Is this about two-channel stereo recordings played through two loudspeakers vs the same two-channel stereo recordings played through 3 speakers with an added center channel? If so, the result of the EQ compensation will depend on how the particular recordings are mixed and which compensations are already in place.I was looking for another image and clearing out photos stuff in my phone when I came across the ff. even more crude "models" of the phantom center dip in one of A. Grimani's lecture slides:
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This maybe helps illustrate partially why I mentioned I only load my phase shuffler DSP settings under certain conditions.
If we assume we are talking about modern multi-microphone recordings and that the recordings in most cases are mixed using two speakers in a traditional stereo configuration, we also should assume that all the different sound objects in the mix (no matter where in the stereo field those individual sound objects may be placed) are already "sculptured" with EQ the way the mixing engineer thought they sounded good. If he/she thought something was missing in the sound of the sound object that is somewhere in the phantom center field, we should assume he would already have made an EQ compensation to those sound objects until he was satisfied with the end result. (Don't forget that the mixing engineer hears the end result of the mix through two speakers with the very same phantom problem as the end-user will.)
If we talk about recordings made with a stereo microphone technique, then an EQ compensation for the phantom center is more likely a solution to the problem. But still... if a modern mixing/mastering EQ program is used with the function of Mid/Side equalization, we still don't know if some sort of compensation is already in place.
As you can see, the stereo phantom problem can already have been addressed/handled in the mix, with or without the mixing engineer's knowledge of this particular phantom problem. In most cases as the end-users, we don't know what is done in the mix, but we should assume that if the mixing engineer hadn't been happy with how the mix sounded (and in this particular discussion, how the sound objects panned somewhere in the phantom field sounds), he would have probably done something about it.
And as you can see (#2), there can never be a "one-trick" EQ solution to the problem no matter if a center speaker is added for the playback of the two-channel stereo recording or not. It's a case-by-case solution depending on the particular recordings, it can even introduce a new problem as a "two-stacked" overcompensation if the problem is already addressed in the mix. If a center channel is added it's even possible a "negative" EQ compensation is needed as a solution to some particular recordings.