...Even with a flat on-axis response, do the two responses of the two speakers simply add and make a +3dB at all frequencies ....
Given two perfectly identical speakers (in magnitude and phase), they will sum to +6 dB in SPL at one observation point perfectly equidistant from them both, in a reflection free environment. SPL=20*log("A") and "2A" = +6dB. Vary from 'perfect" on any of those attributes, and < 6 dB will result.
Add in room reflections and resonances, and difference between speakers increases again.
Finally, binaural hearing is different than a microphone at one location, so we don't hear things exactly the same way the mic would show it.
Here is a measurement of my right speaker without EQ.
1) On axis, at 60cm.
2) At listening position.
(Left speaker is the same with a bit more bass.)
The speakers are toed-in so that they cross one meter behind my head (where is a wall).
What would you do?
Following assumes 2 speaker stereo, no sub.
1. EQ the speaker for its response errors in the design:
- Measure your speakers somewhere you can take at least a 5 ms reflection free gate. This will only give you 200Hz resolution in the outcome but you only want broad based eq and generally not sharp eq anyway
- Measure on the listening axis, and at least at the two axes that represents a ray for the side wall bounces to the listening chair, and at least +/- 5 deg up or down. Measure at least 3' out from the baffle, more for a large speaker. Diffraction effects will not be fully accurately captured if you measure too close to the speaker.
- There are AES papers to help justify this and its also my personal experience that its often a good practice to toe in the speakers so they intersect about 2 to 3' in front of you. Define the listening axis as the speaker direction pointing at you with this toe in. For one, this gives you a better "average" of the diffraction response for a typical speaker with the drivers mounted center of the cabinet but it also gives a bit better representation of the speakers radiated room response
- DON'T EQ it perfectly flat for on the listening axis. Diffraction effect varies fairly appreciably in the mid range for even relatively small changes in the axis of observation and driver summing will change even within your +/- 5 degree window
- Start with EQ so its broadly flat (start with half or third octave averages) on the listening axis but if you see some consistent off axis irregularity (say a consistent peak) that you don't see on the listening axis, start with eqing about 1/3 to 1/2 of that peak out, even if it makes it a bit non-flat on axis. Avoid filling big holes unless they are consistent on and off axis. One common example in many speakers is that the crossover point features a dip off axis in the lower frequency driver (because it is more directional) followed by a peak in the higher frequency driver (because it will have broad dispersion in that range). It takes some skill and experience to get a good blend as possible. Sometimes, it helps to reduce on axis 1 to 2 dB just where the tweeter starts to take over.
- Doing more measurement points will give you more accuracy (the idea behind the "spinerama") but at least these 5 directions are a must IME.
2. EQ the speaker for your in room response at your listening position, but just below the room's transition frequency, usually ~ 250Hz. A very simple way to get close is to play 1/3 octave warble tones (the frequency varies up and down about an average) and use an RTA app and get it roughly flat at the listening position with both speakers playing. If you want to measure using REW and the like, OK, but use some frequency averaging (1/6 to 1/3 oct) because even minor changes in observation point can change the shape and center frequency of the peaks. Again, avoid filling big holes, focus on reducing peaks.
3. Apply some low frequency positive shelving below ~ 250Hz to target the Harman trained listener target attached.
4. Listen. The technique in #1 may sound bright if the room is highly reflective and the tweeter broad in dispersion. For example, you can take a long gate measurement of one speaker at a time, apply some smoothing (1/3 oct) and compare it to the upper response in the Harman trained listener curve and target that.
5. Pop a cold one, give it some extended listening to become acclimated to the new tonal balance. It will be different and that may be enough reason to not like it at first. We get used to the errors in our set ups and that skews initial impressions, at least until the listener "breaks in" with the new eq.
6. If still you don't like the outcome after a couple weeks, who cares if its "right" or not, tweak EQ by ear. Use measurements to try and find the areas that are still problematic.
7. Simplify the various Eqs into fewer settings that give the same result, if possible.