User 'jlovegren' :
'Might' is the preterite form of 'may', and both can be used as present tense modals. It originally meant "to be strong, to have power".
Source: p 123, Line 660; Antigone, Oedipus the King, Electra; by Sophocles, E Hall et al
TUTOR [to the chorus]. Might I inquire of you if I have come
To the royal palace of the lord Aegisthus?
Is the use of might here right? The Tutor's question isn't past in any way; so why would you use the preterite might, as per the grey above? I also read this.