Before I comment, I would like to say that the topic is not limited to
Ampico pianos.  It seems as if Mason & Hamlin used its size "A" piano
(5'8") for experimentation during the 1920's and 1930's.

I have no idea how many variations exist, but I have seen over ten.
Unfortunately, I did not make detailed notes.   In general, the
variations are not just the structure of the wound bass strings as is
suggested by most prior comments.

Here are the areas that I have observed to contain differences:

1. treble bridge splits into "Y" at the bass end or does not split;

2. high treble strings in top section have three possible different
bearing surfaces behind of the tuning pins: some are metal bars, some
are wood, some are aliquots;

3. I'm not sure about this, but there seems to be some differences in
muting the strings behind the bridge.

The Mason & Hamlin string scale numbers, as others have stated, are
cast into the plate at the tail of the piano.  Here are some of the
numbers I've seen (not a complete list):

  A3, A4, A4x, A5, A5x (not sure about this),
  A6, A6x (not sure about this), A7, A7x, A9

I do believe the stringer's handbook contains all of these and more.

My personal 1930 Mason & Hamlin piano carries the A9 identification.
That is the most common that I have seen and it is consistently the
most mellow of all Mason's I've heard.

For anyone wanting to maintain the original bass string design, consult
the stringer's handbook or consult Schaff Piano who has string scale
sticks for almost all pianos.

Ernie was the Schaff string expert (now long retired).  When strings
arrived for duplication, he would lay them out and compare them to the
strings to his huge collection of scale sticks.  In a few minutes, he
would confirm his sticks were correct, and send the order to the
production department where 100-year-old winding machines would
duplicate the bass strings.  Schaff had them all: Mills Violano, Hobart
Cable, Stein, Steinway, whatever.  I watched the operation for hours.

Back then, the production of strings was divided into two departments.
New piano strings for Kimball were on one side of the room and
replacement string orders from technicians were on the other side.
All the lathes were powered from old overhead line shaft belts.

The operators would lay the scale stick on the front of the lathe and
then select the wire gauge.  One end of the string then was formed into
a loop for the hitch pin.  The wire would be flattened on each end
where the windings would begin and then placed into a chuck.  The
winding would begin, staying within the limits of the scale stick.

After the wire was wound, the winding was tapered down on each end.
Then the operator would go to the next marking on the stick and make
the next string.  Each completed string was placed on a wire loop,
keeping all strings in sequence.  When finished, the loop was tied and
tagged.

This was purely string duplication.  The topic has become rescaling.
I don't want to take sides on this.  But rescaling is based on the
fact that we know more than the designers did 80+ years ago.  Rescalers
advocate improving certain parameters for a more optimum sound.  But
maybe not everyone wants those parameters improved.   I don't know.

I wish I had made videos at Schaff.

Bob Taylor
Missouri