The real reason to offset the tweeter on baffle?

Notice the "question mark" since I have not run all the simulations, but it's a matter of intuition. Some speakers have the tweeter offset on the baffle to minimize baffle diffraction at least that is what most people think it would be.

But the other reason that is not usually spoken off is if the tweeter is offset, and the woofer is at the center, their diffraction signature is different at different frequency.

For example, if both tweeter and woofer are at right at center, then they will happen to have a dip and peak at the same frequencies (or approximately) which can be pretty bad. For example, on a 8in. width baffle, the diffraction dips at about 4K - 5KHz, but they would both dip at the same frequencies so it could be pretty bad potentially.

But if the tweeter is offset, then the tweeter and woofer will dip at a slightly different frequencies so you sort of spread out the diffraction so it won't be as bad.

If you use shallow xover slope, it is more serious. But if you are using steep slope xover, then it is not quite as serious. For example, if you cross at 3KHz but using shallow slope, then on the tweeter or the woofer will be more seriously affected by diffraction. But if you're using steep slope, then it's either or but not both, or if you lucky, the steep slope may filter out the drivers before diffraction set in.
 

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In general, the narrower the baffle, the higher the diffraction dip. Likewise the wider the baffle, the diffraction dip will be at lower freq. respectively.

I guess you could try something similar to B&W 805. The tweeter "baffle" will be much more smaller vs. the woofer, so I guess the tweeter diffraction dips will be at quite a bit higher frequencies vs. the woofer. I mean the baffle design won't need to be as fancy but it just needs to be different for the tweeter and woofer in term of the "width".

805-black-800-series-diamond-speakers.jpg
 
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Offsetting the tweeter evens out the power response a bit if you sit mostly in between the speakers, at the expense of worse in room power response. Most of my designs are tweeter in middle because the crossover is easier to design and I only sit directly in between 25% of the time. Some designers like Jeff Bagby have had excellent results with offsetting. There is nothing that beats rounding the corners of the baffle with at least a 1" diameter for reducing baffle interaction. IMO.
 
If you offset the tweeter you can also gain slightly better time alignment, if you firing the speaker straight ahead with no toe in then have the tweeters on the ”outside”, if you toe in your speakers, firing straight at you, then have the tweeters oriented on the ”inside”
 
Is this the Linkwitz quote you mean?: Frontiers
"Sound diffraction at the edge of a box speaker baffle is claimed to degrade stereo imaging. I have not experienced this myself for speakers with typical flat baffles for drivers up to 8" (20 cm), nor have I seen scientific evidence. The low amplitude diffracted sound wave occurs so early after the direct sound (<500 us), that the precedence effect does not come into play and summing localization occurs [6]."
(doesn't mention alignment though).
His site is a monster & I keep on finding interesting distractions there...