'antiphonically' originates from Greek, specifically the word 'antiphōnos' (from 'anti-' + 'phōnē'), where 'anti-' meant 'opposite' or 'in return' and 'phōnē' meant 'voice' or 'sound'.

'antiphonically' changed from the Greek term 'antiphōnos' into Late Latin 'antiphona' and Old French 'antiphone', then entered Middle English as 'antiphon' and developed into the adjective 'antiphonic', from which the adverb 'antiphonically' was formed in modern English.

Initially it referred specifically to a 'responsive song or chant' (a musical form). Over time it broadened to describe anything done in a responsive or alternating manner, giving the modern adverbial sense 'in an antiphonic/alternating way'.