If you plan on making or adapting a collet chuck, it does not matter what is your taper because the collet chucks thread on the spindle nose.?
Using the chucks with the Morse taper will extend far out in front of the spindle and introduce their own additional runout.
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I can't speak for the 37, but my 1922 34 is morse 4 in the headstock (1"
ID bore) and morse 3 in the tailstock.? I.e. not SB proprietary.