41844 Ways to Tune a Piano

Here's the big list I generated! This gives twelves pitches per octave, as fractions and as cents values. The twelve pitches in the octave all have to be related to each other by just intervals. In each tuning, there is a tree of simple intervals that relates the twelve pitch classes.

One could certainly extend the notion of simple intervals, e.g. to include ratios like 8:7. How exactly these intervals should appear on the piano keyboard, I don't know. With this list of 41844 tunings, the intervals appear on the keyboard in their conventional way: minor thirds are three half-steps, etc.