I tried to specify what the name of the vowel "I" is in my dialect and it seems that the IPA table doesn't have it on it. Reading up on the definitions I believe that it should be called "near-close front unrounded vowel", since it is much like the "close front unrounded vowel, but the tongue and mouth are slightly more relaxed. I would say it is directly between the "near-close front unrounded vowel" and the "close-mid front unrounded vowel".
It can be heard in this video: Bairisch für Einsteiger ("Des is...")
So am I right to call it "near-close front unrounded vowel" or am I missing something?