Speaker phase observation and question?

Some speakers, e.g., Vandersteen, are purposely designed to have all drivers in the same, positive phase.  As Mr. Squires implies, Vandersteen does not use a flat baffle.

" I have made a couple of observations. When connected in positive phase (red - red, black - black), the speakers put out pretty substantial bass, but the mids and treble are somewhat subdued. Upon reversing the phase, the mids and treble open up substantially, and the bass becomes somewhat subdued. To my ears, I actually prefer the reversed phased."

Somethings wrong. Even though your speakers don't use first order xovers, you shouldn't have that much change. Can you list your amp and speaker cables? Be very specific with your speaker cables. (brand, model, single or biwire,)

Vandersteen also uses first order filters which don't honk up phase
...
and his crossovers are incredible feats of engineering without a big baffle to smooth frequency response - a big baffle is a nice flat horn

wiring a driver out of phase to attempt to fix a steep filters phase shift is NOT excellent crossover design...
but the magazine guys love it...

" Vandersteen also uses first order filters which don't honk up phase "

I have 3 pairs. I also had the exact same pair of speakers as the OP, and was able to do a direct comparison. Yes, Vandersteen is a better design, but I don't think that's the problem. If you look at the OP's description of the of complaint, it looks like a problem that needs to be fixed.

" When connected in positive phase (red - red, black - black), the speakers put out pretty substantial bass, but the mids and treble are somewhat subdued. Upon reversing the phase, the mids and treble open up substantially, and the bass becomes somewhat subdued."

I've seen several times where speaker cables were not labeled correctly. If the cables are terminated as a biwire config, and a mistake was made on either the high or low cables, but not both, it sounds like the OP's problem. One way the bass is correct, but the highs are not. After the swap, the highs are good, but the bass is now bad. The problem keeps going back and forth, and if you're not aware of what's going on, It'll drive you crazy.

Keep in mind that this is a guess on my part because we have no idea of what the OP's system is.

Thanks for the informative response Erik.