Hello!  I think the origin of the expression "three-bell nasty"
is to be found in the introduction of John E.T. Clark's book,
"Musical Boxes":

  "'It must be at last 200 years old,' she said. ...  Before I opened
  the lid of the box I could see that it was not even 100 years old,
  never mind 200; it might have been 50 and was one of the cheap and
  nasty kind with three bells all tuned to the same note, and the
  movement was contained in a varnished softwood case. ...

  "I explained carefully and at length that this type of box was
  popular between about 1895 and 1910 ... (and) that as musical boxes
  they really were not worth anything but they had pleased a class of
  people who could afford nothing better."

Browsing through my reprint of the 1901 Nicole Freres (London)
catalogue, there certainly are "Some Special lines in cheap Musical
Boxes", the basic model having a 3-1/2-inch cylinder movement with
"about" (!) 31 teeth encased in a 14-inch box!

Christofer Noering
Stockholm, Sweden