Here's what rhymes with tetrarchae.
guy chi quae kai by my high why die lie thy y buy cry sky tie vi hi shy sigh bi bye dye fi hy nigh pi pie thai thigh vie dei ly psi rye ty wir awry hai lye mai muy nai wry cy fy lai luy mei sy tai thei wai phi dry try fly rely alkali spy fry ply sly alibi pry tri trie lullaby pri sty aquae stye lanai drachmai slier apply reply thereby deny nearby occupy whereby hereby defy glorify goodbye purify nullify ratify belie decry pupae untie mollify ramify bonsai ossify retry spry triply amebae blowfly horrify petrify turfy scurfy barfly shanghai ripply banzais yuppify supply imply clarify comply modify nuclei qualify classify verify certify gratify underlie amplify fortify pacify rectify samurai unify beautify falsify termini terrify typify amoebae codify descry edify liquefy mortify overlie vilify deify preoccupy stratify ultrahigh calcify liquify mummify prettify vitrify beatify gentrify overbuy justify satisfy stimuli multiply specify signify simplify testify butterfly notify alveoli diversify magnify standby crucify dignify personify resupply dragonfly firefly stultify vivify emulsify reunify stupefy cumuli overfly scarify versify declassify refortify speechify dandify identify quantify disqualify solidify acidify detoxify electrify mystify misapply reclassify revivify dissatisfy hyperbolae syllabify exemplify intensify indemnify objectify oversupply demystify transmogrify solemnify oversimplify misidentify