A 31edo approximation with some pure 5/4 and 7/4 intervals

Gene wrote:

> This has a gamut of 12 meantone (56/5)^(1/6) fifths, and so 6 =
> 12-6 pure 7/5s, and 18 1/4-comma 5^(1/4) fifths, and so 14 = 18-4
> pure 5/4s. The difference between this and 31edo is subtle, but you
> can bring it out, eg by using two-part harmony. What Vicentino
> would have made of it I don't know.

Hi, Gene!

My guess is that Vicentino would accept this as one nuance of his
first archicembalo tuning: the fifthtone or enharmonic diesis
steps are all large enough (at least 35 cents so so), and the
subtle gradations are an interesting variation on either
1/4-comma (where we get two sizes of an interval type
differing by 6.07 cents) or 31-EDO (with a single size for
each).

And I'd say it's a fine 31-note circle, as well as a very
creative one!

So we get a compromise between the variety of circulating
1/4-comma and the greater accuracy of 31-EDO for 11/9, for
example.

What Vicentino or others were likely to tune by ear in the 16th
century is another question; but I'd say that if 31-EDO is
legitimate, and Lemme Rossi took it as the correct tuning in
1666, then this is, too!

Congratulations!

Peace and love,

Margo

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:

> And I'd say it's a fine 31-note circle, as well as a very
> creative one!

Thanks, Margo.