The concept of lexical set is a useful technique for differentiating accents or dialects within a language. A lexical set is a set of all words/syllables that are pronounced with the same vowel. These sets partition the syllables in the language, and then how different sets might merge (like the caught/cot merger) can help identify a particular dialect. A particular lexical set is labeled with one of its primary members. For example, there lexical sets
BATH including bath, pass, path, sample,...
PALM including palm, father, ...
In AmE these two sets are distinguished, but in BrE (RP) they are merged (supposedly; for me, palm and father are different).
There is a chart that lays out the merges among lexical sets for English dialects.
My question is this. Are there any such similar lexical sets done for other language families? I would think that German, Italian or Chinese would be amenable to such analysis having complex internal intelligible/unintelligible relations in their families.
(I'm looking for either references for such similar analysis in other language families, or an explanation of why the lexical set method is or is not a good tool for a particular language family).
Addendum: even though I accepted an answer, it didn't answer exactly what I"m looking for. I am hoping for, in the context of very similar varieties of a language, a list of vowel 'contexts' such that within one variety all instances of any particular context are pronounced with the same vowel (this seems to be the definition of Wells' tool. For example, in the set of German dialects there could be a list of words that help distinguish the dialects by a complete inventory of vowel contexts, i.e. not just a simple maken/machen line (a single distinguishing element), but the set of all vowel contexts that helps distinguish all the dialects.