A Palm Springs, California, listener was taught that when the word the is followed by a vowel, it should be pronounced with a long e, and otherwise with a schwa sound. However, there’s no grammatical basis for such a rule. This is part of a complete episode.
I was taught ‘the’ with a schwa as the one under current discussion, while the the “long e” (actually a dotted i…) variant indicated emphasis on status as either the sole example (i.e. one and only… “The Holy See” Γ°i ?ho?li si) or most important example (e.g. “The Book” Γ°i b?k, meaning The Bible)