@Orangery Yes, sorry about I hadn't tested it and the numberbox outlet was not connected to the [+ ] object, but worse than that was the random notes cause some notes hang when playing more than one note if playing polyphonically. The best I could come up with to address that, was to count the note-on and note-off and when sum was zero perform an all notes off (cc 123).
out-of-tune-3.pd

@Balwyn

Thanks very much for sorting it. The patch works really well with some microtonal tunings. My intention was to record some miniatures to demonstrate its usefulness but Audacity is giving me a hard time at the moment (something to do with my VSTHost set up).

Replacing "random 9 /+2" with "random 9/-11" produces a different harmony. as the randomly generated notes are now an octave lower. So for example, C3, E3 would become E2, C3.