Conventional delineations of The Nine Muses' spheres and names are dissatisfying, questionable, vague, overlapping, redundant.
More likely explanations may be:
Kleio (Κλειώ) - Goddess of the key, Goddess who opens the divine channel
Euterpe (Εὐτέρπη) - Goddess of turning (τρέπ=turn), turn of phrase, looking at things in a new light, asking questions, questioning (έρωτημα)
Thaleia (Θάλειά) - Goddess of growth, coaxing forth (ideas, art) from budding beginnings
Melpomene (Μελπομένη) - Goddess of determination, sticking with an idea, putting a lid on it and focusing on it exclusively; μέλω=to be an object of care or thought + lid, cover (πομ)
Terpsichore (Τερψιχόρη) - Goddess of soulful expression, of the choir/chorus
Erato (Ἐρατώ) - Goddess of expression of passionate love
Polyhymnia (Πολύμνιά) - Goddess of creating many hymns
Ourania (Οὐρανίη) - Goddess of interpreting the stars
Kalliope (Καλλιόπηι) - Goddess of beautiful (Καλλι) + bridging? everything? (π)
This Hymn to the Muses probably began a second day's performances. The Hymn to Mnemosyne, Goddess of Memory, immediately preceded this one and seemed to indicate at the end that it was time for sleep (at least for the audience, initiates would presumably go through initiation and then sleep). The end of this hymn suggests it occurs at sunrise.
This Hymn begins with lots of loud noises, a way to draw attention back to the stage and the performance, in much the same way that the special effects sounds of thunder in the Hymn to Zeus would have riveted everyone's attention at the commencement of the first day of performances.
Recall that the first Hymn of Orpheus begins with a Hymn to the Muse that introduced all the deities who would be featured. This second day, again, begins with homage to the Muses. It is a well-respected convention of poets to commence their work by paying homage to the Muses, as demonstrated in the examples, below (from Theoi.com) (note that the first three examples are from Line 1 of the piece):
Homer, Odyssey 1. 1 ff (trans. Shewring) (Greek epic C8th B.C.E.) :
"Goddess of song (Mousa, Muse), teach me the story of a hero . . .
Pindar, Olympian Ode 9. 80 ff :
"Now may invention grant my tongue, riding the Mousai's (Muses') car, fit words to tell my tale . . .
Pindar, Paean 7 :
"But I pray to Mnamosyna (Memory), the fair-robed child of Ouranos (Uranus, Sky), and to her daughters [the Mousai, Muses], to grant me ready resource
Sappho, Fragment 128 :
"Hither now, tender Kharites (Charites, Graces) and lovely-haired Moisai (Muses) . . .
Aristophanes, Frogs 870 (trans. O'Neill) (Greek comedy C5th to 4th B.C.E.) :"Invoke the Mousai (Muses) with a song.
Bacchylides, Fragment 1 (trans. Campbell, Vol. Greek Lyric IV) (C5th B.C.E.) :"Famous lyre-players [the Mousai, Muses], daughters of high-ruling Zeus, come hither,
Apollonius Rhodius, Argonautica 4. 1380 ff :
"I [the poet] am the mouthpiece of the Mousai (Muses)
Callimachus, Iambi Fragment 14 :
"O Mousai (Muses) fair and Apollon to whom I [the poet] make libation
Alcman, Fragment 3 :
"Mosai Olympiades (Olympian Muses) fill my heart with longing for a new song . . .
Terpander, Fragment 4 (trans. Campbell, Vol. Greek Lyric II) (C7th B.C.E.) :"Let us pour libation to the Mousai (Muses), the daughters of Mnamas (Memory), and to the leader of the Mousai, Leto's son [Apollon]
Plato, Phaedrus :
"Sokrates: Come, O ye Mousai (Muses), melodious, as ye are called,
Oppian, Halieutica 3. 5 (trans. Mair) (Greek poet C3rd C.E.) :
"The kindly Mousai (Muses) have furnished forth my mind and have crowned me with the gift divine of song and given me to mix a sweet draught for your ears and for your mind.
Virgil, Georgics 2. 475 ff (trans. Fairclough) (Roman bucolic C1st B.C.E.) :
"But as for me [Virgil the poet]--first may the Musae (Muses), sweet beyond compare, whose holy emblems, under the spell of mighty love, I bear, take me to themselves, and show me heaven's pathways,
Apuleius, Metamorphoses (Retitled post-mortem: The Golden Ass) 11. 224 ff (trans. Walsh) (Roman novel C2nd C.E.) :
"Hymning a charming song composed to music by a talented poet with the aid of the Musae (Muses)."
