'inharmonic' originates from Latin-derived negative prefix 'in-' combined with 'harmonic', which ultimately comes from Greek 'harmōnikos' (from 'harmōnia'), where 'harm-'/ 'harmō-' meant 'joining, fitting together'.

'harmonic' came into English via Late Latin 'harmonicus' and Medieval/Old French forms from Greek 'harmōnikos'. The English word 'inharmonic' was formed in modern English by adding the negative prefix 'in-' to 'harmonic'.

Initially, related words centered on 'joining' or 'agreement' (harmony). Over time, 'inharmonic' retained the general sense 'not in agreement' but became specialized in acoustics to mean 'partials not integer multiples of the fundamental'; it also keeps the broader sense 'discordant'.