[link to original on tumblr]
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Those chords aren't unusual at all. In fact, there's a whole Wikipedia page about these chords and their various permutations. Incidentally, much of "Time of the Season" uses these same chords (albeit in a different order) in the same key.
But, like a lot of other Zombies songs, there are some weird key changes in "Kind of Girl" and "Beechwood Park," and even those are sort of similar. Both are mostly in E minor, but "Kind of Girl" veers into Bb during the bridge ("But more of that another day…"), and a section of "Beechwood Park" ("All roads in my mind…") is in Eb. Bb and Eb are adjacent in the Circle of Fifths.
These same sorts of key changes (that is, changes to keys that are distant by three or four places in the Circle of Fifths) are present in "I Must Move," "I Want Her She Wants Me," and "Care of Cell 44." I mentioned that here, although I have to correct what I said about "Care of Cell 44" - at the end of every other phrase in the verses, it changes from G major to Bb major, not to Eb major. I got confused because the two flats in the key of Bb are Bb and Eb.
Like I've mentioned before, I don't know that much about keys and tonality. Aside from what I learned in a semester of beginner piano four years ago, I'm completely self-taught as far as theory goes. But I think I have this right.
I knew that Chris White wrote "Beechwood Park," but I couldn't remember who'd written "Kind of Girl." I was surprised to find that it was Rod Argent. Their writing is similar at times, but these chord progressions and key changes were so similar that I thought they would be from the same writer.