'asonant' originates from French, specifically the word 'assonant', where the prefix 'as-' (from Latin 'ad-') meant 'to/toward' and 'soner' (from Latin 'sonare') meant 'to sound'.

'asonant' changed from Old French/French 'assonant' (present participle of 'assoner'), which in turn derives from Late Latin 'assonare' (from 'ad-' + 'sonare'), and was borrowed into English as 'asonant'/'assonant'.

Initially it carried the sense 'to make similar in sound' or 'to sound toward', and over time it evolved into the descriptive adjective meaning 'characterized by similarity of vowel sounds'.