The questions here relate to proper phasing of drivers at and away from the crossover region. For simplicity lets talk about 2nd order. In order to get positive summing we generally invert one of the drivers. The first question regards exceptions.
If one or both speakers have a slight peak just prior to the roll-off (or possibly if there is too much overlap) it is possible that wiring them in phase could cause the "suck out" to compensate for the bumps and give the flatter response. Are there any negatives to doing that? So I guess it kind of boils down to "is the flattest response the only consideration?".
The second question relates to absolute phase outside of the crossover region. It is likely that when an instrument such as an oboe plays a note with the fundamental close to the upper end of the midrange or mid-woofer that the bulk of the overtones will be on the tweeter. Is there any advantage to these overtone being in the original phase relationship to the fundamental? Are there any time domain advantages to having the drivers in phase away from the crossover? If there is then it seems that there might be some advantage to arranging the crossover so that this is possible.
If one or both speakers have a slight peak just prior to the roll-off (or possibly if there is too much overlap) it is possible that wiring them in phase could cause the "suck out" to compensate for the bumps and give the flatter response. Are there any negatives to doing that? So I guess it kind of boils down to "is the flattest response the only consideration?".
The second question relates to absolute phase outside of the crossover region. It is likely that when an instrument such as an oboe plays a note with the fundamental close to the upper end of the midrange or mid-woofer that the bulk of the overtones will be on the tweeter. Is there any advantage to these overtone being in the original phase relationship to the fundamental? Are there any time domain advantages to having the drivers in phase away from the crossover? If there is then it seems that there might be some advantage to arranging the crossover so that this is possible.
play around in a simulator (VituixCAD etc) and see if the response is flat-ish in the regions of interest, across different listening angles. If so, the answer is you’ll be fine.
A bit more detail: it's not a problem per se when different sound sources sum out of phase. If you consider the output from a woofer cone, as the signal frequency increases (and wavelength becomes shorter and closer to the dimension of the cone), you start to get different SPL depending on your listening axis. This comes from the output from every part of the cone, interacting with varying phase. This is what is commonly referred to as "beaming". Well, not much different if your different sources are coming from the same cone or an adjacent one. Of course, baffle diffraction effects are a step beyond that but outside the scope of your question.
In short: if your drivers combine and gives you flat response where you want it (consider the potential off-axis listening angles and the overall power response), it's nothing to worry about.
In short: if your drivers combine and gives you flat response where you want it (consider the potential off-axis listening angles and the overall power response), it's nothing to worry about.
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You're talking about tipping either side of the 90 degree middle ground, so it should be easy enough to see. Yes, in some circumstance you might do this but you need to look at the bigger picture. One is what happens out wide in frequency, and the other is what happens out wide in directivity.
Absolute phase being flat is not considered to be essential.. (although sometimes it is a sign of other things that are not related to your question.) On the other hand if it is extreme enough it could be a problem. Such limits (GD) are known and understood.
I always check phase together with fr response. Properly designed is flat response, and no obrupt change in phase. Wrong phase often shows on fr response as dip. But it may not, so its important to see phase too. Its available in rew just by click of a button.