Hi Philippe,  Of course, you are correct about the so-called "rigid
notation" which appears on many carillons (as Robbie mentioned) and on
Francoise Nicole boxes very early.  Having heard 2 of these boxes, it
is certainly a horrible misnomer for someone unfamiliar with the music
on one of these musical boxes, because they are anything but rigid in
the beauty of the arrangements.

However, this grid marking was of very short duration, followed by
index marks around the cylinder which indicates the distance between
the tooth tips and therefore, the width of space allowed for one note
through whatever number of tunes is played by the box.

For the rest of the cylinder arrangers and markers, did they have
temporary and removable grids?  Were the arrangers and the person who
marked the cylinders the same person?

It seems odd that no where in the literature related to musical boxes
have I seen a picture or diagram of a graph or grid work that could
have been followed by the "marker." On the other hand, I have several
and have seen many more tune arrangements on fairly rigid paper, and
they include the tuning scale, but no pinning pattern.

It seems as though every question related to early cylinder musical
boxes brings on more questions, but few definitive answers.

I'll look forward to other opinions and information.

Beatrice Robertson