Please see below a lengthy explanation of gamme numbers from one of
my colleagues in the Musical Box Society of Great Britain, who is not
himself a subscriber to MMD:

A gamme number is a reference number found associated with cylinder
musical boxes, particularly those made by Nicole Freres of Geneva.
It used to be thought, and still is by some, that the gamme number
referred to the musical programme, i.e., the particular collection
of tunes, as in the early days of collecting there did indeed seem
to be a unique and direct relationship between the two.

However, a little more thought and research leads to a different
explanation; the word "gamme" is the French word for "scale", i.e.,
a sequence of musical notes such as the chromatic scale found on
a piano or organ. In the context of musical boxes, however this
becomes "a sequence of musical notes, of the same or differing pitches,
necessary to play an item or items of music so arranged as to require
these notes."

It follows, therefore, that a musical box gamme does not necessarily
follow strictly the chromatic scale of the piano or organ; it may omit
some notes as not required for a particular set of arrangements or may
be repeated on adjacent teeth for emphasis or for the mandolin effect
found on musical boxes of the later period.  It is not surprising that
a French word was used as early development of cylinder musical boxes
occurred in Geneva which is in the French speaking part of Switzerland.

Thus, whilst a maker may set the physical limits of a musical box,
such as the length of the steel comb and thereby the number of teeth
it could have, it is the arranger of the music who determines the
pitches to which these teeth have to be tuned in order to play the
pieces of music he has arranged.

These latter may be any number, let us say 12 or more of which some
have wide popularity and some to meet requests from customers; from
these, the maker can select a musical programme for a particular
musical box that suits the current demand or sales requirements.

Thus, a Gamme Number becomes a unique reference number for the
instruction passed between an arranger and comb tuner, "For a musical
box to be pinned with and then to play all or any selection of these
arrangements, you will need a comb tuned to the attached Gamme; the
maker would then give this a unique reference number -- "the Gamme
Number."

As an example of this, during my researches into Sacred Airs on
cylinder musical boxes, I found Nicole Freres, Serial No 19616 dating
from circa 1840/1841 with a programme six hymns for which the comb
had to be tuned to Gamme No 411.  This gamme number was also noted as
having been used later for the combs of four 4 Air boxes, Serial Nos.
28524 (circa 1850-51), 34140 & 34171 (circa 1856/7) and 36715 (circa
1860), all of which have a programme of just four of the hymns
selected from of the original six found on No 19616.

So, for those still holding the belief that a gamme refers to the
musical programme, they must then answer the question: "In a very busy
workshop, with work in hand on dozens of musical boxes, how else is
the integrity of a particular box and its musical programme to be
maintained?"

As noted above, gamme numbers are particularly associated with Nicole
Freres and MBSGB's Registrar, in the process of compiling the Register
of Cylinder Musical Boxes that have survived the years, has also been
able to construct a Nicole Gamme File, listing all the gamme numbers
known to-date as having been used by Nicole, and the musical boxes
found to-date with musical programmes using each gamme.

As to where a gamme number may be found; almost invariably it will be
found on Nicole Freres tune sheets and also on those of other makers
but not necessarily so in their cases; in addition, usually it can be
found scratched on the left end cap of the cylinder thus "G xxxx" --
thus indicating that the cylinder needs to be linked with a comb tuned
to that gamme; and then similarly scratched on the base lead or the
underside of the comb stock, again indicating that it requires
cylinder(s) with a matching gamme.

I hope the above helps to understand something of the processes
involved in making a musical box in the 19th century and so increase
your enjoyment of your own musical box(es).

I must end with a plug for The Register of Cylinder Musical Boxes
maintained by MBSGB and a plea for all owners of cylinder musical
boxes to take the time to register them.  (NB: Owner details are _not_
NOT recorded.)  Currently, The Register has 12,500 entries and is an
invaluable tool for research into cylinder musical box history; it
is also useful on those occasions, thankfully rare, when a musical box
is stolen as it can provide the police with useful evidence as to the
description and nature of the stolen item.

David Worrall
MBSGB Executive Committee Member

It is acknowledged that in some cases not all the data sought will
be available, so just register what you can.  More information is
available on the MBSGB website: https://www.mbsgb.org.uk/ 

Submitted on behalf of David Worrall by MMD subscriber Alison Biden,
MBSGB.