76. Μουσῶν, - of the Muses, Goddesses of Inspiration
θυμίαμα - incense
λίβανον. - of Lebanon, frankincense
Μνημοσύνης - Mnemosyne, Goddess of Memory = Mind (Μνη) + house, tower, enclosure, slip for shipbuilding (μοσύν)
Ζηνὸς - Zenos/Zeus, God of Fertilzing Principle/Spark of Fire/Life; Rain/Lightning
ἐριγδούποιο - upon; very (ἐριγ) + any loud, heavy sound, thud, din or battle, roar of the sea, loud (δούποιο) = "loud-sounding, loud-thundering" (referring to Zeus as loud, probably stage directions)
θύγατρες, - daughters = divine (θύ) + earth's (γα) + extension (τρες)
Μοῦσαι - Muses
Πιερίδες, - of Pieria, the coastal region around Mount Olympos, "home" of the Muses
μεγαλώνυμοι, - great, majestic (μεγαλ) + named (ώνυμοι) = "with great name"
ἀγλαόφημοι, - glorious (ἀγλαό) + fame, praise, reputation; prophesy, utter (φημοι) = "of splendid fame"
θνητοῖς, - mortal
οἷς - bear, carry, convey
κε - core
παρῆτε, - entreat, ask, implore, ask a favor
ποθεινόταται, - longed for, desired, dear to, exciting a tender longing
πολύμορφοι, - many, multi, poli (πολύ) + shape, form (μορφοι) = mult-formed, manifold
πάσης - all, whole
παιδείης - youth, childhood
ἀρετὴν - excellent, good; Arete is the Goddess of virtue, excellence, goodness
γεννῶσαι - create, produce from oneself, engender, produce, generate, parent
ἄμεμπτον, - above (ἄ) + reproach, blame (μεμπτον) = above reproach, blameless
θρέπτειραι - one who nurses, nourishes, feeds, fosters, brings up; teaches
ψυχῆς, - of the soul, Psyche
διανοίας - thought, intention, purpose, intellect = directed (δια) + mind (νοίας)
ὀρθοδότειραι, - "giver of right judgment" = straight (ὀρθο) + giver (δότειραι)
καὶ - and
νόου - mind
εὐδυνάτοιο - well directed = essence pure (εὐ) + strong, mighty, powerful, influential, capable, dynastic (δυνάτοιο)
καθηγήτειραι - one who guides, teaches, leads
ἄνασσαι, - Queens
αἳ - arising divine-power, eternal
τελετὰς - complete, fulfill; initiate, make magically potent, mystic rites
θνητοῖς - mortal
ἀνεδείξατε - lift and show, proclaim, declare, manifest, show-forth = arising (ἀνε) + show, prove, display (δείξατε)
Κλειώ - κλείς = key, Kleio, Goddess of Fame, Renown; celebrate, call (Kleio opens up/unlocks the channel to the divine)
τ’ - too then
Εὐτέρπη - Euterpe, "delightful, charming," essence pure (Εὐ) + delight, gladden, cheer, enjoy?? (τέρπη); wicker-frame/basket for drying things? stretch essence outflow-of all?? έρωτημα=interrogative, question inviting an answer, that which is asked, questioning; έρπη=creeping thing, reptile, snake, anything that crawls (insect, small mammal, reptile; beast or animal that goes on all four legs; anything that crawls i.e. baby, reptile); ἕρπω=move on the ground; πῆς=child; έρῶ=say, speak, tell, proclaim; ἕρως=love; έρωή=quick-motion, rush, force or swing of a shovel, throw a spear; ἕτερος=either, one or the other of two, one follows on another, another, another with a sense of difference; different, other, different; on one side; uneven; stronger on one side (probably: stretch/extend essence flow of the whole, of the territory=probably more related to questioning or maybe warfare or maybe family/clan/companion solidarity?, probably keep balanced tension under the same roof--- the "delight" is derived from Ψ which is the soul, "stretch/extend the soul")
Θάλειά - Thaleia, rich, plentiful, abundance, young shoot, young branch, olive shoots, sprout, grow, thrive, heat, first-fruits, of the sea, bed-chamber, wedding-bed chamber, den, lair, "divine arising loosened"
τε - too then
Μελπομένη - Melpomene, celebrate with dance and song, sing (Μελπο) + strong, mighty (μένη), μέλω=to be an object of care or thought, care for, take an interest in + lid, cover; drink, draft; Phoenician (πομ)
τε - too then
Τερψιχόρη - Terpsichore, Pythagorean name for 9 = enjoyment, delight, territory of the soul (Τερψι) + chorus, dancers, choir (χόρη)
τ’ - too then
Ἐρατώ - Erato, of love, the lovely, love warmly/passionately
τε - too then
Πολύμνιά - Polymnia, multi, many, poli (Πολ) + hymns (ύμνιά)
τ’ - too then
Οὐρανίη - Ourania, astronomy, the heavens
τε - too then
Καλλιόπηι - Kalliope = beautiful (Καλλι) + opening, hole; in what way, how; in such manner as; to which place, whither; somewhere, anywhere; religious awe, due reverence; juice, gravy; as many, as many as; appearance, sight, power of seeing (όπηι) ( this is all over the place; όπη="entity under-the-same roof shared-enter; entity bridged shared-center") καλλωπισμα= ornament, adornment; beautiful eyes? beautiful feet?
σὺν - together with
μητρὶ - the Mother
καὶ - and
εὐδυνάτηι - well directed = essence pure (εὐ) + strong, mighty, powerful, influential, capable, dynastic (δυνάτοιο)
θεᾶι - Goddesses
Ἁγνηι. - Pure, Holy
ἀλλὰ - but
μόλοιτε, - meta entity loosen (μόλ) + fate (οιτε)
μύσταις, - mystic, mysterious, mystai, initiates
πολυποίκιλοι, - multi- many, poli (πολυ) + many-colored, diverse, intricate, changeable (ποίκιλοι) = much-variegated, manifold
ἁγναί, - pure ones
εὔκλειαν - "good repute, glory, honored, famed" = essence pure (εὔ) + call; key (κλειαν)
ζῆλόν - zeal, eager rivalry, emulation; pride, honor, glory; jealous; vie with, emulate
τ’ - too then
ἐρατὸν - love, bring together
πολύυμνον - multi, many, poli (πολύ) + hymns (υμνον) = abounding in songs, famous, much sung of
ἄγουσαι. - August ones; also, morning light (this could be stage directions to sing hymns as the sun rises)