> of COURSE if you approximate the tones with very small ratios, they will likely form a convex lattice, since very small ratios are all near the center of the lattice!
I don't think that's what that part is saying. Small ratios i.e. ratios close to 1 like 16/15, 24/25, 27/25 don't appear near the center. Simple ratios such as 3/2 etc are the ones that appear near the center. If I understand it correctly this section is simply describing a transformation that collapses several points into one, equivalent to collapsing several similar notes into one.
I don't think that's what that part is saying. Small ratios i.e. ratios close to 1 like 16/15, 24/25, 27/25 don't appear near the center. Simple ratios such as 3/2 etc are the ones that appear near the center. If I understand it correctly this section is simply describing a transformation that collapses several points into one, equivalent to collapsing several similar notes into one.