View source for 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 [[User:FloraC|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.

<div style="margin: 20px 10px">[[File:Fjs regions.png|1000px|FJS regions of the octave]]</div>

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

<div style="margin: 20px 10px">[[File:FJS regions with primes.png|1000px|FJS regions of the octave with primes marked]]</div>

You can also mess around with interactive versions of these images using my [https://www.yacavone.net/fjs-explorer/ Custom FJS Explorer], where you can also set different values for the radius of tolerance. For example, [https://www.yacavone.net/fjs-explorer/?rotPreset=2 here] is a visualization using FloraC's proposed radius of tolerance. [[User:M-yac|M-yac]] ([[User talk:M-yac|talk]]) 22:41, 19 June 2021 (UTC)

== Limiting fifthspan instead of radius of tolerance ==
It seems to me that the choice of the radius of tolerance is made so the names would not be based on augmented or diminished intervals. In that case, having a fixed radius of tolerance is a wrong approach. I suggest that, when we create a name for an interval, we base it on the closest perfect, major or minor interval, i. e. inverval with fifthspan between -5 (m2) and +5 (M7). This seems to achieve the idea of FJS better than a radius of tolerance.