3/14 comma meantone (Riccati)

I calculated the least squares approximation with generators
corresponding to the 7 and 12 ets which keeps octaves exact and which
optimizes by the tunings for the classic JI diatonic scale,
1-9/8-5/4-4/3-3/2-5/3-15/8-(2). The result was the 3/14 comma
meantone system, which people (according to my search here) have
derived in other ways. It just keeps popping up...

--- In tuning@y..., genewardsmith@j... wrote:

> I calculated the least squares approximation with generators
> corresponding to the 7 and 12 ets which keeps octaves exact and
which
> optimizes by the tunings for the classic JI diatonic scale,
> 1-9/8-5/4-4/3-3/2-5/3-15/8-(2).

In my opinion, this scale is completely unrelated to actual musical
usage of the diatonic scale. There's no musical precedent for
treating D-A as a dissonance or as any different from the other
fifths.

> The result was the 3/14 comma
> meantone system,

A happy coincidence.

> which people (according to my search here) have
> derived in other ways. It just keeps popping up...

It's nice because it minimizes the maximum weighted error of the
consonant intervals, when the intervals are weighted inversely
proportionally to their odd-limit (3:2 gets weight 1/3, 5:4 gets
weight 1/5, 5:3 gets weight 1/5).