Dionysos subsequently rescued his mother from Hades and conferred immortality upon her under her new name, Thyone (the starry crown of the constellation Ariadne).
This is a first-pass attempt to translate the hymn.
44. Σεμέλης, - Semele
θυμίαμα - incense
στύρακα. - styraka, storax
Κικλήσκω - call, summon, invite, invoke, implore = core divine-power (Κι) + core loosen (κλ) + artfully, in a practiced manner (ήσκω)
κούρην - daughter = core entity pure outflow-of (κούρ) + ninth (ην)
Καδμηίδα - of Kadmeia, Cadmean, ancient inhabits of Greecian Thebes, descendants of Cadmus/Kadmos (credited with introducing the Phoenician-based alphabet to Greece circa 2000 BCE - 800 BCE) (so, Semele is very ancient) = jar, vessel, urn (Καδ) + (divine-medium shared-center divine-power directing arising (μηίδα) -also- (cadmia, calamine, zinc ore (used in the production of brass))
παμβασίλειαν, - all Queen, all- Basiliean
εὐειδῆ - beautiful, well-shaped, comely = essence pure (εὐ) + form, shape, pattern, figure (ειδῆ)
Σεμέλην, - Semele, mortal mother of Dionysos, the God of wine = synchronized beginning (Σε) + object of care or thought, concern; musical phrase, music; limb; honey; meta essence loosened (μέλ) + ninth (ην)
ἐρατοπλόκαμον, - lovely tressed = lovely, beloved (ἐρατο) + braids (πλόκαμον)
βαθύκολπον, - "with dress falling in deep folds" = deep (βαθύ) + fold of a garment, fold, crease, bosom, lap, vagina, womb, any bosom-like hollow (κολπον) (possible double-meaning since she was the lover of Zeus!)
μητέρα - mother of
θυρσοφόροιο - thyrsus- bearing (the thysus is the pinecone-tipped staff of Dionysos)
Διωνύσου - Dionysos, the God of wine
πολυγηθοῦς, - much-cheering, delightful, gladsome = many, multi, poli (πολυ) + rejoice, cheerful (γηθοῦς)
ἣ - shared center
μεγάλας - great, megalas, magnificent, splendid
ὠδῖνας - travail, anguish of childbirth/parturition = bring-forth directed-trajectory divine-power tipping-point
ἐλάσσατο - release, drive, set in motion, drive away, expel = essence loosened
πυρφόρωι - to be a torch-bearer, to be a bearer of sacred fire, carry fire = fire (πυρ) + bear, carry (φόρωι)
αὐγῆι - light, daylight, dawn, morning light (the conflagration brought forth Dionysos to the light of day)
ἀθανάτου - immortal= arising above divine tipping-point/mortality
φλεχθεῖσα - kindle, inflame, burn, burn up, light up, blaze (φλεχ) + holy (θεῖσα)
Διὸς - Dios, Zeus, God of the rain storms, male fertilizing principle
βουλαῖς - of the council, epithet of certain Gods and Goddesses as having status in the Council Chamber, i.e., Hestia
Κρονίοιο - Kronion, (son) of Kronos
τιμὰς - held in honor, esteemed, valued, prized, honor, revere, reverence
τευξαμένη - make, produce by work or art, technology (τευξα) + spirit, passion, strength, force, might (μένη)
παρ' - having to do with, alongside
ἀγαυῆς - illustrious, brilliant, glorious, noble, stately, proud
Περσεφονείης - Persephone, Goddess of afterlife and new life in spring
ἐν - in, within
θνητοῖσι - mortals (tipping point of mortal death distinguishes mortals from divinity) (divine tipping-point (θν) + heart/the seat of life=ητοῖσι; so, when the heart stops a mortal life ends and is by definition not divine)
βροτοῖσιν - mortal = basis (β) + rotates (ροτ) + entity (οῖσιν) (possibly describing reincarnation, a series of mortal lives)
ἀνὰ - arising
τριετηρίδας - triennial festival, celebrated every third year = three (τρι) + term of years (ετηρ) + (ίδας) (in practice, every other year)
ὥρας,- period, season, horai
ἡνίκα - at the time when, whenever, when, at which point of time
σοῦ - thou
Βάκχου - Bakchos
γονίμην - productive, fertile, fruitful, born in lawful wedlock, generative power
ὠδῖνα - travail, anguish of childbirth
τελῶσιν - toll
εὐίερόν - holy, fit for sacrifice = essence pure (εὐ) + holy (ίερόν)
τε - too then
τράπεζαν - table, dining-table, eating-table, money-changer's counter, any table or flat surface on which a thing rests, platform, slab
ἰδὲ - in that case, then; behold; form, shape, semblance
μυστήριά - mystery
θ' - divine
ἁγνά. - pure (may refer to bringing an offering to the altar or possibly some symbol)
νῦν - now, at present
σέ, - thou
θεά, - Goddess
λίτομαι, - simple, plain, frugal, unadorned
κούρη - daughter
Καδμηίς, - of Kadmos
ἄνασσα, - queen, lady, anassa
πρηύνοον - of gentle mind, soft, mild, gentle, tame
καλέων - beautiful
αἰεὶ - eternal
μύσταισιν - mysterious
ὑπάρχειν. - foundation, beginning, being, underpinning