--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > I wouldn't want to include any outside the 5-limit linear temperaments
> > having the following 18 vanishing commas. And I wouldn't mind leaving
> > off the last four.
>
> Your wishes can be accomodated by setting bounds for size and
> epimericity. For the short list, we have size < 93 cents and
> epimericity < 0.62, the only five limit comma which would be added to
> the list if we used these bounds would be 1600000/1594323. Presumably
> you have no objection to that, as it appears on your long list.

I could live with it, but I'd rather not.

> The long list has size < 93 and epimericity < 0.68. If we were to use
> these bounds, we would add 6561/6250 and 20480/19683. The second of
> these, 20480/19683, has epimericity 0.6757, which is a sliver higher
> than the actual maximum epimericity of your long list, 0.6739, and so
> setting the bound at 0.675 would leave it off. What do you make of the
> 6561/6250 comma? If you had no objection to letting it on to an
> amended long list, you'd be in business there as well.

I'd rather not.

What I don't like about both of these proposals is the "corners" in
the cutoff line. I prefer straight or smoothly curved cutoffs.