Checking if monitor speakers are out-of-phase?

You could run a 1Hz sine wave at just enough level to see the woofers move and confirm if they are moving in sync. Some sound cards however filter out before that so depending on the card this will/won't work but something like that really is the most definitive as far as woofers go anyway. You don't even really need to see it well, I've been known to do this test and just place my fingers on the woofers and be able to tell if they are in phase. For example my RME will go all the way down to DC so the test would work but all sound cards don't do that.

I can't see any speaker excursion with a 1Hz sine wave. But I did put on a Joe Locke Quintet tune called Cecil B. DeBop, not in Reaper just using VLC Player. This track has very heavy bass and drum hits. Light touch on the woofer surround and with every thump of the drum both drivers are definitely moving outward. But this is with one of my speaker cables having reverse polarity, so it suggests something is up with the monitors and they are out of phase with each other somehow.

The simplest way to check polarity, is using a 1,5V AA battery as a "sound" source...

In case it wasn't clear, render the test samples you use first. That way you have them right there in a track on the screen to compare phase with the speaker recordings you make. The test sample from the tone generator will be the master. You'll be able to look at each driver and see if it's correct or reverse polarity in the recordings. So not only one speaker vs the other but each one against a reference.

I think what I'm going to do next is a sweep test with monitors in phase (same setup as above for each speaker) and see if there's any obvious irregularity. These are supposed to be 50Hz - 20kHz +/- 1.5dB.

I'd do this: Render/freeze a couple second long sample of each test tone. Just 100Hz and 6k are fine too. They're each clearly within each drivers' range respectively. Then play from those samples when you record the speakers. You'll have: <original sample> <left speaker recording> <right speaker recording> You only need to record it with normal connections. Reversing the polarity of the input is academic at this point. You might want to reverse the left and right inputs to the two speakers and make another pass though. Just in case someone wants to ask if it could be the outputs on your interface. And OK, there's no digital input. It sounds like one of these is simply wired up reverse polarity on the analog input. Unless there's digital signal processing ability in those things. And that includes the ability to flip the polarity. And then different firmware would have different defaults... Could be. All speculation on that bit though.

If there's DSP in there... Is there a mode that connects the analog input coming from outside directly to the analog input to the speaker's crossover input? Because if there is, I'd want to bypass the AD and DA conversions needed to get in and out of that DSP! Lo grade AD/DA conversions is how you make things sound shitty for no good reason. Actually flashing matching firmware would be an elegant and proper solution. (Presumably over that old serial connection. So a serial to USB adapter... Careful with that. Cheaper ways to find paperweights.) Next choice (ruling out bypassing DSP and/or if it's the root cause) would be to flip the polarity on the input jack. Unless it's so built up with a PCB soldered jack to make it a PITA. Something is just appealing to me about hand writing "positive phase" with a sharpie on the front of the thing following that. :D

Hmmm... I'd still prefer to swap the wires at the speakers. No soldering, no non-standard leads that will probably be forgotten down the track. Leave a note inside the box, re-assemble & move on.

Did the test again with a reference waveform (top track). I simply rendered the JS Tone Generator first, panned the track to one monitor only and played the tone while recording the same monitor's output. TRS speaker cables had normal polarity (+tip/-ring/sleeve). The monitor on the right is the one with the "Positive Phase" sticker. 100 Hz 6 kHz So, as predicted, it appears the monitor that does not have the "Positive Phase" sticker is the one that has inverted phase. This test confirms (again) that both the tweeter and the woofer have inverted phase. I think I'm going to just reverse the wiring to the drivers on the monitor that has the problem. There are clips that just pull off. Given they're a pair might as well make it permanent that they're in phase with each other. The other test I did was a sweep, 5Hz - 20kHz, and I was going to look for irregularities in the waveform that might indicate the monitors are still not functioning according to spec (50Hz - 20kHz +/- 1.5dB) but I realized I don't have a microphone that has a flat enough response for that kind of test.

alanofoz is right. Reverse at the speaker.