Greek 'eu-' (good) + 'phone' (sound) — the mirror opposite of 'cacophony,' sweetness of voice vs. harshness.
The quality of being pleasing to the ear, especially through a harmonious combination of sounds in words or phrases.
From Late Latin 'euphōnia,' from Greek 'euphōnía' (sweetness or goodness of sound, pleasantness of voice), a compound of 'eu-' (good, well, pleasant, true) + 'phōnē' (voice, sound, tone, utterance). The prefix 'eu-' derives from PIE *h₁su- (good, well), the same root found in Greek 'eulogia' (blessing, praise), 'euphemism' (good speech), 'eulogy,' 'euthanasia,' 'euphoria,' 'evangelist' (good news), and the name 'Eugene' (well-born). The noun 'phōnē' derives from PIE *bʰeh₂- (to speak, to say, to shine), and gives 'phone,' 'phonetics,' 'phonograph,' '
The prefix 'eu-' (good) and the root 'phōnē' (sound) appear throughout English in contrasting pairs: 'euphony' (good sound) versus 'cacophony' (bad sound), just as 'eulogy' (good speech) contrasts with 'dysphoria' (bad feeling). The 'eu-' prefix also hides inside 'euthanasia' (good death) and 'eureka' (I have found it well).