מֶה, מָה, מַה - Meh, Mah, Ma - What's the difference?

Question

What causes the difference in vowelization of the Hebrew word for "what"? In some contexts it is מֶה, in others - מָה, and in yet others - מַה. The hypothesis that an acquaintance and I converged on was that only when preceding a guttural (or lower) consonant is it מֶה, but this was falsified by "במה מדליקין".

What is the rule governing this change?

(Apologies for the imprecise transliteration in the title. My American English-speaking conscience couldn't bear to make a kamatz an 'o' and I saw no better alternative.)

Answer 1

I believe (no source) it's the same as the vowel changes for the definite article ה־‏‎, when the word מה is connected to the word after it (i.e., has a טעם משרת or has a hyphen after it). I don't know the rules for מה with a טעם מפסיק‎. Update: Exceptions noted by user WAF in a comment show my belief, as stated above, to be wrong in all generality for later Hebrew (though perhaps still correct in some subset of cases and/or for Biblical Hebrew).

The rules for the definite article ה־‏ are as follows, taken from ספר מפתח הדלת by Chaim Lenchitz, copyright 2004, revised edition, 5766:

Use the first applicable rule:

• Before a stressed ה or ע with a kamatz gadol, the prefix has a kamatz gadol.
• Before a ה,‎ ח, or ע with a kamatz gadol (or, seemingly, a chataf kamatz), the prefix has a segol.
• Before an א,‎ ה,‎ ע, or ר, the prefix has a kamatz gadol.
• The prefix has a patach.

But there are some exceptions in the מסורה‎.