To buy them time between improvisations, the singer-poets repeated stories (such as that of Agamemnon's murder in The Odyssey) and used recurring epithets -- pithy tags attached to characters ("grey-eyed Athena ," "swift-footed Achilles") -- and epic (or Homeric) similes, or repetitive poetic comparisons ("rosy-fingered Dawn," "the wine-dark sea"). It is important to remember that The Iliad and The Odyssey were originally oral entertainment -- much of the pleasure for the ancient Greeks came not from the narratives with which they were familiar, but rather from the sound of the poetry, which is still unmatched in the epic poetic tradition for its beauty and grandeur.
Throughout The Odyssey, Greek values and the Greek culture are constantly shaped by the flow of the author’s pen, which narrates a story with an intricate plot. The epic allows the modern-day public know about the times when men fought with their hands and their heads, when the gods dominated cultures, and when love and faithfulness meant something. The Odyssey is a great work of a great poet, Homer, who not only captures the essence of the ancient Greek spirit and culture, but also tells a story that can be passed down from generation to generation, without any fear of growing old.
The word “formula”, despite its usefulness, encourages a tired approach to the line, the assumption being that these ancient iterative forms are more limited than literature. I don’t think you can detect the scale of the Odyssey, its mighty open-endedness and the mystery of its creatures, until you’ve developed a sense of its different attitude to Time, as expressed in particular through this Dawn formula. You have to read its cyclical stuckness, its sideways movement, its minimalist music not just as a compositional aid but as something more like the neurotic patterning of the Egyptian Book of the Dead, in which Dawn (a crimson human torso with spreading hands) is a point of contact between two worlds – a prayer.