serial vs. parallel revisisted

Hi all,

In triple checking everything, I am a little baffled at the half vs.
parallel thing.

Let me set the ground work so you can let me know if I am missing
something.

steppers typically have 4 coils.

series or full winding uses 2 coils per side, connected so the
current flows in series thru the coils.

half coil only energizes 2 of the 4 coils. 2 coils are not used.
This is often termed parallel, but that would really be a misnomer.

true parallel, would use each pair of windings, connected directly to
the PS, so each coil would fire at full voltage.

6 wire cannot be wired in a true parallel arrangement. only full or
half winding.
4 wire are - by manufacturer - parallel.

half coil vs. true parallel would offer roughly a 3% increase (per
Gecko white paper). half or true parallel would both use full motor
amps.

I think I have been using parallel to refer to half coil when it is
actually not a true parallel wiring.

a little quirk is that the Gecko white paper kinda ends one page with
part of the text on one page and the rest on the next. But then, I
am easily confused.

That leaves me to the question of why is a half coil and parallel
powered exactly the same ? seems with 2 coils in play, the current
could be increased.

In my testing to try to figure out what I can do to/with these
motors, I am wondering if a half coil, full amp connection would make
them move, where the series at half current does not.

Dave