I thought that the auxiliary note of a lower mordent (or other ornaments) was simply the note before in the scale unless the mordent had an accidental on top of it. However, I ran into this discussion providing a much more complex rule explaining essentially that the auxiliary note should be a half-tone down unless the note played immediately before or after the mordent was a full tone below or when the mordent is applied to a 3rd or 7th. Given that I never heard this before and that the full discussion leaves a lot of confusion as to how the accidental should be interpreted in that case, I am having doubts about that entire explanation.
Can someone explain simply what are the rules for playing the auxiliary note of lower (and upper) mordents, with and without accidentals? Examples welcomed.
Thank you