User talk:FloraC/Critique on Functional Just System

Visualizing the gap in the FJS

I recently uploaded some images that might help visualize the gap FloraC mentions. In the below, the horizontal line represents the octave, then for each fifth shift in the FJS master algorithm, the octave-reduced Pythagorean interval corresponding to it is marked and a box is drawn around that mark which stretches 51c (the value of the standard radius of tolerance) in both directions. Regions defined by values later in the list will appear behind those defined by earlier ones, and overlaps are drawn using separate colors for clarity.

The blue regions are those pesky gaps! Here's a version of the same image with some prime intervals marked:

You can also mess around with interactive versions of these images using my Custom FJS Explorer, where you can also set different values for the radius of tolerance. For example, here is a visualization using FloraC's proposed radius of tolerance. M-yac (talk) 22:41, 19 June 2021 (UTC)