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5. καλλίσφυρος, τανίσφυρος and εὔσφυρος in Hesiod
αἵ ῥα πολυσπερέες γαῖαν καὶ βένθεα λίμνης
πάντῃ ὁμῶς ἐφέπουσι, θεάων ἀγλαὰ τέκνα.
It is difficult to infer any meaning from this use of the word because it appears in the simple summation of a catalogue. But it nevertheless seems an important description because it applies to the group of rivers as a whole, tying together the entire passage.
Ζῆλον καὶ Νίκην καλλίσφυρον ἐν μεγάροισι.
Since Styx and her sisters were earlier identified as τανίσφυρος, it is not surprising that Styx’s female offspring should acquire a related epithet. For it has already been noted that epithets are often transferred from a parent to an offspring. Nike is here an extension of Styx and of her identity.
ἠγάγετο Κλυμένην καὶ ὁμὸν λέχος εἰσανέβαινεν.
ἡ δέ οἱ Ἄτλαντα κρατερόφρονα γείνατο παῖδα.
καλλίσφυρος does not refer to her name but to her patronymic, and this combination recalls the conclusion of the catalogue and the mention of the τανίσφυροι ὠκεανῖναι. τανίσφυροι ὠκεανῖναι and καλλίσφυρον Ὠκεανίνην occupy the same position in the hexameter and are phrases almost identical in meter and in sound. The use of the epithet is generated by the mention of the name. But once again it must be noted that καλλίσφυρος has different metrical value from τανίσφυρος. It could not be primarily the metrical exigencies of the line that generate the use of these related epithets, but it must be the thematic connotations of the epithets that associate them with these characters. These two phrases provide a straightforward indication that the uses of τανίσφυρος and καλλίσφυρος are generated by the same themes and have the same connotations.
πνοιάς τε ζαέων ἀνέμων σὺν Κυματολήγῃ
ῥεῖα πρηΰνει καὶ ἐυσφύρῳ Ἀμφιτρίτῃ.
Amphitrite is the only one of the Nereids named twice in the catalogue, and so her name stands out among the spirits of water.
Περσηὶς Κίρκην τε καὶ Αἰήτην βασιλῆα.
Αἰήτης δ’ υἱὸς φαεσιμβρότου Ἠελίοιο
κούρην Ὠκεανοῖο τελήεντος ποταμοῖο
γῆμε θεῶν βουλῇσιν, Ἰδυῖαν καλλιπάρηον·
ἣ δή οἱ Μήδειαν ἐύσφυρον ἐν φιλότητι
γείναθ’ ὑποδμηθεῖσα διὰ χρυσῆν Ἀφροδίτην.
This passage is, once again, about sexual mingling and procreation, about the birth of a child to Iduiya, a daughter of Okeanos. Medea’s identification as εὔσφυρος continues the thematic pattern of the epithet’s appearance in the Theogony. Medea is a particularly colorful and sinister variant of the sea figures who receive the epithet. As Hesiod indicates, she is a niece of Kirke, an alluring but demonic character strongly connected both with her sexuality and with death. Medea herself appears elsewhere as no less of a compelling and evil force. Her character and powers are described frequently, most notably in Euripides’ play,  as both a passionate wife and a murderess. She is a descendant of Okeanos with overt sexual and morbid qualities.
Ἡρακλέης ἔκτεινε, κακὴν δ’ ἀπὸ νοῦσον ἄλαλκεν
Ἰαπετιονίδῃ καὶ ἐλύσατο δυσφροσυνάων …
ὄφρ’ Ἡρακλῆος Θηβαγενέος κλέος εἴη
πλεῖον ἔτ’ ἢ τὸ πάροιθεν ἐπὶ χθόνα πουλυβότειραν.
She appears only as a point of reference in an account of her son’s heroism. She is important because she is the mother of Heracles, who by Zeus’ will is increasing his κλέος and approaching his destined immortalization. The next passage, in fact, in which Alcmene is καλλίσφυρος is a description of Heracles’ transformation from mortal to immortal and of his ascent to Olympos:
ἲς Ἡρακλῆος, τελέσας στονόεντας ἀέθλους,
παῖδα Διὸς μεγάλοιο καὶ Ἥρης χρυσοπεδίλου,
αἰδοίην θέτ’ ἄκοιτιν ἐν Οὐλύμπῳ νιφόεντι·
This passage parallels both in theme and in diction the description of Heracles’ transformation in Odyssey xi where καλλίσφυρος appears.  It also echoes the language and subject of the earlier passage in the Theogony where Alcmene receives the same epithet. For the mention of Heracles’ increasing κλέος in line 526 is a foreshadowing of this event. So there is a consistent thematic correlation among the passages about Heracles where this epithet occurs.
