Re: [tuning] Digest Number 3639

If done as a recurrent sequence metameantone is done by exact-integers and allows for an infinate amount of such animals to seed it From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>

No, your calculations are quite correct. This observation of *almost* exact-integer beat rates has come up a few times here and particularly on the tuning-math list. Gene in particular has posted a great deal about it -- I hope he'll point you to some relevant postings and/or articles.

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

I'm not sure if this is directly related, Kraig (but I'm willing to be
proved wrong!) -- I believe what George was talking about was much more
along the lines of this very recent post from Gene:

/tuning/topicId_59904.html#59904

In other words, for quite a number of simple n/d-comma meantones (such
as 1/7-comma, 2/11-comma, 1/5-comma, 3/11-comma, etc), the beat rate
ratios are *almost* (to quite a few digits!), but not quite, simple-
integer ratios (2, 5/2, 3, and -3, respectively, for these examples).
Metameantone is not precisely a simple n/d-comma meantone and hence its
*exact* beat rate ratio of 1:1 is not a counterexample to this pattern.
There is, however, a simple n/d-comma meantone which has a beat rate
ratio of *almost* exactly 1:1 and hence follows this pattern, while of
course being an extremely close approximation to metameantone. I won't
spoil the answer for you Kraig should you decide to look into this
yourself.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> If done as a recurrent sequence metameantone is done by exact-
integers
> and allows for an infinate amount of such animals to seed it From:
> "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
>
> No, your calculations are quite correct. This observation of *almost*
> exact-integer beat rates has come up a few times here and
> particularly on the tuning-math list. Gene in particular has posted a
> great deal about it -- I hope he'll point you to some relevant
> postings and/or articles.
>
>
>
> --
> Kraig Grady
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles