'harmonic' originates from Greek, specifically the word 'harmōnia', where the root 'harm-' meant 'fit' or 'join together'.

'harmōnia' passed into Latin as 'harmonia' and Old French as 'harmonie', and from Middle English the modern English 'harmony' and adjective 'harmonic' developed; the adverb 'harmonically' was formed by adding the adverbial suffix '-ally' to 'harmonic'.

Initially it meant 'agreement, joint fitting' in a broad sense; over time the term became strongly associated with the musical sense of 'concord of sounds', and the modern adverb now commonly denotes either musical concord or more general agreement/consistency.