πρίν γε φόνον τείσαιτο κασιγνήτων μεγαθύμων
ἧς ἀλόχου, μαλερῷ δὲ καταφλέξαι πυρὶ κώμας
ἀνδρῶν ἡρώων Ταφίων ἰδὲ Τηλεβοάων.
After killing Elektryon, Amphitryon carries off his daughter Alcmene as his bride. This combination of murder and romantic conquest is not uncommon in hero cycles and appears similarly in the stories of Medea and Marpessa. But this particular union is unusual because Amphitryon is barred from his wife’s bed; their marriage is ἄτερ φιλότητος (15). He cannot consummate their relationship until he avenges the death of Alcmene’s brothers. Once again, εὔσφυρος appears in a context of sexuality and abduction, but this instance is a negative variation of the familiar theme. It is a situation of forced abstention rather than of forced fulfilment.
εὐνῇ καὶ φιλότητι μίγη, τέλεσεν δ’ ἄρ’ ἐέλδωρ·
This passage presents an explicit contrast with the earlier one, describing the fulfilment of love that replaces the earlier lack of it.
He refers to his parents’ marriage as a complete and joyful one. Alcmene is united with her mortal husband. The early sexual taboo has been lifted, the disruptive divine interference has disappeared and the natural relationship endures. This is the third and final passage which refers to the marital status and, implicitly, to the sexual union, and it is the final place where εὔσφυρος or τανίσφυρος appears in the poem.
ζώει δ’ ἔνθά περ ἄλλοι Ὀλύμπια δώματ’ ἔχοντες
ἀθάνατος καὶ ἄγηρος, ἔχων καλλ[ίς]φυρον Ἥβην,
παῖδα Διὸς μεγάλοιο καὶ Ἥρης χρυσοπεδίλου·
This passage is another illustration of the connection between this specific theme and the series of epithets in question. 
ἣ Περσῆ’ ἔτεκεν κρα]τ̣ε̣[ρὸ]ν μ[ής]τωρ[α] φόβοιο.
The poet only mentions her in a catalogue, as the mother of Perseos, but this fact invokes the circumstance of that birth and of her rape by Zeus, a situation which Zeus recalls in Iliad XIV 319 and where Danae is also καλλίσφυρος.
[ πρὸς ἀνθρώπων ἀ]παναίνετο φῦλον ὁμιλ[εῖν
ἀνδρῶν ἐλπομένη φεύγ]ε̣ιν γάμον ἀλφηστάων̣[.
[ ]τ̣ανι̣σ̣φ̣ύ̣[ρ]ο̣υ̣ εἵνεκα κού[ρης
She appears similarly as [τ]ανίσφ̣υ̣ρ[ο]ς… κούρη in the narration of the contest her father Schoineos establishes for the winning of her as a bride (75.6). Each suitor must race with Atalanta. If he wins, he may take her off as his bride; if he loses, he must die. Hippomenes wins, gaining possession of Atalanta and avoiding death.
αἶ]ψα [δ’ ἄ]ρ̣’ ἀ[λλ]ήλοις[ι]ν ἔρις καὶ ν[εῖκος] ἐτ[ύχθη
Σισύφωι ἠδ’ Αἴθωνι τανισφύρο[υ εἵ]νεκα [κούρης,
The matter is finally settled when Poseidon abducts her to the island of Koos and has children by her (55–57). This translation to an island has morbid overtones, as it does elsewhere. The entire episode, the rape and the translation, involve themes of sexuality, death and rebirth which are common to the other myths where the epithets appear.
υἱὸς Λαέρταο πολύκροτα μήδεα εἰδώς.
δῶρα μὲν οὔ ποτ’ ἔπεμπε τανισφύρου εἵνεκα κούρης·
As in many other examples, the epithet associated thematically with one character transfers to that character’s child, who is simply an extension of the parent’s identity. In light of this transfer, Leda’s description as καλλίσφυρος in the Hymn to the Dioskouroi is perhaps all the more significant.