Just a note for the historically curious: Mechanical Music Boxes seem to have first been produced in the early 19th century, derived from musical snuff boxes which were first made for gentlemen to impress ladies with in the last quarter of the 18th century. Apparently, the key device invented at that time was a metal tuning comb which would always stay in tune (as opposed to stringed instruments, which had to be retuned by adjusting the tension of the strings, something which would be impractical for music boxes!). So widespread availability of advanced metallurgy and machining methods were key to producing this device, much of which first was done in the clock-producing regions of the Black Forest and Switzerland.
The 19th century music boxes were often quite elaborate, they used either discs or cylinders on which the music was impressed by raised points which would sound that part of the comb. They also often had bells which sounded and of course figures which twirled. Often, the cylinders or discs could contain several songs, and could sometimes even be changed to provide even more available songs--a very elaborate music box might have fifty or so songs available.
They were of course superseded in the 20th century by record players. But because of the use of the tunining comb, the music box does actually have a unique sound which is not reproduced by any other musical instrument.
Given the upper end technology in World of Storm and Fury is the end of the 18th century, this would mean that the music box given Jillian (which they called a 'mechanical chamber orchestra') would probably be one of the first such devices to exist in the world. It is also fairly elaborate for such a new device, with the capability to play four songs.