Thanks for your ideas and also questions.  Here are some answers,
or attempts at them:

 [ Mark Kinsler wrote in 190215 MMDigest:

MK> There might be motorized versions of this movement, but its
playback speed would have to be the same as your recording speed.

Well, not really; I would just punch it again with a different speed.
However, the speed should not be lower, otherwise the repetition would
be even worse than it already is (by design).

MK> Do you mean a music box in which the [4-minute] tune is coded with
pins on a rotating cylinder?

First, yes. This is what my customer asked for, and so I also asked it
here.

MK> If so, the answer is "no".

Thanks.  That clarifies this.

Second, I think my customer asked for what she *thought* a typical
music box would look like, namely, that it has this "barrel" in it.  But
I believe that anything else that fulfills her wish -- a self-running
thing that plays "real music box sounds" (what "specialists" would call
a comb) -- would be acceptable.  So, ...

MK> But if you're content to leave the music on a paper or Mylar
Leporello loop (I've never heard that term before) and use some
variation of the mechanism shown in your video, sure.  It shouldn't be
all that tough to do.  It would seem that anyone who can repair clocks
or old-time tape recorders ought to be able to do the job.  It also
depends on how elegant the final result has to look, though I believe
my clock-parts people could supply enough golden cherubs and scrollwork
to satisfy any taste.  Heck, even _I_ could do it."

... is also a good answer.  However, I doubt your "shouldn't be all that
tough", in terms of cost.

I have just started attaching a contraption to my grinding machine --
a simple rectangular frame with a sliding table and two cranks to move
it.  Right now, it's half done and has cost me about an hour of design
time and two hours of building.  So this simple thing will cost me some
 five hours.  At a sensible rate, that would be at least a hundred
bucks or the like.

I cannot imagine that one can do that music machine job in less than
15 to 20 hours, including design and purchasing, which would be at
least 500 dollars or euros, wouldn't it?  And that would be the raw
machine, without a sound-enhancing case.

Re Spencer Chase's remark [190215 MMDigest]:

SC> This whole thread bothers me.  The result has to be just like
a music box but it needs to be "improved" in all sorts of ways and
it must be cheap.
 
If a music box can play for 4 to 5 minutes and is not more expensive
than a few hundred dollars or euros, then there's nothing to be
improved.  My question was "only": Is there such a music box?   A
hand-cranked Sankyo paper strip movement does not qualify because
of that expectation of me and her that "it plays by itself".

(I assume "just like a music box " means that it plays by itself;
I have never seen or heard of a classical music box that one needs to
crank while it plays, and also my customer would not expect that, for
the same reason.  But we both might simply not know enough about what
has been done out there in the last 100 years.)

SC> I can think of at least a few ways to achieve the goal without
cutting gears or making any complicated or precise mechanical
components. Only existing mechanisms would be needed plus a simple
add-on device, but it would not be possible for a few dollars or pounds
or euros.  The idea is simple but it would take time to perfect.

That's why I asked for the cost already in the heading of my initial
posting -- I am not so much interested in ideas, but in an available
mechanism.  I'll contact Gérard Dabonot!

Thanks again for your answers -- and also your questions!

(There is an interesting topic behind all this, I think: What are the
*expectations* of laymen about music boxes (and here I count myself as
a layman)?  Just watch the end of the film, "For a Few Dollars More",
to understand what "layman" Ennio Morricone [the composer] assumed that
a music box inside a pocket watch should be able to do: the playing
time of the piece until it starts to repeat, and the chromatic notes
are, well, ambitious!)

Harald M. Mueller

 [ Hear the melody at https://www.youtube.com/watch?v=7tiTzQoEWDw 
 [ Ennio Morricone -- Musical Pocket Watch Theme "Watch Chimes 2"
 [ -- Robbie