Tilting Midrange and Tweeter toward axis

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I'm building a pair of satellite midrange/tweeters with a single sub-woofer. It seems that tilting (wedging) the MR and tweeters of each satellite slightly toward a common axis for each speaker, focused on the primary listening area, would help with imaging since the MR and tweeter would then have identical path lengths to the listener. I'm sure I'm not the first to consider this, but cannot find a discussion of any drawbacks.
 
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