Some additions, changes, and new discoveries re my Greiner and/or
Bremond box posting:

The vertical lines scribed on the cylinder for each tooth line up with
the last (eighth) tune, not the first.  This is a Bremond feature.
Does that rule out Greiner, even in his partnership with Bremond?

Both combs are forged with 30 teeth each, as posted -- but the bass
comb has a 31st tooth neatly screwed on to the treble side, next to the
organ!  It is a second D above Middle C (the box is in the key of C).

In addition to the "g[amme]116" marked on the organ, the cylinder's
great wheel also has "g116" scribed on its side along with the serial
7656.  However, the treble comb has "117" scratched on its bottom (plus
note names in French scratched under the teeth).  I wonder if the 31st
tooth was added to the bass comb to make gamme 116 match up with the
treble of 117?  Was this sort of hacking more likely in a small
workshop than a large factory?

I have partly fixed the tune change problem.  It now advances only
one tune, but the advance occurs partly at the end of one tune and
the beginning of the next, so your decision to repeat or change the
tune should be made before the tune ends, and not changed when
restarting the box.

The combs actually double the organ's melodic line, and the top
octave is fully chromatic.  There are shutoff levers for the drum and
castenet, but the organ and bells are always enabled.

Mike Knudsen