied to the visible appearance of the Moon, which is one reason why many contemporary polytheists prefer to use a lunisolar calendar, such as Hellenion’s reconstructionist Attic calendar (off-site link; this is not an endorsement of Hellenion as an organization), which like the modern Hebrew calendar employs intercalation.
It is also feasible to keep a Julian- or Gregorian-aligned calendar for some purposes, and observe the moon for others.
3 Astronomical and astrological timing
beginning and end of the dayzodiac ~ months; lunaries
4 The Hebdomad and other Weeks
5 Other observations of time
year count and beginning of the year (various counts)
Proclus, On the Republic, vol. 2 – p. 284f of the translation (spring Zeus, summer Ares, autumn Aphrodite [Kore?], winter Kronos; all Hermes) – cf. Diodorus (Kronos winter, Aphrodite spring, …?)
Proclus on time, different time cycles, different seasons and planets etc. (Essay 13 and elsewhere)
Sun at different seasons (Macrobius), divisions of time of the Moon/month (PGM, etc.)
day and night, morning and afternoon (gods and heroes); stuff at sunrise/rise of other stars; Hesiod: morning and evening
Apophrades; Egyptian days; etc.
(in)auspicious times (for divination)
-ieron hmar (Schol. Il.)
-Scholia on Pindar: ierourgein tois hrwsi
-Scholia on Hesiod: pros meshmbrian
-DL: hrwsi d‘ apo mesou hmeras
6 New year and other annual festivals
Status: work in progress