Language comes in many varieties, including dialects, sociolects, idiolects, and established hybrids known as creoles and pidgins. When non-native speakers acquire foreign languages, they also vary in the degree to which imperfect learning affects their speech. This is immediately apparent when one listens (on the BBC World Service, for instance) to speakers who struggle with the global lingua franca, English.
As a medium of effective linguistic communication, of course, broken English must often serve because its producers may not have the luxury of speaking only when they know their version of English is grammatically correct. What they say, unfortunately, can easily grate on the ear of a native speaker (or of a foreigner whose English is impeccable) because it is a species of what can––for the nonce––be called CACOGLOSSIA (< Gk κακός [kakos] ‘bad, evil’ + γλῶσσα [glossa] ‘tongue, language’).
Cacoglossia is a phenomenon that ought to alert one to the conceptual truth of the assertion that speaking a language is like playing a musical instrument. When a person plays an instrument badly and produces cacophony, it is strictly parallel to the ill-formedness of the speech of those who have an imperfect command of the language they are using to communicate. Beauty, as regards both music and speech, can only obtain when the product and the underlying design (= grammar, score) of each sound domain are in harmony.