Euler genera and combination product sets

I didn't realize until today what a close relationship exists between combination product (multi)sets and Euler genera. Combine n)0, n)1 ... to n)n for some n-multiset and get an Euler genus.

Gene wrote:

>I didn't realize until today what a close relationship exists between
>combination product (multi)sets and Euler genera. Combine n)0, n)1 ...
>to n)n for some n-multiset and get an Euler genus.

No? That's what Wilson calls a "grand slam". See pages
34 and 35:
http://anaphoria.com/dal.PDF

and also page 23, where the series is represented as consecutive
slices through the figure.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:

> No? That's what Wilson calls a "grand slam". See pages
> 34 and 35:
> http://anaphoria.com/dal.PDF
>
> and also page 23, where the series is represented as consecutive
> slices through the figure.

I like words first, and pictures afterwards. Then I know what the pictures depict.

At 08:56 PM 6/27/2010, you wrote:
>
>--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
>> No? That's what Wilson calls a "grand slam". See pages
>> 34 and 35:
>> http://anaphoria.com/dal.PDF
>>
>> and also page 23, where the series is represented as consecutive
>> slices through the figure.
>
>I like words first, and pictures afterwards. Then I know what the
>pictures depict.

I do too, but he clearly labels fig. 20b "combination product sets
0|6 thru 6|6" and similarly fig. 35. And the whole article is about
a keyboard to play this arrangement, as clearly stated in fig. 20
and the main text.

-Carl