Just to add to all the fine explanations of the use of Gamma numbers in
music boxes.  Gamma numbers were used by many of the music box makers
but most of them did not mention them as clearly as Nicole Frères on the
tunesheet.  Before the use of Gamma numbers Nicole used tune numbers, you
can find them scratched in the cylinder endcap.  Somewhere around serial
number 10.000 (ca.1830) the switch to the Gamma number system must have
been made.  Many Gamma numbers (Musiknummers) of the makers from Prague
and Vienna can be found on the Austrian website http://eiou.at/index.html 

Niko Wiegman.