An astute reader of and long-time subscriber to this blog, Lone Coleman, who is a native speaker of Danish and speaks English perfectly well, alerted me to the fact that not all accents are the same, hence this addendum.
It is true that certain accents are harsher than others. The closer a non-native speaker’s accented English approaches standard English, the better the “music” of the outcome. Occasionally, a typical accent (like the French) can even seem charming and easy on the ear. C’est le ton qui fait la musique!