FWIW, I made a PIC 12-note octave generator a few years back:

http://chip.aeug.org/oct54all.asm

  I've since made better ones, using an adder-accumulator method and
Scenix parts.  This achieved the "top-octave" (C9=4186.01Hz) with
negligible error.

  The example in the URL works reasonably well.  Worst-case pitch error is
0.54%.

   --Crow

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