Periodically rhymes with:
methodically, methodically, chronically, clinically, comically, critically, cynically, diametrically, electrically, electronically, empirically, ethically, fanatically, geographically, hermetically, historically, intrinsically, journalistically, magically, magnetically, majestically, mathematically, methodically, metrically, mineralogically, optimistically, parenthetically, pathetically, philosophically, physically, politically, pragmatically, ritualistically, romantically, sardonically, scientifically, skeptically, statistically, surgically, symbolically, sympathetically, tactically, technically, technologically, theatrically, theoretically, therapeutically, uncritically
Periodically sounds like:
paradoxical, paradoxically, particle, periodical, portugal, portugalia, pretzel, pritzl, prodigal, prodigiously, protigal, protocol