Today I’m going to talk about perhaps one of the most annoying parts of practicing Hellenic polytheism. The dating of the Noumenia on the appropriate lunar phase. Because there is a lot of confusion sometimes about this, and even I, who has been doing this for years now, sometimes get mistaken. So here we go.
The Noumenia (Νουμηνία) or New Moon celebration is the first day of the lunar month in Hellenic polytheism. It is a pretty important occasion in the household cultus, as the blessings of various Gods are asked for the new month, and they are given worship and offerings in return. The presiding deities are Selene Noumenia (Σελήνη Νουμήνια) and Apollon Noumenios (Ἀπόλλων Νουμήνιος). The former is Moon herself, worshipped appropriately when she appears once more in the night sky after her dark phase. The latter presides as the tutelary deity over the celebrations of the Noumenia.
Besides these two other Gods are also honoured, most notably the various household Gods: the Theoi Ephestioi (Θεοί Ἐφεστίοι, “Gods around the Hearth”, the Gods inside the house), the Theoi Herkeioi (Θεοί Ἑρκείοι, “Gods of the Courtyard”, which includes only Zeus Herkeios (Ζεύς Ἑρκεῖος), or may include the Penates in terms of Roman polytheism or a Greco-Roman syncretic practice), and the Theoi Strophaioi (Θεοί Στροφαῖοι, “Gods at the Door”, which Gods as Apollon Agyieus (Ἀπόλλων Ἀγυιεύς) and Hermes Enodios (Ἑρμῆς Ἐνόδιος), who guard the borders of the household and protect household members when they venture outside of the household).
Yet other deities may also be honoured, such as Zeus and Hera, and any deities that members of the household are devoted to, or that they find appropriate. In Hellas herself, many who practice their ancestral religion use the first hymn in the collection known as the Orphic Hymns (Ὀρφικοί Ὕμνοι) – the “Prayer to Mousaios”, minus the introductory lines about Orpheus instructing Mousaios in the Orphic rites – in their Noumenia celebration , as do I myself.
So far, so good. But now for the confusing part. In modern times, the new moon is defined by astronomers as being the dark phase of the moon. So when you look up “new moon” in lunar calendar apps, that’s what you are going to get. The ancient Hellenes, however, defined the new moon as being the day after the dark phase of the moon. Which is more logical when you think about it, for how can the moon be “new” when she is not visible? It makes more sense that she is “new” when the moon crescent is again visible following her dark phase. The Noumenia, then, takes place on the evening of the first sighting of the moon following the dark phase.
This is very important to get right, because on the night dark phase of the moon, which astronomers define the “new moon” as, Hellenic polytheists celebrate Hekate’s Deipnon (Ἑκάτης Δεῖπνον), also known as Hena kai Nea (“Ἑνά και Νεά”, Old and New), honouring Hekate as she roams through the night with angered spirits of the dead in her trail, spirits of those who died and did not receive proper burial, or for some other reason can not cross over into the House of Hades.
Hekate is honoured on this occasion with an evening meal, a Deipnon in Hellenic, which is traditionally left for her at crossroads where three roads meet. The form in which she is worshipped there is Trioditis (Ἑκάτη Τριοδῖτις), and she is asked to, as she roams the world with miasmatic presences from the Underworld in her wake, to let any miasma (μίασμα, “stain, defilement”, something ritually unclean) affecting the household be absorbed into that mass and thus purify the household of it. Thus, it is also appropriate to address her as Apotropaia (Ἀποτροπαῖα, “Averter (of Evil)”) in reference to her purifying role.
Furthermore, it is advised that in the days leading up to the Deipnon, the house is completely cleaned, to further underscore the removal of miasma and the old worries for Hekate’s Deipnon, and the bringing in of purity and new blessings at the Noumenia. The Deipnon can also be a good occasion to make good on vows that have yet to be fulfilled on your end of the deal, or get other stuff that you have been avoiding done, so you can start the new month without all these distractions on your mind when the Noumenia comes.
A further complication can occur because the ancients defined the beginning of the day differently than we do. In our modern times, the day begins at what is, in fact, an arbitrarily defined “midnight”, with the evening belonging to the previous day, and most of the night, morning, and actual day belonging to the following day. The ancients, on the other hand, defined the day as beginning at sunset, when the sun had disappeared completely below the horizon, up to the next sunset. This can have consequences as it is the evening following the first sighting of the moon crescent that is celebrated as Noumenia.When this occurs early in the evening, that evening will count as Noumenia, with the previous night having been the Deipnon. But if the crescent becomes visible only later during the night, or in the morning, or at noon, then it will be the evening after that which will be the Noumenia, with the evening before the sighting of the moon crescent being the Deipnon.
Is your head spinning yet?
 According to the Liddell, Scott, Jones Ancient Greek Lexicon (LSJ), the Roman Penates are called Herkeioi (Ἑρκεῖοι) in the Hellenic language. See the entry for ἑρκεῖος.
 A public domain translation by Thomas Taylor is available for free here. It is a poetic translation, making it perhaps more useful for ritual contexts than the more accurate translation by Apostolos Athanassakis, which was recently re-published and can be found here. You can find the texts in original Hellenic here.
 See “Hellenic Polytheism : Household Worship (Volume 1)“, published by the Hellenic polytheist organisation Labrys, which operates in Hellas herself.