If we look at all-number optimization, we can consider septimal meantone in the 7, 8, 9 and 10 limits, for all the different p values.

Since anything other than p=2 or p=infinity is asking for a headache, I did those for the 8-limit. The minimax calculation simply gave us our old friend, 1/4-comma meantone. For rms I got stretched octaves:

2~1200.416 cents 3~1897.321 cents. If we take the ratio, we get

.580551, which still doesn't quite do it for us.

>If we take the ratio, we get .580551, which still doesn't

>quite do it for us.

What ratio is that? Blackwood's r?

-Carl

--- In tuning-math@yahoogroups.com, "Carl Lumma <clumma@y...>" <clumma@y...> wrote:

> >If we take the ratio, we get .580551, which still doesn't

> >quite do it for us.

>

> What ratio is that? Blackwood's r?

It's the ratio between the approximation for 3 and the approximation for 2, minus one; or in other words the log base the approximation for two of the approximation for 3/2. This is relevant since in the end we want to relate it all back to a division of the octave.