Attn: Monz, for Tonalsoft encyclopedia

Here is a definition I am using in a Sloane integer sequence entry; it
would be nice to have a Tonalsoft entry on "Pepper ambiguity" to link to.

We may define the p-limit Pepper ambiguity, for any odd prime p, as
the maximum of the ratios of the errors of the nearest approximation
to the members of the p-limit tonality diamond to the next nearest. In
the 5-limit, that means we look at the ratios of the errors for the
nearest approximations to 3/2, 5/4 and 5/3 to the next nearest. The
concept was proposed by Pepper Keenan.

> Pepper Keenan.

That's Keenan Pepper.

-C.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> We may define the p-limit Pepper ambiguity, for any odd prime p, as
> the maximum of the ratios of the errors of the nearest approximation
> to the members of the p-limit tonality diamond to the next nearest. In
> the 5-limit, that means we look at the ratios of the errors for the
> nearest approximations to 3/2, 5/4 and 5/3 to the next nearest. The
> concept was proposed by Pepper Keenan.

Sorry, this should say "any odd number greater than one" not "any odd
prime".

We may define the n-limit Pepper ambiguity, for any odd number n
greater than one, as the maximum of the ratios of the errors of the
nearest approximation to the members of the n-limit tonality diamond
to the next nearest. In the 7-limit, that means we look at the ratios
of the errors for the nearest approximations to 3/2, 5/4, 5/3, 7/4,
7/5 and 7/6 to the next nearest. The concept was proposed by Pepper
Keenan.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Pepper Keenan.
>
> That's Keenan Pepper.

Duh. Right you are. Why does the world contain a Pepper Keenan and a
Keenan Pepper, anyway?

Sorry, Keenan.