Also known as Hebdeman Ἑβδέμαν "the seventh" and polyphthoon πολύφθοον "many utterances" or "many cakes"
The Theophania is a festival welcoming Apollon home to Delphi from Hyperboria, with cake, music, and the reopening of the oracle. Though it is uncertain which date this was celebrated on historically, academic consensus agrees that it was likely the 7th of Bysios, also known as polyphthoon (πολύφθοον) "the day of many cakes" or “many utterances”, and Apollon's birthday. This is the first day of the season where the oracle opens, and the Pythia gives her readings.
How Apollon’s laurel sapling shakes! How all the shrine does tremble! Away, away, you impure! Do you not see Phoibos Apollon kicking at the doors with his fair foot? The Delian palm tree gently nods its head, of a sudden, and the swan sings beautifully in the air. Open, you door-bolts, of your own accord! Open, you locks! The god is no longer far away. Young men, get ready for the song and the dance!
– Callimachus’s Hymn to Apollo
Βυσίου [μην]ὸς τὰν hεβδέμαν καὶ [τ]ὰν hενάταν Bysios month the seventh and the ninth
– A Collection of Greek Ritual Norms (CGRN) – Two excerpts from the dossier of regulations of the Labyadai at Delphi $^{5}$
Apollon's return to Delphi, and his birthday. Also the day the Pythia gave her oracles (in some time periods, said to have been the only day). It is a festivity of the theophaneia type.
We know of a paian composed by Alkaios, describing the celebrations that attend Apollo’s long-anticipated first arrival at Delphi from the land of the Hyperboreans (Himerius Or. 48.10-11 = Alcaeus Fr. 307c), and the Theophania would have been an obvious occasion for its first performance.
– Hugh Bowden, Athens and Delphi in the Classical Period: Exploring a Religious Relationship$^{13}$
Accordingly “Bysios” is “pysios,” the month of oracular inquiry, in which men ask questions and obtain responses from the god; for this is the legitimate and traditional procedure. In this month, then, oracles used to be given and the seventh day of this month they consider the birthday of the god. They call this day the day of Many Utterances (Polyphthoös πολύφθοον) not because they then bake cakes (phthoïs), but because it is a day when many inquire of the god and receive many oracles. For only recently have monthly oracles been given out to inquirers; formerly the prophetic priestess was wont to give responses but once a year on this day, as Callisthenes and Anaxandrides have recorded.
– Plutarch, Greek questions
A feast with (a） offerings of the cake called φθοΐς; the day was, according to Plutarch, called πολύφθοον, which, though he gives another interpretation, is clearly from φθοΐς
– W. Smith, LLD, W. Wayte, G. E. Marindin, A Dictionary of Greek and Roman Antiquities $^{86}$
It is probable that this day corresponds to the Delphic Theophania mentioned by Herodotus. Some scholars believe that the Theophania on the 7th of Bysios was also the occasion of Alcaeus’ paean, but this cannot be reconciled in any way with the “middle of summer,” however conceived.
– T. Bilić, Calendric Aspects of Myths and Cults Involving Apollo's Visit to Hyperborea$^{45}$