Euclidean tuning

A pure octave variant for TOP-mean can be worked as follows: instead of dividing the weighted val by its mean, divide by n, the number of scale steps in an octave. That makes the first coordinate exactly 1. Hence, the linear combination of t*u + (1-t)*v will also have first coordinate 1, and selecting the t which gives the point nearest the JI point will give a tuning with pure octaves for the corresponding linear temperament.

I propose Euclidean tuning as a name; the obvious extension of the idea works for any regular temperament of whatever rank which actually has octaves in it.