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Default Wiring of speaker

I acquired secondhand recently a pair of Yamaha NS-690 speakers,
series III. These are mirror-image speakers with three drivers and
pots for the mid and tweeter levels. I used to own these same model
speakers, only those were the first series, which were basically the
same, except the speaker alignment was not mirrored.

After hooking them up, I noticed a distinct lack of bass response,
which I thought was odd, as I remember them having excellent bass. I
figured I had accidentally reversed one of the leads from the amp, but
checking this I determined that the leads were connected correctly. It
seemed nonetheless that the speakers were out of phase. I tested this
by placing them face to face and then listening to a recording with
prominent bass whacks (track 6 of Enigma MCMXC A.D.). When I wired
them out of phase, the bass was definitely louder. I deduced that the
woofers were connected out of phase with one another.

I unscrewed the woofers from the from of both speakers and determined
that they were indeed wired incorrectly. The red lead was connected to
the left terminal on the left speaker, but to the right terminal on
the right speaker (looking at the drivers from the front, the open
side). The mid-range units were wired with the yellow wire to the
right terminal and the black on the left; the tweeters were wired with
the pink lead on the left, black on the right. These again were the
same in both speaker systems. Only the woofers were inconsistent. The
soldering appeared to be original, from what I could tell.

Obviously reversing the leads on one of the woofers will bring them
into agreement with phase, but how do I determine which one is wired
correctly? I connected a single 1.5-volt AAA battery to the systems
and determined that the left woofer moves outward with a positive
voltage, and the right one moves inward with the same positive voltage
applied. This proves that the speakers are wired inconsistently, but I
have no idea which one to reverse.

Any ideas? Also, why are the tweeter and midrange wired in opposite
fashion?
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