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4. καλλίσφυρος and τανίσφυρος in the Homeric Hymns
ναίει τερπόμενος καὶ ἔχει καλλίσφυρον Ἥβην.
This line is almost identical to Odyssey xi 603. And as in this passage in the Odyssey, Heracles’ union with Hebe is the symbol of his new state of existence. Hebe appears elsewhere in the Homeric Hymns, but only here does she bear this epithet. She is καλλίσφυρος only because she reflects Heracles’ entrance into the Olympian community.
Τυνδαρίδας Λήδης καλλισφύρου ἀγλαὰ τέκνα,
Κάστορά θ’ ἱππόδαμον καὶ ἀμώμητον Πολυδεύκεα.
Leda appears only as a point of reference, as a genealogical identification. The epithet pertains as much to her offspring as it does to her. Leda appears elsewhere in the Hymns, but only here is she καλλίσφυρος, in her identity as the mother of the ἀγλαὰ τέκνα and the consort of Zeus. The description of Hebe in the Hymn to Heracles and in the Odyssey illustrated earlier how a quality is transferred from a male to his female counterpart. And certainly the identification of parent and child and the transference of qualities from one to the other is a common feature in Greek poetry.  In light of this association, this use of καλλίσφυρος is comparable to its other uses in the Hymns and in Homer. The ambiguity of the Dioskouroi’s origin and their possible translation from mortal to immortal recall the Heraclean tradition and his association with the epithet.
ἀθανάτων βουλῇ τε καὶ ἔργμασιν ἔξοχ’ ἀρίστους.
In her union with an Olympian god she is like other recipients of the epithet. Unlike Leda, Danae or Marpessa, however, Leto is not a mortal, but a Titaness. There is no mingling of mortal and immortal, no tension between these two realms of existence. In this respect Leto does not fit into the pattern of the earlier examples.
αὐτὴν ἠδὲ θύγατρα τανίσφυρον ἣν Ἀϊδωνεὺς
The crucial facts are all stated, and one of them is that Persephone is τανίσφυρος.
εἰδήσεις· δὴ γὰρ μέγα ἅζομαι ἠδ’ ἐλεαίρω
ἀχνυμένην περὶ παιδὶ τανυσφύρῳ·
τανίσφυρος refers to the same character as it did earlier, but it appears here with another noun. In line 2 it qualifies θύγατρα, while here it qualifies παιδὶ, a word of different metrical value from the first. This discrepancy suggests that it is the character and her situation, and not metrical exigencies, that prompt the use of the epithet.
ἑστήκει πανάφυλλον· ἔκευθε δ’ ἄρα κρῖ λευκὸν
μήδεσι Δήμητρος καλλισφύρου·
Even in its specific isolated context the use of the epithet here is noteworthy. For, as Richardson points out,  there are other epithets of identical case, metrical value and position that the poet could employ as easily. Demeter is, for example, χρυσαόρου in line 4 of this same hymn and πολυφόρβης in Hesiod Theog ony 912. The epithet has a functional equivalent in the same poem and so its use ought to be explained on other grounds.